Details

Time bar (total: 4.2s)

sample30.0ms

Algorithm
intervals
Results
9.0ms187×body80valid
6.0ms16×body1280valid
4.0ms26×body640valid
2.0ms16×body320valid
1.0ms11×body160valid

simplify102.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (15.0ms)

IterNodesCost
0165
1355
2765
31375
42854
54594
67194
78484
810644
913974
1021014
1150024

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.5b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ y (+ y 1.0))
2.6b
(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
12×times-frac
11×add-sqr-sqrt add-cube-cbrt
4×add-exp-log associate-/r* add-cbrt-cube distribute-lft-out
3×associate-/l*
2×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
1×cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ fma-udef div-inv
Counts
2 → 45
Calls
2 calls:
6.0ms
(/ y (+ y 1.0))
0.0ms
(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series102.0ms

Counts
2 → 6
Calls
2 calls:
36.0ms
(/ y (+ y 1.0))
65.0ms
(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify128.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (122.0ms)

IterNodesCost
0203263
1708238
23148232
35002228

prune157.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ y 1.0))
0.3b
(cbrt (+ y 1.0))
0.3b
(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
11.1b
(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
32×cbrt-prod *-un-lft-identity
22×add-sqr-sqrt
16×cbrt-div
14×add-cube-cbrt
11×pow1
9×swap-sqr
8×flip3-+ pow1/3 flip-+ distribute-lft-out
7×associate-*r* associate-*l*
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:
2.0ms
(cbrt (+ y 1.0))
2.0ms
(cbrt (+ y 1.0))
20.0ms
(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
0.0ms
(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

series387.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(cbrt (+ y 1.0))
101.0ms
(cbrt (+ y 1.0))
118.0ms
(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
65.0ms
(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify59.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0365866
11251798
25001736

prune369.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ y 1.0))
0.3b
(cbrt (+ y 1.0))
0.3b
(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
9.9b
(fma (/ (/ y (* (* (cbrt (+ y 1.0)) (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))) (cbrt (cbrt (+ y 1.0))))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
32×cbrt-prod *-un-lft-identity
22×add-sqr-sqrt
16×cbrt-div
14×add-cube-cbrt
11×pow1
9×swap-sqr
8×flip3-+ pow1/3 flip-+ distribute-lft-out
7×associate-*r* associate-*l*
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:
2.0ms
(cbrt (+ y 1.0))
2.0ms
(cbrt (+ y 1.0))
20.0ms
(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
0.0ms
(fma (/ (/ y (* (* (cbrt (+ y 1.0)) (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))) (cbrt (cbrt (+ y 1.0))))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

series387.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(cbrt (+ y 1.0))
103.0ms
(cbrt (+ y 1.0))
117.0ms
(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
65.0ms
(fma (/ (/ y (* (* (cbrt (+ y 1.0)) (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))) (cbrt (cbrt (+ y 1.0))))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify60.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0370970
11275891
25001833

prune443.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ y 1.0))
0.3b
(cbrt (+ y 1.0))
0.3b
(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
14.7b
(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (* (* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0))))) (- x 1.0) 1.0)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
32×cbrt-prod *-un-lft-identity
22×add-sqr-sqrt
16×cbrt-div
14×add-cube-cbrt
11×pow1
9×swap-sqr
8×flip3-+ pow1/3 flip-+ distribute-lft-out
7×associate-*r* associate-*l*
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:
2.0ms
(cbrt (+ y 1.0))
2.0ms
(cbrt (+ y 1.0))
20.0ms
(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
0.0ms
(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (* (* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0))))) (- x 1.0) 1.0)

series389.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(cbrt (+ y 1.0))
102.0ms
(cbrt (+ y 1.0))
120.0ms
(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
64.0ms
(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (* (* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0))))) (- x 1.0) 1.0)

simplify66.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0368983
11259902
25001819

prune385.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.7b

regimes153.0ms

Accuracy

96.7% (0.3b remaining)

Error of 7.6b against oracle of 7.3b and baseline of 15.2b

bsearch94.0ms

Steps
ItersRangePoint
10
2.146431404007219e+23
3.553954463737904e+37
2.739133723068897e+23
4
-1451612.104863074
-956540.4353308786
-1433265.003794283

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03517
13517

end0.0ms

sample696.0ms

Algorithm
intervals
Results
295.0ms6050×body80valid
97.0ms671×body640valid
70.0ms398×body1280valid
61.0ms553×body320valid
26.0ms328×body160valid