Details

Time bar (total: 11.2s)

sample435.0ms

Algorithm
intervals
Results
84.0ms41×body2560valid
64.0ms99×body1280valid
18.0ms52×body640valid
7.0ms30×body320valid
3.0ms17×body160valid
2.0ms17×body80valid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0135
1175
2195
3195

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x (sin x)) (- x (tan x)))
2.2b
(- x (tan x))
2.2b
(- x (sin x))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt *-un-lft-identity
29×add-cube-cbrt
25×times-frac
18×prod-diff
14×distribute-lft-out-- difference-of-squares
7×add-log-exp
6×fma-neg
5×add-exp-log associate-/r* add-cbrt-cube associate-/l*
4×flip3-- flip--
3×pow1 expm1-log1p-u log1p-expm1-u
2×sub-neg diff-log associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-sub div-exp clear-num div-inv
Counts
3 → 110
Calls
3 calls:
14.0ms
(/ (- x (sin x)) (- x (tan x)))
3.0ms
(- x (tan x))
22.0ms
(- x (sin x))

series180.0ms

Counts
3 → 9
Calls
3 calls:
79.0ms
(/ (- x (sin x)) (- x (tan x)))
60.0ms
(- x (tan x))
41.0ms
(- x (sin x))

simplify56.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
04721059
11737854
25001854

prune254.0ms

Filtered
119 candidates to 79 candidates (66.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
1.0b
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
2.2b
(- x (sin x))
26.9b
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt *-un-lft-identity
22×add-cube-cbrt
15×times-frac
9×prod-diff
6×add-exp-log add-cbrt-cube add-log-exp
5×associate-/l* distribute-lft-out-- difference-of-squares
4×pow1 expm1-log1p-u log1p-expm1-u
3×cbrt-prod fma-neg associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg pow1/3 diff-log div-sub div-exp clear-num fma-udef div-inv
Counts
4 → 91
Calls
4 calls:
1.0ms
(cbrt x)
9.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
3.0ms
(- x (sin x))
0.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series1.1s

Counts
4 → 12
Calls
4 calls:
174.0ms
(cbrt x)
512.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
31.0ms
(- x (sin x))
335.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

simplify46.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03421106
11187942
25001897

prune265.0ms

Filtered
103 candidates to 79 candidates (76.7%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
1.0b
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
2.2b
(- x (sin x))
26.9b
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt *-un-lft-identity
22×add-cube-cbrt
15×times-frac
9×prod-diff
6×add-exp-log add-cbrt-cube add-log-exp
5×associate-/l* distribute-lft-out-- difference-of-squares
4×pow1 expm1-log1p-u log1p-expm1-u
3×cbrt-prod fma-neg associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg pow1/3 diff-log div-sub div-exp clear-num fma-udef div-inv
Counts
4 → 91
Calls
4 calls:
1.0ms
(cbrt x)
9.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
3.0ms
(- x (sin x))
0.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

series1.1s

Counts
4 → 12
Calls
4 calls:
183.0ms
(cbrt x)
530.0ms
(/ (- x (sin x)) (fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x))))
32.0ms
(- x (sin x))
336.0ms
(fma (* (cbrt x) (cbrt x)) (cbrt x) (- (tan x)))

simplify45.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03421106
11187942
25001897

prune314.0ms

Filtered
103 candidates to 79 candidates (76.7%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (/ (- x (sin x)) (+ x (- (tan x)))) 3)
0.0b
(cbrt (pow (/ (- x (sin x)) (+ x (- (tan x)))) 3))
2.2b
(+ x (- (tan x)))
2.2b
(- x (sin x))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
184×*-un-lft-identity
100×add-sqr-sqrt times-frac
68×cbrt-prod
62×unpow-prod-down cube-prod
58×add-cube-cbrt
42×distribute-lft-out
21×distribute-rgt-neg-in distribute-lft-out-- difference-of-squares
10×add-log-exp
9×prod-diff
8×associate-/r/
7×add-exp-log add-cbrt-cube
5×pow1 flip3-+ flip-+
4×expm1-log1p-u log1p-expm1-u div-inv
3×pow-unpow fma-def fma-neg
2×cube-div cube-mult unpow3 pow-exp sum-log rem-cube-cbrt sqr-pow
1×cbrt-undiv +-commutative neg-sub0 pow-to-exp associate-+r- sub-neg cbrt-div flip3-- pow-pow pow1/3 diff-log div-exp unsub-neg neg-log flip-- rem-cbrt-cube
Counts
4 → 214
Calls
4 calls:
17.0ms
(pow (/ (- x (sin x)) (+ x (- (tan x)))) 3)
22.0ms
(cbrt (pow (/ (- x (sin x)) (+ x (- (tan x)))) 3))
5.0ms
(+ x (- (tan x)))
4.0ms
(- x (sin x))

series261.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(pow (/ (- x (sin x)) (+ x (- (tan x)))) 3)
79.0ms
(cbrt (pow (/ (- x (sin x)) (+ x (- (tan x)))) 3))
50.0ms
(+ x (- (tan x)))
37.0ms
(- x (sin x))

simplify101.0ms

Algorithm
egg-herbie
Counts
226 → 226
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
07562521
133532249
250012197

prune325.0ms

Filtered
226 candidates to 98 candidates (43.4%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes36.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.3b

bsearch74.0ms

Steps
ItersRangePoint
10
9.558161037350472e-13
0.8818080259852756
0.027208711435501284
5
-0.041603525395973645
-0.015510049556855336
-0.026896790136361697

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02921
12921

end0.0ms

sample6.4s

Algorithm
intervals
Results
3.4s1588×body2560valid
1.9s2762×body1280valid
627.0ms1826×body640valid
214.0ms945×body320valid
79.0ms509×body160valid
42.0ms370×body80valid