Details

Time bar (total: 7.9s)

sample99.0ms

Algorithm
intervals
Results
29.0ms60×body10240exit
21.0ms46×body1280valid
18.0ms318×body80valid
10.0ms39×body640valid
4.0ms24×body320valid
1.0ms9×body160valid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (39.0ms)

IterNodesCost
04716
112416
236516
3137616
4500115

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 eps) x)
0.0b
(* (+ 1.0 eps) x)
0.0b
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
3.3b
(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
16×add-sqr-sqrt
13×add-cbrt-cube
12×add-exp-log
10×add-cube-cbrt
9×associate-*l*
8×pow1
6×associate-*r*
4×expm1-log1p-u times-frac associate-*l/ log1p-expm1-u associate-/l* add-log-exp
3×prod-exp cbrt-unprod distribute-lft-out
2×cbrt-undiv flip3-+ div-exp pow-prod-down *-commutative flip-+ associate-/l/ unswap-sqr
1×flip3-- frac-2neg clear-num associate-/r* flip-- fma-udef div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 84
Calls
4 calls:
10.0ms
(* (- 1.0 eps) x)
13.0ms
(* (+ 1.0 eps) x)
22.0ms
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
0.0ms
(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

series345.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (- 1.0 eps) x)
27.0ms
(* (+ 1.0 eps) x)
49.0ms
(/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x))))
235.0ms
(fma (/ (exp (- (* (+ 1.0 eps) x))) 2.0) (- 1.0 (/ 1.0 eps)) (/ (+ 1.0 (/ 1.0 eps)) (* 2.0 (exp (* (- 1.0 eps) x)))))

simplify49.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0462738
11805635
25002628

prune486.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.7b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 0.5 (pow x 2))
1.6b
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
5.2b
(/ (pow x 3) eps)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
36×times-frac
31×add-cube-cbrt *-un-lft-identity
16×unpow-prod-down
13×add-exp-log
12×cube-prod associate-/l*
8×associate-*r*
7×add-cbrt-cube
6×sqr-pow
4×cube-mult unpow3 unswap-sqr
3×pow1 expm1-log1p-u div-exp associate-*l* prod-exp associate-/r* log1p-expm1-u add-log-exp
2×pow-to-exp pow-exp unpow2
1×cbrt-undiv frac-2neg clear-num *-commutative cbrt-unprod fma-udef div-inv
Counts
3 → 106
Calls
3 calls:
6.0ms
(* 0.5 (pow x 2))
0.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
5.0ms
(/ (pow x 3) eps)

series98.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(* 0.5 (pow x 2))
52.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
21.0ms
(/ (pow x 3) eps)

simplify58.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0305506
11561465
25001451

prune253.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.7b

localize15.0ms

Local error

Found 4 expressions with local error:

5.2b
(/ (pow x 3) eps)
10.6b
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
10.6b
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
10.6b
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
32×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down cube-prod associate-/l*
9×add-exp-log cbrt-prod
6×add-cbrt-cube
4×pow1 expm1-log1p-u cube-mult unpow3 log1p-expm1-u add-log-exp sqr-pow
3×pow1/3 div-exp associate-/r*
1×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
Counts
4 → 106
Calls
4 calls:
5.0ms
(/ (pow x 3) eps)
0.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
0.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
1.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
21.0ms
(/ (pow x 3) eps)
379.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
386.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
379.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

simplify51.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0271803
11222747
25002738

prune395.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 3.6b

localize25.0ms

Local error

Found 4 expressions with local error:

5.2b
(/ (pow x 3) eps)
5.2b
(/ (pow x 3) eps)
10.6b
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
10.6b
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
72×times-frac
56×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
24×unpow-prod-down cube-prod associate-/l*
14×add-exp-log
8×cube-mult unpow3 add-cbrt-cube sqr-pow
6×cbrt-prod div-exp associate-/r*
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×cbrt-undiv pow-to-exp frac-2neg pow1/3 pow-exp clear-num div-inv
Counts
4 → 160
Calls
4 calls:
5.0ms
(/ (pow x 3) eps)
5.0ms
(/ (pow x 3) eps)
0.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
1.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

series819.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(/ (pow x 3) eps)
30.0ms
(/ (pow x 3) eps)
383.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
384.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

simplify51.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0271926
11222878
25002872

prune646.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.6b

regimes177.0ms

Accuracy

96.1% (0.7b remaining)

Error of 5.5b against oracle of 4.8b and baseline of 21.5b

bsearch135.0ms

Steps
ItersRangePoint
8
0.01694346711308432
10.298044827647965
0.025088100216671332

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06357
17157
27157

end0.0ms

sample2.9s

Algorithm
intervals
Results
782.0ms1867×body10240exit
765.0ms1723×body1280valid
560.0ms10037×body80valid
312.0ms1237×body640valid
102.0ms618×body320valid
35.0ms324×body160valid