Details

Time bar (total: 3.5s)

sample18.0ms

Algorithm
intervals
Results
4.0ms184×body80valid
2.0ms23×body640valid
2.0ms15×body1280valid
1.0ms16×body320valid
1.0ms18×body160valid

simplify88.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (13.0ms)

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

prune7.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.6b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ y (+ y 1.0))
4.2b
(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)

series101.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(/ y (+ y 1.0))
58.0ms
(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify118.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (113.0ms)

IterNodesCost
0203263
1708238
23148232
35002228

prune155.0ms

Filtered
51 candidates to 40 candidates (78.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1 (+ y 1.0))
0.1b
(* y (/ 1 (+ y 1.0)))
6.3b
(fma (* y (/ 1 (+ y 1.0))) (- x 1.0) 1.0)

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
36×*-un-lft-identity
28×add-sqr-sqrt
26×times-frac
21×add-cube-cbrt
18×associate-*r*
16×add-exp-log
10×add-cbrt-cube
7×distribute-lft-out
6×pow1
4×div-exp prod-exp associate-/r* associate-/r/
3×expm1-log1p-u associate-*l* log1p-expm1-u associate-/l* add-log-exp unswap-sqr
2×cbrt-undiv rec-exp flip3-+ 1-exp cbrt-unprod flip-+ div-inv
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative fma-udef inv-pow
Counts
3 → 92
Calls
3 calls:
6.0ms
(/ 1 (+ y 1.0))
20.0ms
(* y (/ 1 (+ y 1.0)))
0.0ms
(fma (* y (/ 1 (+ y 1.0))) (- x 1.0) 1.0)

series125.0ms

Counts
3 → 9
Calls
3 calls:
25.0ms
(/ 1 (+ y 1.0))
41.0ms
(* y (/ 1 (+ y 1.0)))
58.0ms
(fma (* y (/ 1 (+ y 1.0))) (- x 1.0) 1.0)

simplify54.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0324499
11447427
25002381

prune227.0ms

Filtered
101 candidates to 61 candidates (60.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.1b

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)))
13.8b
(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

rewrite31.0ms

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))
21.0ms
(* (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)

series392.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(cbrt (+ y 1.0))
102.0ms
(cbrt (+ y 1.0))
122.0ms
(* (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)

simplify57.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0365866
11251798
25001736

prune351.0ms

Filtered
109 candidates to 78 candidates (71.6%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y)
0.6b
(cbrt y)
0.6b
(cbrt y)
13.4b
(fma (/ (* (cbrt y) (cbrt y)) (/ (+ y 1.0) (cbrt y))) (- x 1.0) 1.0)

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×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×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
1.0ms
(cbrt y)
1.0ms
(cbrt y)
1.0ms
(cbrt y)
0.0ms
(fma (/ (* (cbrt y) (cbrt y)) (/ (+ y 1.0) (cbrt y))) (- x 1.0) 1.0)

series670.0ms

Counts
4 → 12
Calls
4 calls:
204.0ms
(cbrt y)
195.0ms
(cbrt y)
194.0ms
(cbrt y)
77.0ms
(fma (/ (* (cbrt y) (cbrt y)) (/ (+ y 1.0) (cbrt y))) (- x 1.0) 1.0)

simplify46.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 3 (41.0ms)

IterNodesCost
0104277
1278244
21012231
35002227

prune200.0ms

Filtered
61 candidates to 54 candidates (88.5%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.0b

regimes276.0ms

Accuracy

97.4% (0.2b remaining)

Error of 7.5b against oracle of 7.3b and baseline of 14.7b

bsearch83.0ms

Steps
ItersRangePoint
8
1.8356171221150663e+19
2.397212652695638e+23
4.176509822734759e+19
7
-2595256309730746.0
-118859067955370.34
-2555995508154242.0

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02713
12713

end0.0ms

sample444.0ms

Algorithm
intervals
Results
146.0ms6104×body80valid
71.0ms728×body640valid
43.0ms386×body1280valid
31.0ms467×body320valid
22.0ms315×body160valid