Details

Time bar (total: 8.0s)

sample137.0ms

Algorithm
intervals
Results
39.0ms54×body1280valid
37.0ms310×body80valid
26.0ms48×body640valid
8.0ms62×body80overflowed
7.0ms21×body320valid
2.0ms9×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (38.0ms)

IterNodesCost
04716
112416
236516
3137616
4500115

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.8b

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))))
5.3b
(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)))))

rewrite46.0ms

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)
9.0ms
(* (+ 1.0 eps) x)
25.0ms
(/ (+ 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)))))

series339.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (- 1.0 eps) x)
31.0ms
(* (+ 1.0 eps) x)
44.0ms
(/ (+ 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 (41.0ms)

IterNodesCost
0462738
11805635
25002628

prune336.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 0.5 (pow x 2))
3.4b
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
6.6b
(/ (pow x 3) eps)

rewrite14.0ms

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:
5.0ms
(* 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:
25.0ms
(* 0.5 (pow x 2))
52.0ms
(fma 1.3877787807814457e-17 (/ (pow x 3) eps) (- 1.0 (* 0.5 (pow x 2))))
22.0ms
(/ (pow x 3) eps)

simplify60.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0305506
11561465
25001451

prune271.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
1.6b
(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
3.4b
(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
185×times-frac
83×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
24×add-exp-log
14×cube-mult unpow-prod-down unpow3 cube-prod sqr-pow
13×associate-/r*
12×div-exp
10×div-inv
9×add-cbrt-cube
8×associate-/l*
6×cbrt-prod
4×pow1 expm1-log1p-u pow-exp log1p-expm1-u add-log-exp
3×cbrt-undiv
2×pow-to-exp pow1/3 prod-exp
1×frac-2neg clear-num associate-/r/ fma-udef
Counts
4 → 184
Calls
4 calls:
1.0ms
(cbrt x)
4.0ms
(cbrt x)
8.0ms
(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
0.0ms
(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))

series499.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(cbrt x)
184.0ms
(cbrt x)
47.0ms
(/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x))
81.0ms
(fma 1.3877787807814457e-17 (/ (pow (* (cbrt x) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))

simplify154.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 2 (137.0ms)

IterNodesCost
07211771
143251200
250011152

prune575.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
3.4b
(fma 1.3877787807814457e-17 (/ (pow (* (log (exp (cbrt x))) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
10.9b
(log (exp (cbrt x)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×log-pow
6×exp-prod
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×log-prod
2×pow1/3
1×rem-log-exp fma-udef
Counts
4 → 56
Calls
4 calls:
0.0ms
(cbrt x)
0.0ms
(cbrt x)
0.0ms
(fma 1.3877787807814457e-17 (/ (pow (* (log (exp (cbrt x))) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
2.0ms
(log (exp (cbrt x)))

series645.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(cbrt x)
194.0ms
(cbrt x)
80.0ms
(fma 1.3877787807814457e-17 (/ (pow (* (log (exp (cbrt x))) (cbrt x)) 3) (/ eps x)) (- 1.0 (* 0.5 (pow x 2))))
182.0ms
(log (exp (cbrt x)))

simplify61.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0139339
1329286
21862275
35001275

prune284.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.4b

regimes151.0ms

Accuracy

96.3% (0.6b remaining)

Error of 4.1b against oracle of 3.5b and baseline of 20.2b

bsearch148.0ms

Steps
ItersRangePoint
7
0.003211336228265424
0.056513619206862806
0.003370189059752992

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05537
16137
26137

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.3s1780×body1280valid
1.2s9970×body80valid
603.0ms1240×body640valid
236.0ms1913×body80overflowed
216.0ms627×body320valid
75.0ms316×body160valid