Details

Time bar (total: 3.6s)

sample32.0ms

Algorithm
intervals
Results
13.0ms81×body1280valid
4.0ms184×body80valid
4.0ms41×body640valid
2.0ms26×body320valid
1.0ms15×body160valid

simplify64.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0113
1183
2273
3503
41153
53293
616333
750023

prune2.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.6b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(exp (* a x))
4.6b
(- (exp (* a x)) 1.0)

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×*-un-lft-identity
12×add-cube-cbrt exp-prod
9×prod-diff
6×add-log-exp
3×fma-neg associate-*r* associate-*l*
2×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
1×sub-neg flip3-- exp-to-pow diff-log *-commutative flip-- rem-exp-log distribute-lft-out-- difference-of-squares unswap-sqr
Counts
2 → 51
Calls
2 calls:
4.0ms
(exp (* a x))
7.0ms
(- (exp (* a x)) 1.0)

series54.0ms

Counts
2 → 6
Calls
2 calls:
13.0ms
(exp (* a x))
41.0ms
(- (exp (* a x)) 1.0)

simplify93.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 3 (88.0ms)

IterNodesCost
0208321
1654240
23113229
35001202

prune98.0ms

Filtered
57 candidates to 37 candidates (35.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New49857
Fresh000
Picked101
Done000
Total50858

Merged error: 9.1b

Counts
58 → 8

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (exp (* a x)))
0.0b
(exp (* a x))
0.0b
(exp (* a x))
4.7b
(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
36×exp-prod
21×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity sqrt-pow1
9×associate-*r* associate-*l* add-log-exp
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×exp-to-pow sqrt-prod *-commutative unswap-sqr
2×rem-exp-log
1×rem-sqrt-square pow1/2 fma-udef
Counts
4 → 84
Calls
4 calls:
5.0ms
(sqrt (exp (* a x)))
4.0ms
(exp (* a x))
4.0ms
(exp (* a x))
1.0ms
(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

series137.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(sqrt (exp (* a x)))
13.0ms
(exp (* a x))
13.0ms
(exp (* a x))
86.0ms
(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

simplify71.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0179372
1544336
22234334
35002334

prune213.0ms

Filtered
96 candidates to 71 candidates (26.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New92496
Fresh167
Picked101
Done000
Total9410104

Merged error: 9.1b

Counts
104 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (* a x))
0.0b
(exp (* a x))
0.0b
(expm1 (log1p (exp (* a x))))
39.6b
(fma (sqrt (exp (* a x))) (sqrt (expm1 (log1p (exp (* a x))))) (- 1.0))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
24×exp-prod
14×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
8×add-log-exp
6×associate-*r* associate-*l*
5×log1p-expm1-u
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube
2×expm1-log1p exp-to-pow *-commutative rem-exp-log unswap-sqr
1×fma-udef expm1-udef
Counts
4 → 68
Calls
4 calls:
4.0ms
(exp (* a x))
5.0ms
(exp (* a x))
1.0ms
(expm1 (log1p (exp (* a x))))
1.0ms
(fma (sqrt (exp (* a x))) (sqrt (expm1 (log1p (exp (* a x))))) (- 1.0))

series232.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(exp (* a x))
13.0ms
(exp (* a x))
52.0ms
(expm1 (log1p (exp (* a x))))
153.0ms
(fma (sqrt (exp (* a x))) (sqrt (expm1 (log1p (exp (* a x))))) (- 1.0))

simplify57.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0140346
1421304
21719293
35002293

prune206.0ms

Filtered
80 candidates to 58 candidates (27.5%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New79180
Fresh189
Picked011
Done000
Total801090

Merged error: 9.1b

Counts
90 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(cbrt (fma (sqrt (exp (* a x))) (sqrt (expm1 (log1p (exp (* a x))))) (- 1.0)))
39.6b
(fma (sqrt (exp (* a x))) (sqrt (expm1 (log1p (exp (* a x))))) (- 1.0))
39.6b
(fma (sqrt (exp (* a x))) (sqrt (expm1 (log1p (exp (* a x))))) (- 1.0))
39.6b
(fma (sqrt (exp (* a x))) (sqrt (expm1 (log1p (exp (* a x))))) (- 1.0))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
5×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×cbrt-prod fma-udef
1×pow1/3
Counts
4 → 43
Calls
4 calls:
1.0ms
(cbrt (fma (sqrt (exp (* a x))) (sqrt (expm1 (log1p (exp (* a x))))) (- 1.0)))
1.0ms
(fma (sqrt (exp (* a x))) (sqrt (expm1 (log1p (exp (* a x))))) (- 1.0))
1.0ms
(fma (sqrt (exp (* a x))) (sqrt (expm1 (log1p (exp (* a x))))) (- 1.0))
1.0ms
(fma (sqrt (exp (* a x))) (sqrt (expm1 (log1p (exp (* a x))))) (- 1.0))

series664.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(cbrt (fma (sqrt (exp (* a x))) (sqrt (expm1 (log1p (exp (* a x))))) (- 1.0)))
152.0ms
(fma (sqrt (exp (* a x))) (sqrt (expm1 (log1p (exp (* a x))))) (- 1.0))
155.0ms
(fma (sqrt (exp (* a x))) (sqrt (expm1 (log1p (exp (* a x))))) (- 1.0))
155.0ms
(fma (sqrt (exp (* a x))) (sqrt (expm1 (log1p (exp (* a x))))) (- 1.0))

simplify59.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 3 (53.0ms)

IterNodesCost
0134715
1406574
21733451
35001390

prune211.0ms

Filtered
55 candidates to 50 candidates (9.1%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New53255
Fresh088
Picked011
Done101
Total541165

Merged error: 9.1b

Counts
65 → 11

regimes372.0ms

Accuracy

96.7% (0.7b remaining)

Error of 9.0b against oracle of 8.2b and baseline of 29.8b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03125
13125

end0.0ms

sample922.0ms

Algorithm
intervals
Results
426.0ms2660×body1280valid
138.0ms1353×body640valid
103.0ms5452×body80valid
51.0ms786×body320valid
18.0ms403×body160valid