Details

Time bar (total: 5.9s)

sample99.0ms

Algorithm
intervals
Results
27.0ms60×body1280valid
21.0ms52×body10240exit
18.0ms327×body80valid
9.0ms37×body640valid
4.0ms23×body320valid
1.0ms6×body160valid

simplify38.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (36.0ms)

IterNodesCost
04716
112416
236516
3137616
4500115

prune9.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 eps) x)
0.0b
(exp (- (* (+ 1.0 eps) x)))
0.0b
(exp (- (* (- 1.0 eps) x)))
1.9b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
74×exp-neg
72×frac-times
56×neg-sub0 exp-diff
38×associate-*l/
36×associate-*r/
29×flip3-- flip--
27×flip3-+ flip-+
18×un-div-inv
12×add-sqr-sqrt exp-prod
10×*-un-lft-identity add-log-exp
8×add-cube-cbrt
6×pow1 add-exp-log add-cbrt-cube
5×associate-*l*
4×expm1-log1p-u log1p-expm1-u rem-exp-log
3×associate-*r*
2×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in neg-log
1×sub-neg fma-neg diff-log prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 159
Calls
4 calls:
6.0ms
(* (- 1.0 eps) x)
3.0ms
(exp (- (* (+ 1.0 eps) x)))
4.0ms
(exp (- (* (- 1.0 eps) x)))
17.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series276.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (- 1.0 eps) x)
26.0ms
(exp (- (* (+ 1.0 eps) x)))
30.0ms
(exp (- (* (- 1.0 eps) x)))
192.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify145.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 2 (109.0ms)

IterNodesCost
012903714
147013419
250013397

prune433.0ms

Filtered
171 candidates to 92 candidates (53.8%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 1 expressions with local error:

6.8b
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
1.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series38.0ms

Counts
1 → 3
Calls
1 calls:
38.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify30.0ms

Algorithm
egg-herbie
Counts
13 → 13
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
04289
113678
272278
3500275

prune53.0ms

Filtered
13 candidates to 11 candidates (84.6%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3)
4.0b
(cbrt (pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3))
6.8b
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×unpow-prod-down cube-prod
4×pow1 add-exp-log add-cbrt-cube
3×expm1-log1p-u pow-unpow log1p-expm1-u add-log-exp
2×cube-mult unpow3 sqr-pow
1×pow-to-exp pow-pow pow1/3 pow-exp rem-cbrt-cube fma-udef rem-cube-cbrt
Counts
3 → 58
Calls
3 calls:
2.0ms
(pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3)
2.0ms
(cbrt (pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3))
1.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series148.0ms

Counts
3 → 9
Calls
3 calls:
67.0ms
(pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3)
38.0ms
(cbrt (pow (fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2)))) 3))
43.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify220.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0169545
1620511
24809505
35001505

prune157.0ms

Filtered
67 candidates to 37 candidates (55.2%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 12.0 (pow x 2))
0.2b
(/ (cbrt (fma (pow x 3) 8.0 (- 8.0 (* 12.0 (pow x 2))))) 2.0)
6.8b
(fma (pow x 3) 8.0 (- 8.0 (* 12.0 (pow x 2))))
10.8b
(cbrt (fma (pow x 3) 8.0 (- 8.0 (* 12.0 (pow x 2)))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
23×add-cube-cbrt *-un-lft-identity
18×times-frac
15×cbrt-prod
11×add-exp-log
8×associate-*r*
7×add-cbrt-cube
6×associate-/l*
4×pow1 expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp unswap-sqr
3×associate-*l* prod-exp associate-/r*
2×unpow2 sqr-pow
1×cbrt-undiv pow-to-exp frac-2neg pow1/3 div-exp pow-exp clear-num *-commutative cbrt-unprod fma-udef div-inv
Counts
4 → 93
Calls
4 calls:
5.0ms
(* 12.0 (pow x 2))
4.0ms
(/ (cbrt (fma (pow x 3) 8.0 (- 8.0 (* 12.0 (pow x 2))))) 2.0)
1.0ms
(fma (pow x 3) 8.0 (- 8.0 (* 12.0 (pow x 2))))
1.0ms
(cbrt (fma (pow x 3) 8.0 (- 8.0 (* 12.0 (pow x 2)))))

series541.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* 12.0 (pow x 2))
316.0ms
(/ (cbrt (fma (pow x 3) 8.0 (- 8.0 (* 12.0 (pow x 2))))) 2.0)
41.0ms
(fma (pow x 3) 8.0 (- 8.0 (* 12.0 (pow x 2))))
153.0ms
(cbrt (fma (pow x 3) 8.0 (- 8.0 (* 12.0 (pow x 2)))))

simplify53.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
04431032
11565971
25001927

prune303.0ms

Filtered
105 candidates to 80 candidates (76.2%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

regimes147.0ms

Accuracy

97.1% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 17.7b

bsearch130.0ms

Steps
ItersRangePoint
8
0.24450492938876567
1440.7712708818249
76.79611313935149

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04935
15735
25735

end0.0ms

sample2.9s

Algorithm
intervals
Results
828.0ms1923×body10240exit
761.0ms1695×body1280valid
569.0ms10116×body80valid
335.0ms1260×body640valid
103.0ms594×body320valid
39.0ms324×body160valid