Details

Time bar (total: 3.8s)

sample19.0ms

Algorithm
intervals
Results
5.0ms193×body80valid
2.0ms18×body1280valid
2.0ms20×body640valid
1.0ms18×body320valid
0.0ms7×body160valid

simplify111.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (18.0ms)

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: 14.9b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ y (+ y 1.0))
2.0b
(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite7.0ms

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:
5.0ms
(/ y (+ y 1.0))
0.0ms
(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series102.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(/ y (+ y 1.0))
65.0ms
(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify131.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (126.0ms)

IterNodesCost
0203263
1708238
23148232
35002228

prune156.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.8b

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)))
10.0b
(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

rewrite28.0ms

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)

series390.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(cbrt (+ y 1.0))
103.0ms
(cbrt (+ y 1.0))
119.0ms
(* (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)

simplify61.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0365866
11251798
25001736

prune366.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0))
2.0b
(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
2.0b
(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
2.0b
(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-prod fma-udef
1×pow1/3
Counts
4 → 43
Calls
4 calls:
1.0ms
(cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0))
0.0ms
(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
0.0ms
(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
0.0ms
(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series311.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0))
65.0ms
(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
57.0ms
(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
62.0ms
(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify77.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 3 (71.0ms)

IterNodesCost
0168405
1501355
21834340
35002325

prune240.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
0.3b
(cbrt (cbrt (+ y 1.0)))
0.4b
(pow (cbrt (cbrt (+ y 1.0))) 4)
12.4b
(fma (/ (/ y (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (pow (cbrt (cbrt (+ y 1.0))) 4))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
46×cbrt-prod
36×*-un-lft-identity
26×add-sqr-sqrt
18×add-cube-cbrt
16×cbrt-div
12×pow1
10×unpow-prod-down
9×swap-sqr
8×pow1/3 distribute-lft-out
7×add-exp-log flip3-+ associate-*r* associate-*l* flip-+
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
3×pow-unpow
2×pow-pow associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-to-exp pow-plus pow-exp prod-exp *-commutative cbrt-unprod fma-udef sqr-pow
Counts
4 → 111
Calls
4 calls:
19.0ms
(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
2.0ms
(cbrt (cbrt (+ y 1.0)))
6.0ms
(pow (cbrt (cbrt (+ y 1.0))) 4)
0.0ms
(fma (/ (/ y (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (pow (cbrt (cbrt (+ y 1.0))) 4))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

series463.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
102.0ms
(cbrt (cbrt (+ y 1.0)))
177.0ms
(pow (cbrt (cbrt (+ y 1.0))) 4)
65.0ms
(fma (/ (/ y (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (pow (cbrt (cbrt (+ y 1.0))) 4))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify88.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
05771086
120741005
25002946

prune456.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.8b

regimes132.0ms

Accuracy

95.7% (0.3b remaining)

Error of 7.9b against oracle of 7.6b and baseline of 15.2b

bsearch91.0ms

Steps
ItersRangePoint
9
125490.8565836802
93306293809.51114
92001499739.10446
8
-5.72718536644542e+38
-2.1694148392982545e+34
-2.228795784817071e+34

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02610
12610

end0.0ms

sample449.0ms

Algorithm
intervals
Results
152.0ms6066×body80valid
67.0ms729×body640valid
45.0ms374×body1280valid
40.0ms540×body320valid
13.0ms291×body160valid