Details

Time bar (total: 2.8s)

sample41.0ms

Algorithm
intervals
Results
13.0ms59×body1280valid
10.0ms90×body10240exit
6.0ms57×body640valid
2.0ms28×body320valid
2.0ms93×body80valid
1.0ms19×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
074
184
284

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.6b

localize4.0ms

Local error

Found 2 expressions with local error:

0.3b
(/ (exp x) (- (exp x) 1.0))
5.1b
(- (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:
30.0ms
(/ (exp x) (- (exp x) 1.0))
14.0ms
(- (exp x) 1.0)

simplify194.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 3 (188.0ms)

IterNodesCost
0237520
1786429
24651416
35001404

prune157.0ms

Filtered
73 candidates to 50 candidates (68.5%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

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)))
0.0b
(fma 1/6 (pow x 3) x)
12.8b
(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)))
0.0ms
(fma 1/6 (pow x 3) x)
0.0ms
(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

series141.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
73.0ms
(fma 1/6 (pow x 3) x)
27.0ms
(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify95.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0178458
1614416
23125414
35002414

prune181.0ms

Filtered
58 candidates to 45 candidates (77.6%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (exp x))
0.0b
(cbrt (exp x))
0.0b
(cbrt (exp x))
12.8b
(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
1.0ms
(cbrt (exp x))
1.0ms
(cbrt (exp x))
1.0ms
(cbrt (exp x))
0.0ms
(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

series264.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(cbrt (exp x))
78.0ms
(cbrt (exp x))
80.0ms
(cbrt (exp x))
26.0ms
(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify40.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 3 (35.0ms)

IterNodesCost
081257
1210233
21070227
35001221

prune226.0ms

Filtered
61 candidates to 49 candidates (80.3%)
Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

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))

series62.0ms

Counts
2 → 6
Calls
2 calls:
15.0ms
(+ (fma 1/12 x (/ 1 x)) 1/2)
47.0ms
(fma 1/12 x (/ 1 x))

simplify37.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 3 (33.0ms)

IterNodesCost
090129
1306121
21283120
35001119

prune59.0ms

Filtered
34 candidates to 26 candidates (76.5%)
Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes73.0ms

Accuracy

94.9% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 11.5b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02413
12413

end0.0ms

sample1.1s

Algorithm
intervals
Results
389.0ms2256×body1280valid
278.0ms2515×body10240exit
174.0ms1646×body640valid
57.0ms821×body320valid
54.0ms2865×body80valid
21.0ms413×body160valid