Details

Time bar (total: 5.4s)

sample19.0ms

Algorithm
intervals
Results
4.0ms43×body1280valid
3.0ms141×body80valid
3.0ms32×body640valid
2.0ms27×body320valid
1.0ms13×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.2b
(cbrt (+ x 1.0))
0.5b
(cbrt x)
2.9b
(- (cbrt (+ x 1.0)) (cbrt x))

rewrite42.0ms

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:
5.0ms
(cbrt (+ x 1.0))
1.0ms
(cbrt x)
31.0ms
(- (cbrt (+ x 1.0)) (cbrt x))

series423.0ms

Counts
3 → 9
Calls
3 calls:
89.0ms
(cbrt (+ x 1.0))
182.0ms
(cbrt x)
151.0ms
(- (cbrt (+ x 1.0)) (cbrt x))

simplify52.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04301315
113941045
25001981

prune279.0ms

Filtered
108 candidates to 69 candidates (63.9%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt x)
0.5b
(cbrt x)
0.5b
(cbrt x)
2.9b
(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×pow1/3
1×sub-neg flip3-- fma-neg diff-log prod-diff flip-- difference-of-squares
Counts
4 → 56
Calls
4 calls:
0.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)
12.0ms
(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

series919.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(cbrt x)
377.0ms
(cbrt x)
180.0ms
(cbrt x)
185.0ms
(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

simplify141.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (136.0ms)

IterNodesCost
0260403
1906328
24583314
35001311

prune258.0ms

Filtered
68 candidates to 60 candidates (88.2%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 10.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (cbrt (+ x 1.0)))
0.3b
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.5b
(cbrt x)
27.1b
(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
38×cbrt-prod
31×*-un-lft-identity
23×add-sqr-sqrt
16×cbrt-div
15×add-cube-cbrt
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 → 97
Calls
4 calls:
3.0ms
(cbrt (cbrt (+ x 1.0)))
22.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
1.0ms
(cbrt x)
0.0ms
(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

series644.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(cbrt (cbrt (+ x 1.0)))
108.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
188.0ms
(cbrt x)
257.0ms
(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

simplify53.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0532894
11786828
25001783

prune412.0ms

Filtered
109 candidates to 78 candidates (71.6%)
Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.4b
(pow (cbrt (cbrt (+ x 1.0))) (+ 3 1))
0.5b
(cbrt x)
26.9b
(fma (cbrt (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (pow (cbrt (cbrt (+ x 1.0))) (+ 3 1)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
38×cbrt-prod
35×*-un-lft-identity
25×add-sqr-sqrt
17×add-cube-cbrt
12×pow1 cbrt-div
10×unpow-prod-down
9×swap-sqr
8×pow1/3 distribute-lft-out
7×add-exp-log associate-*r* associate-*l*
6×flip3-+ flip-+
4×expm1-log1p-u frac-times pow-unpow add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-pow associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×unpow-prod-up pow2 pow-to-exp pow-plus pow-exp prod-exp *-commutative cbrt-unprod fma-udef sqr-pow
Counts
4 → 107
Calls
4 calls:
22.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
9.0ms
(pow (cbrt (cbrt (+ x 1.0))) (+ 3 1))
1.0ms
(cbrt x)
0.0ms
(fma (cbrt (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (pow (cbrt (cbrt (+ x 1.0))) (+ 3 1)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

series694.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
154.0ms
(pow (cbrt (cbrt (+ x 1.0))) (+ 3 1))
178.0ms
(cbrt x)
257.0ms
(fma (cbrt (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (pow (cbrt (cbrt (+ x 1.0))) (+ 3 1)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

simplify91.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
06201088
12578957
25002921

prune468.0ms

Filtered
119 candidates to 86 candidates (72.3%)
Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.8b

regimes111.0ms

Accuracy

98.9% (0.2b remaining)

Error of 11.7b against oracle of 11.5b and baseline of 30.6b

bsearch119.0ms

Steps
ItersRangePoint
10
7.712829756242493e-08
8770343.893451896
3388.194569600337
8
-7.499698800938951e+63
-2.3514850841259314e+60
-4.44245620170887e+61

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07951
17951

end0.0ms

sample530.0ms

Algorithm
intervals
Results
185.0ms1723×body1280valid
110.0ms1317×body640valid
88.0ms4008×body80valid
37.0ms626×body320valid
13.0ms326×body160valid