Details

Time bar (total: 3.2s)

sample35.0ms

Algorithm
intervals
Results
15.0ms92×body1280valid
4.0ms39×body640valid
4.0ms164×body80valid
2.0ms28×body320valid
0.0ms7×body160valid

simplify61.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0113
1183
2273
3503
41153
53293
616423
750013

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.7b

Counts
2 → 1

localize191.0ms

Local error

Found 1 expressions with local error:

2.7b
(- (exp (* a x)) 1.0)

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
9×prod-diff
8×add-cube-cbrt
3×fma-neg add-log-exp
1×pow1 add-exp-log expm1-log1p-u sub-neg flip3-- diff-log add-cbrt-cube flip-- log1p-expm1-u distribute-lft-out-- difference-of-squares
Counts
1 → 28
Calls
1 calls:
5.0ms
(- (exp (* a x)) 1.0)

series34.0ms

Counts
1 → 3
Calls
1 calls:
34.0ms
(- (exp (* a x)) 1.0)

simplify80.0ms

Algorithm
egg-herbie
Counts
31 → 31
Iterations

Useful iterations: 3 (77.0ms)

IterNodesCost
0162253
1526172
22608161
35002125

prune53.0ms

Filtered
31 candidates to 18 candidates (58.1%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New27431
Fresh000
Picked011
Done000
Total27532

Merged error: 7.9b

Counts
32 → 5

localize7.0ms

Local error

Found 2 expressions with local error:

2.7b
(- (exp (* a x)) 1.0)
2.7b
(log (exp (- (exp (* a x)) 1.0)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt *-un-lft-identity
18×prod-diff
17×add-cube-cbrt
14×log-prod
11×exp-sum
6×log-pow
5×exp-prod
4×add-log-exp
3×pow1 fma-neg
2×add-exp-log expm1-log1p-u sub-neg add-cbrt-cube log1p-expm1-u distribute-lft-out-- difference-of-squares
1×log-div flip3-- exp-diff diff-log rem-log-exp flip--
Counts
2 → 59
Calls
2 calls:
5.0ms
(- (exp (* a x)) 1.0)
6.0ms
(log (exp (- (exp (* a x)) 1.0)))

series69.0ms

Counts
2 → 6
Calls
2 calls:
36.0ms
(- (exp (* a x)) 1.0)
33.0ms
(log (exp (- (exp (* a x)) 1.0)))

simplify91.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 3 (85.0ms)

IterNodesCost
0225523
1633357
22823283
35001265

prune83.0ms

Filtered
65 candidates to 34 candidates (52.3%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New65065
Fresh033
Picked011
Done011
Total65570

Merged error: 7.9b

Counts
70 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
11.3b
(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
15.6b
(* (pow a 3) (pow x 3))
15.9b
(* (pow a 2) (pow x 2))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
32×unswap-sqr
28×add-exp-log unpow-prod-down
20×associate-*r* associate-*l* sqr-pow
18×prod-exp
14×add-cube-cbrt *-un-lft-identity cube-prod
12×pow-to-exp pow-exp
10×unpow2
8×add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×cube-mult unpow3 pow-prod-down *-commutative cbrt-unprod fma-udef
Counts
4 → 134
Calls
4 calls:
1.0ms
(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
1.0ms
(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
9.0ms
(* (pow a 3) (pow x 3))
10.0ms
(* (pow a 2) (pow x 2))

series300.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
99.0ms
(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
63.0ms
(* (pow a 3) (pow x 3))
31.0ms
(* (pow a 2) (pow x 2))

simplify80.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
0369802
11836699
25001656

prune296.0ms

Filtered
146 candidates to 81 candidates (55.5%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1451146
Fresh112
Picked101
Done022
Total1474151

Merged error: 5.0b

Counts
151 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1/6 (pow (* x a) 3) (* a x))
0.2b
(pow (* x a) 3)
11.3b
(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
15.9b
(* (pow a 2) (pow x 2))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
19×add-exp-log
16×unswap-sqr
15×unpow-prod-down
11×sqr-pow
10×prod-exp unpow2
9×add-cube-cbrt *-un-lft-identity add-cbrt-cube
8×associate-*r* associate-*l* pow-exp
7×pow1 pow-to-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow
2×pow-pow pow-prod-down cbrt-unprod fma-udef rem-cube-cbrt
1×cube-mult unpow3 cube-prod *-commutative
Counts
4 → 97
Calls
4 calls:
1.0ms
(fma 1/6 (pow (* x a) 3) (* a x))
4.0ms
(pow (* x a) 3)
1.0ms
(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
7.0ms
(* (pow a 2) (pow x 2))

series250.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(fma 1/6 (pow (* x a) 3) (* a x))
42.0ms
(pow (* x a) 3)
90.0ms
(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
34.0ms
(* (pow a 2) (pow x 2))

simplify56.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0278520
11235418
25002414

prune219.0ms

Filtered
109 candidates to 68 candidates (62.4%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1072109
Fresh101
Picked101
Done112
Total1103113

Merged error: 0.0b

Counts
113 → 3

regimes140.0ms

Accuracy

99.1% (0.2b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 21.3b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02013

end0.0ms

sample1.0s

Algorithm
intervals
Results
467.0ms2721×body1280valid
151.0ms1307×body640valid
134.0ms5514×body80valid
54.0ms706×body320valid
24.0ms447×body160valid