Details

Time bar (total: 3.1s)

sample37.0ms

Algorithm
intervals
Results
13.0ms94×body1280valid
6.0ms182×body80valid
4.0ms40×body640valid
2.0ms27×body320valid
1.0ms15×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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b
(exp (* a x))
4.1b
(- (exp (* a x)) 1.0)

rewrite19.0ms

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:
4.0ms
(exp (* a x))
14.0ms
(- (exp (* a x)) 1.0)

series53.0ms

Counts
2 → 6
Calls
2 calls:
17.0ms
(exp (* a x))
36.0ms
(- (exp (* a x)) 1.0)

simplify81.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (77.0ms)

IterNodesCost
0173292
1562211
22710200
35002164

prune95.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
11.2b
(* (pow a 2) (pow x 2))
11.8b
(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
14.5b
(* (pow a 3) (pow x 3))

rewrite42.0ms

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:
0.0ms
(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
17.0ms
(* (pow a 2) (pow x 2))
0.0ms
(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
20.0ms
(* (pow a 3) (pow x 3))

series329.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
34.0ms
(* (pow a 2) (pow x 2))
109.0ms
(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
69.0ms
(* (pow a 3) (pow x 3))

simplify75.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
0369802
11845699
25001656

prune374.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.3b

localize8.0ms

Local error

Found 2 expressions with local error:

4.2b
(fma 1/2 (* (pow a 2) (pow x 2)) (* a x))
11.2b
(* (pow a 2) (pow x 2))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
16×unswap-sqr
14×add-exp-log unpow-prod-down
10×unpow2 sqr-pow
9×prod-exp
8×associate-*r* associate-*l*
6×pow-to-exp add-cube-cbrt *-un-lft-identity pow-exp
4×add-cbrt-cube
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
1×pow-prod-down *-commutative cbrt-unprod fma-udef
Counts
2 → 63
Calls
2 calls:
0.0ms
(fma 1/2 (* (pow a 2) (pow x 2)) (* a x))
17.0ms
(* (pow a 2) (pow x 2))

series101.0ms

Counts
2 → 6
Calls
2 calls:
63.0ms
(fma 1/2 (* (pow a 2) (pow x 2)) (* a x))
38.0ms
(* (pow a 2) (pow x 2))

simplify186.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0188337
1727280
24608269
35001269

prune133.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(* (fabs (* x a)) (fabs (* x a)))
4.2b
(fma 1/2 (* (fabs (* x a)) (fabs (* x a))) (* a x))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1
8×add-sqr-sqrt
6×add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube
3×swap-sqr associate-*r* associate-*l*
2×expm1-log1p-u log1p-expm1-u add-log-exp
1×pow2 pow-plus pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod fma-udef unswap-sqr
Counts
2 → 37
Calls
2 calls:
7.0ms
(* (fabs (* x a)) (fabs (* x a)))
1.0ms
(fma 1/2 (* (fabs (* x a)) (fabs (* x a))) (* a x))

series52.0ms

Counts
2 → 6
Calls
2 calls:
9.0ms
(* (fabs (* x a)) (fabs (* x a)))
43.0ms
(fma 1/2 (* (fabs (* x a)) (fabs (* x a))) (* a x))

simplify50.0ms

Algorithm
egg-herbie
Counts
43 → 43
Iterations

Useful iterations: 3 (46.0ms)

IterNodesCost
087278
1336224
21512210
35002204

prune83.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes243.0ms

Accuracy

98.3% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 21.4b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01613

end0.0ms

sample982.0ms

Algorithm
intervals
Results
419.0ms2722×body1280valid
134.0ms1346×body640valid
98.0ms5420×body80valid
48.0ms778×body320valid
16.0ms387×body160valid