Details

Time bar (total: 4.8s)

sample22.0ms

Algorithm
intervals
Results
5.0ms126×body80valid
5.0ms48×body1280valid
3.0ms44×body640valid
2.0ms27×body320valid
0.0ms11×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b
(cbrt (+ x 1.0))
0.6b
(cbrt x)
3.1b
(- (cbrt (+ x 1.0)) (cbrt x))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
64×cbrt-prod
56×*-un-lft-identity
42×prod-diff
41×add-sqr-sqrt
33×add-cube-cbrt
9×distribute-lft-out
7×fma-neg
5×add-log-exp
4×difference-of-squares
3×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u distribute-lft-out--
2×cbrt-div pow1/3
1×sub-neg flip3-- flip3-+ diff-log flip-- flip-+
Counts
3 → 99
Calls
3 calls:
3.0ms
(cbrt (+ x 1.0))
1.0ms
(cbrt x)
10.0ms
(- (cbrt (+ x 1.0)) (cbrt x))

series410.0ms

Counts
3 → 9
Calls
3 calls:
87.0ms
(cbrt (+ x 1.0))
173.0ms
(cbrt x)
150.0ms
(- (cbrt (+ x 1.0)) (cbrt x))

simplify52.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04301315
113941045
25001981

prune240.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 17.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(expm1 (log1p (- (cbrt (+ x 1.0)) (cbrt x))))
0.3b
(cbrt (+ x 1.0))
0.6b
(cbrt x)
3.1b
(- (cbrt (+ x 1.0)) (cbrt x))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
64×cbrt-prod
57×*-un-lft-identity
42×add-sqr-sqrt prod-diff
34×add-cube-cbrt
9×distribute-lft-out
7×fma-neg
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u difference-of-squares
3×distribute-lft-out--
2×cbrt-div pow1/3
1×sub-neg expm1-log1p flip3-- flip3-+ diff-log flip-- flip-+ expm1-udef
Counts
4 → 110
Calls
4 calls:
1.0ms
(expm1 (log1p (- (cbrt (+ x 1.0)) (cbrt x))))
3.0ms
(cbrt (+ x 1.0))
1.0ms
(cbrt x)
9.0ms
(- (cbrt (+ x 1.0)) (cbrt x))

series648.0ms

Counts
4 → 12
Calls
4 calls:
240.0ms
(expm1 (log1p (- (cbrt (+ x 1.0)) (cbrt x))))
87.0ms
(cbrt (+ x 1.0))
174.0ms
(cbrt x)
147.0ms
(- (cbrt (+ x 1.0)) (cbrt x))

simplify65.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05641496
120011206
250011148

prune332.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 17.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ x 1.0))
0.3b
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.6b
(cbrt x)
30.9b
(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
31×cbrt-prod
30×*-un-lft-identity
22×add-sqr-sqrt
14×add-cube-cbrt cbrt-div
11×pow1
9×swap-sqr
8×pow1/3
7×flip3-+ associate-*r* associate-*l* flip-+ distribute-lft-out
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod fma-udef
Counts
4 → 94
Calls
4 calls:
3.0ms
(cbrt (+ x 1.0))
10.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
1.0ms
(cbrt x)
1.0ms
(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

series620.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(cbrt (+ x 1.0))
108.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
176.0ms
(cbrt x)
248.0ms
(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

simplify51.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0479846
11610782
25001727

prune362.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 17.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.3b
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.6b
(cbrt x)
30.9b
(fma (cbrt (* (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))) (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
51×cbrt-prod
49×*-un-lft-identity
37×add-sqr-sqrt
24×cbrt-div
21×add-cube-cbrt
18×pow1 swap-sqr
14×associate-*r* associate-*l*
13×pow1/3
12×flip3-+ flip-+ distribute-lft-out
8×add-exp-log frac-times unswap-sqr
4×expm1-log1p-u associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up add-cbrt-cube log1p-expm1-u add-log-exp
2×pow2 pow-plus prod-exp *-commutative cbrt-unprod
1×fma-udef
Counts
4 → 133
Calls
4 calls:
10.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
10.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
1.0ms
(cbrt x)
1.0ms
(fma (cbrt (* (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))) (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

series634.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
101.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
181.0ms
(cbrt x)
249.0ms
(fma (cbrt (* (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))))) (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

simplify51.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04231355
114081244
250021155

prune467.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 17.5b

regimes86.0ms

Accuracy

98.4% (0.2b remaining)

Error of 18.9b against oracle of 18.8b and baseline of 30.0b

bsearch125.0ms

Steps
ItersRangePoint
8
21.660028671588154
6793.132116615613
3285.3368488500055
10
-1.828180551810585e+69
-1.9710212454209794e+59
-4.462890112366947e+61

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06941
16941

end0.0ms

sample489.0ms

Algorithm
intervals
Results
175.0ms1746×body1280valid
94.0ms1226×body640valid
81.0ms4099×body80valid
36.0ms610×body320valid
12.0ms319×body160valid