Details

Time bar (total: 7.8s)

sample103.0ms

Algorithm
intervals
Results
26.0ms60×body1280valid
22.0ms58×body10240exit
21.0ms330×body80valid
10.0ms42×body640valid
5.0ms30×body320valid
1.0ms10×body160valid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (39.0ms)

IterNodesCost
04716
112416
236516
3137616
4500115

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.7b

localize20.0ms

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))))
5.8b
(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)))))

rewrite47.0ms

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)
10.0ms
(* (+ 1.0 eps) x)
24.0ms
(/ (+ 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)))))

series336.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (- 1.0 eps) x)
26.0ms
(* (+ 1.0 eps) x)
47.0ms
(/ (+ 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)))))

simplify48.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0462738
11805635
25002628

prune343.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 0.5 (pow x 2))
2.6b
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
4.4b
(/ (pow x 3) eps)

rewrite18.0ms

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)

series99.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(* 0.5 (pow x 2))
47.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
21.0ms
(/ (pow x 3) eps)

simplify62.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0305506
11561465
25001451

prune293.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize15.0ms

Local error

Found 4 expressions with local error:

4.4b
(/ (pow x 3) eps)
9.2b
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
9.2b
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
9.2b
(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)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
21.0ms
(/ (pow x 3) eps)
373.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
373.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
368.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

simplify48.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0271803
11222747
25002738

prune430.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.1b

localize19.0ms

Local error

Found 4 expressions with local error:

4.4b
(/ (pow x 3) eps)
4.4b
(/ (pow x 3) eps)
9.2b
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
9.2b
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

rewrite21.0ms

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)
1.0ms
(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)))))

series921.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ (pow x 3) eps)
21.0ms
(/ (pow x 3) eps)
508.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))
367.0ms
(cbrt (fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2)))))

simplify52.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0271926
11222878
25002872

prune668.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.0b

regimes81.0ms

Accuracy

95.6% (0.7b remaining)

Error of 5.5b against oracle of 4.8b and baseline of 20.2b

bsearch147.0ms

Steps
ItersRangePoint
9
0.003342748024832997
311.65670950425
2.3467556829869274

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06340
16940
26940

end0.0ms

sample2.8s

Algorithm
intervals
Results
777.0ms1991×body10240exit
755.0ms1773×body1280valid
546.0ms10064×body80valid
323.0ms1331×body640valid
102.0ms644×body320valid
32.0ms310×body160valid