Details

Time bar (total: 3.5s)

sample35.0ms

Algorithm
intervals
Results
14.0ms88×body1280valid
5.0ms46×body640valid
3.0ms149×body80valid
2.0ms29×body320valid
1.0ms16×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: 31.5b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(exp (* a x))
4.9b
(- (exp (* a x)) 1.0)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt prod-diff
6×add-log-exp
3×fma-neg
2×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
1×sub-neg exp-prod flip3-- exp-to-pow diff-log flip-- rem-exp-log distribute-lft-out-- difference-of-squares
Counts
2 → 40
Calls
2 calls:
2.0ms
(exp (* a x))
4.0ms
(- (exp (* a x)) 1.0)

series50.0ms

Counts
2 → 6
Calls
2 calls:
12.0ms
(exp (* a x))
38.0ms
(- (exp (* a x)) 1.0)

simplify82.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (78.0ms)

IterNodesCost
0173292
1562211
22710200
35002164

prune78.0ms

Filtered
46 candidates to 28 candidates (60.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New40646
Fresh000
Picked101
Done000
Total41647

Merged error: 10.6b

Counts
47 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
10.8b
(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
14.9b
(* (pow a 2) (pow x 2))
18.7b
(* (pow a 3) (pow x 3))

rewrite26.0ms

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)))
11.0ms
(* (pow a 2) (pow x 2))
10.0ms
(* (pow a 3) (pow x 3))

series309.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
104.0ms
(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
36.0ms
(* (pow a 2) (pow x 2))
61.0ms
(* (pow a 3) (pow x 3))

simplify77.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
0369802
11845699
25001656

prune319.0ms

Filtered
146 candidates to 81 candidates (55.5%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1451146
Fresh055
Picked101
Done000
Total1466152

Merged error: 5.1b

Counts
152 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma 1/6 (pow (* x a) 3) (* a x))
0.3b
(pow (* x a) 3)
10.8b
(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
14.9b
(* (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))
41.0ms
(pow (* x a) 3)
90.0ms
(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
35.0ms
(* (pow a 2) (pow x 2))

simplify50.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0278520
11235418
25002414

prune244.0ms

Filtered
109 candidates to 68 candidates (62.4%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1063109
Fresh235
Picked101
Done000
Total1096115

Merged error: 0.1b

Counts
115 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (* x a) 2)
0.2b
(fma 1/6 (pow (* x a) 3) (* a x))
0.3b
(pow (* x a) 3)
10.8b
(fma 1/2 (pow (* x a) 2) (fma 1/6 (pow (* x a) 3) (* a x)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-exp-log
7×add-cbrt-cube
6×add-sqr-sqrt add-cube-cbrt pow-unpow *-un-lft-identity
4×expm1-log1p-u pow-pow pow-exp log1p-expm1-u add-log-exp
2×pow-to-exp unpow-prod-down pow-prod-down prod-exp fma-udef rem-cube-cbrt sqr-pow
1×cube-mult unpow3 cube-prod cbrt-unprod unpow2
Counts
4 → 64
Calls
4 calls:
3.0ms
(pow (* x a) 2)
1.0ms
(fma 1/6 (pow (* x a) 3) (* a x))
4.0ms
(pow (* x a) 3)
1.0ms
(fma 1/2 (pow (* x a) 2) (fma 1/6 (pow (* x a) 3) (* a x)))

series230.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(pow (* x a) 2)
83.0ms
(fma 1/6 (pow (* x a) 3) (* a x))
46.0ms
(pow (* x a) 3)
79.0ms
(fma 1/2 (pow (* x a) 2) (fma 1/6 (pow (* x a) 3) (* a x)))

simplify34.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0171313
1787281
25001281

prune336.0ms

Filtered
76 candidates to 50 candidates (65.8%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New74276
Fresh235
Picked011
Done000
Total76682

Merged error: 0.1b

Counts
82 → 6

regimes208.0ms

Accuracy

98.3% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.4b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02222
12222

end0.0ms

sample1.0s

Algorithm
intervals
Results
474.0ms2678×body1280valid
147.0ms1284×body640valid
133.0ms5524×body80valid
59.0ms785×body320valid
24.0ms412×body160valid