Details

Time bar (total: 31.2s)

sample545.0ms

Algorithm
intervals
Results
282.0ms108×body1280valid
125.0ms66×body640valid
83.0ms22×body2560valid
23.0ms23×body320valid
9.0ms31×body80valid
4.0msbody160valid

simplify9.0ms

Counts
1 → 1
Iterations
IterNodes
310
210
19
06

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.5b

localize25.0ms

Local error

Found 2 expressions with local error:

1.1b
(- (tan (+ x eps)) (tan x))
3.1b
(tan (+ x eps))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt *-un-lft-identity tan-quot add-log-exp
pow1 tan-sum add-cbrt-cube add-exp-log frac-sub add-cube-cbrt insert-posit16
sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 27
Calls
2 calls:
59.0ms
(- (tan (+ x eps)) (tan x))
12.0ms
(tan (+ x eps))

series256.0ms

Counts
2 → 6
Calls
2 calls:
166.0ms
(- (tan (+ x eps)) (tan x))
90.0ms
(tan (+ x eps))

simplify5.6s

Counts
33 → 33
Iterations
IterNodes
53701
41485
3657
2282
1134
070

prune469.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b
(+ (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))
2.4b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
22×add-sqr-sqrt
15×add-cube-cbrt
13×times-frac
tan-quot
add-cbrt-cube add-exp-log add-log-exp
pow1
distribute-lft-out
insert-posit16 associate-/l*
associate-/r* associate-*r* associate-*l* associate-/l/
flip3-+ flip3-- frac-add associate-/r/ flip-+ flip-- difference-of-squares
frac-times cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg diff-log div-exp pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod div-inv distribute-lft-out-- unswap-sqr
Counts
4 → 90
Calls
4 calls:
62.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
18.0ms
(+ (tan x) (tan eps))
34.0ms
(* (tan x) (tan eps))
132.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.4s

Counts
4 → 12
Calls
4 calls:
393.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
172.0ms
(+ (tan x) (tan eps))
174.0ms
(* (tan x) (tan eps))
645.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.9s

Counts
102 → 102
Iterations
IterNodes
33772
21108
1403
0175

prune1.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.8b

regimes352.0ms

Accuracy

85.1% (1.1b remaining)

Error of 15.8b against oracle of 14.8b and baseline of 22.0b

bsearch509.0ms

Steps
ItersRangePoint
7
1.2646124074092217e-114
2.0680036199118397e-113
2.0475257736193414e-113
10
-1.5732111743249695e-12
-8.770347984009294e-24
-6.314638657513539e-20

simplify14.0ms

Iterations
IterNodes
238
138
030

end0.0ms

sample18.3s

Algorithm
intervals
Results
9.5s3287×body1280valid
3.9s1880×body640valid
3.0s659×body2560valid
790.0ms752×body320valid
475.0ms1075×body80valid
220.0ms347×body160valid