Details

Time bar (total: 2.7s)

sample43.0ms

Algorithm
intervals
Results
17.0ms71×body1280valid
9.0ms56×body640valid
3.0ms31×body320valid
2.0ms83×body80valid
2.0ms74×body80overflowed
1.0ms15×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
074
184
284

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.2b

localize4.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (exp x) (- (exp x) 1.0))
3.9b
(- (exp x) 1.0)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt *-un-lft-identity
19×add-cube-cbrt
15×times-frac
9×prod-diff
5×associate-/r* distribute-lft-out-- difference-of-squares
4×add-cbrt-cube add-log-exp
3×add-exp-log fma-neg associate-/l*
2×pow1 expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num div-inv
Counts
2 → 67
Calls
2 calls:
8.0ms
(/ (exp x) (- (exp x) 1.0))
5.0ms
(- (exp x) 1.0)

series45.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(/ (exp x) (- (exp x) 1.0))
14.0ms
(- (exp x) 1.0)

simplify193.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 3 (187.0ms)

IterNodesCost
0237520
1786429
24651416
35001404

prune146.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
0.1b
(fma 1/6 (pow x 3) x)
8.0b
(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
5×add-cbrt-cube
4×add-exp-log
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×fma-udef
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
3 → 49
Calls
3 calls:
3.0ms
(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
1.0ms
(fma 1/6 (pow x 3) x)
0.0ms
(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

series139.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
72.0ms
(fma 1/6 (pow x 3) x)
26.0ms
(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify94.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0178458
1614416
23125414
35002414

prune169.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (fma 1/12 x (/ 1 x)) 1/2)
0.1b
(fma 1/12 x (/ 1 x))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
5×*-un-lft-identity
4×add-log-exp
3×add-sqr-sqrt add-cube-cbrt fma-def
2×pow1 add-exp-log expm1-log1p-u add-cbrt-cube fma-udef log1p-expm1-u
1×+-commutative associate-+l+ flip3-+ sum-log flip-+ distribute-lft-out
Counts
2 → 28
Calls
2 calls:
3.0ms
(+ (fma 1/12 x (/ 1 x)) 1/2)
0.0ms
(fma 1/12 x (/ 1 x))

series60.0ms

Counts
2 → 6
Calls
2 calls:
17.0ms
(+ (fma 1/12 x (/ 1 x)) 1/2)
43.0ms
(fma 1/12 x (/ 1 x))

simplify39.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 3 (35.0ms)

IterNodesCost
090126
1306119
21283117
35001116

prune62.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1.0 (exp x))
0.0b
(/ 1 (- 1 (/ 1.0 (exp x))))
3.9b
(- 1 (/ 1.0 (exp x)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt
79×*-un-lft-identity
70×times-frac
59×add-cube-cbrt
39×prod-diff
20×difference-of-squares
11×associate-/r*
8×add-exp-log
7×add-cbrt-cube
6×associate-/l*
5×div-inv distribute-lft-out-- add-log-exp
4×pow1
3×expm1-log1p-u fma-neg div-exp log1p-expm1-u
2×cbrt-undiv flip3-- frac-2neg clear-num associate-/r/ flip--
1×sub-neg rec-exp pow-flip diff-log 1-exp inv-pow
Counts
3 → 145
Calls
3 calls:
3.0ms
(/ 1.0 (exp x))
17.0ms
(/ 1 (- 1 (/ 1.0 (exp x))))
11.0ms
(- 1 (/ 1.0 (exp x)))

series101.0ms

Counts
3 → 9
Calls
3 calls:
16.0ms
(/ 1.0 (exp x))
47.0ms
(/ 1 (- 1 (/ 1.0 (exp x))))
38.0ms
(- 1 (/ 1.0 (exp x)))

simplify64.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05521839
122981281
250011188

prune174.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes42.0ms

Accuracy

94.6% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 11.8b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02313
12313

end0.0ms

sample1.2s

Algorithm
intervals
Results
527.0ms2252×body1280valid
254.0ms1637×body640valid
88.0ms2880×body80valid
86.0ms826×body320valid
75.0ms2512×body80overflowed
28.0ms405×body160valid