Details

Time bar (total: 3.6s)

sample33.0ms

Algorithm
intervals
Results
12.0ms190×body80valid
6.0ms30×body640valid
3.0ms11×body1280valid
3.0ms18×body320valid
1.0ms7×body160valid

simplify79.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (11.0ms)

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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.6b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ y (+ y 1.0))
1.5b
(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)

series91.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(/ y (+ y 1.0))
53.0ms
(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify111.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (106.0ms)

IterNodesCost
0203263
1708238
23148232
35002228

prune141.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.4b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1 (+ y 1.0))
0.1b
(* y (/ 1 (+ y 1.0)))
3.4b
(fma (* y (/ 1 (+ y 1.0))) (- x 1.0) 1.0)

rewrite28.0ms

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))
19.0ms
(* y (/ 1 (+ y 1.0)))
0.0ms
(fma (* y (/ 1 (+ y 1.0))) (- x 1.0) 1.0)

series115.0ms

Counts
3 → 9
Calls
3 calls:
23.0ms
(/ 1 (+ y 1.0))
38.0ms
(* y (/ 1 (+ y 1.0)))
53.0ms
(fma (* y (/ 1 (+ y 1.0))) (- x 1.0) 1.0)

simplify48.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0324499
11447427
25002381

prune213.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 8.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (+ y 1.0))
0.2b
(cbrt (+ y 1.0))
0.2b
(cbrt (+ y 1.0))
12.2b
(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-div
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 flip-+ distribute-lft-out
1×fma-udef
Counts
4 → 58
Calls
4 calls:
2.0ms
(cbrt (+ y 1.0))
2.0ms
(cbrt (+ y 1.0))
2.0ms
(cbrt (+ y 1.0))
0.0ms
(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

series328.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(cbrt (+ y 1.0))
89.0ms
(cbrt (+ y 1.0))
91.0ms
(cbrt (+ y 1.0))
58.0ms
(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify81.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (74.0ms)

IterNodesCost
0235565
1699515
22697493
35001461

prune272.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (+ y 1.0))
0.2b
(cbrt (+ y 1.0))
0.3b
(* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0))))
11.7b
(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (* (* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (- x 1.0) 1.0)

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
78×cbrt-prod
36×add-sqr-sqrt *-un-lft-identity
28×cbrt-div
18×add-cube-cbrt
12×swap-sqr
11×pow1
10×associate-*r* associate-*l*
9×unswap-sqr
8×flip3-+ pow1/3 flip-+ distribute-lft-out
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp
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 → 111
Calls
4 calls:
2.0ms
(cbrt (+ y 1.0))
2.0ms
(cbrt (+ y 1.0))
24.0ms
(* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0))))
0.0ms
(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (* (* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (- x 1.0) 1.0)

series346.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(cbrt (+ y 1.0))
90.0ms
(cbrt (+ y 1.0))
105.0ms
(* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0))))
60.0ms
(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (* (* (cbrt (cbrt (+ y 1.0))) (cbrt (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (- x 1.0) 1.0)

simplify64.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04201318
114171220
250011108

prune411.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 8.4b

regimes125.0ms

Accuracy

97.1% (0.2b remaining)

Error of 7.4b against oracle of 7.2b and baseline of 13.9b

bsearch123.0ms

Steps
ItersRangePoint
10
5.860167377397631e+23
1.096063319062125e+38
7.037472930354931e+31
10
-1.2929377546055754e+19
-3.016982961048864
-18067858855719976.0

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02810
12810

end0.0ms

sample902.0ms

Algorithm
intervals
Results
400.0ms6168×body80valid
157.0ms717×body640valid
88.0ms354×body1280valid
78.0ms478×body320valid
33.0ms283×body160valid