Details

Time bar (total: 3.0s)

sample32.0ms

Algorithm
intervals
Results
13.0ms87×body1280valid
5.0ms46×body640valid
3.0ms168×body80valid
2.0ms27×body320valid
0.0ms9×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: 30.7b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(exp (* a x))
3.5b
(- (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:
1.0ms
(exp (* a x))
5.0ms
(- (exp (* a x)) 1.0)

series51.0ms

Counts
2 → 6
Calls
2 calls:
17.0ms
(exp (* a x))
34.0ms
(- (exp (* a x)) 1.0)

simplify82.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (78.0ms)

IterNodesCost
0173292
1562211
22710200
35002164

prune96.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
11.8b
(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
13.1b
(* (pow a 2) (pow x 2))
16.4b
(* (pow a 3) (pow x 3))

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:
0.0ms
(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
0.0ms
(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
9.0ms
(* (pow a 2) (pow x 2))
11.0ms
(* (pow a 3) (pow x 3))

series309.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
101.0ms
(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
31.0ms
(* (pow a 2) (pow x 2))
65.0ms
(* (pow a 3) (pow x 3))

simplify75.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
0369802
11845699
25001656

prune361.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize9.0ms

Local error

Found 2 expressions with local error:

5.4b
(fma 1/2 (* (pow a 2) (pow x 2)) (* x a))
13.1b
(* (pow a 2) (pow x 2))

rewrite14.0ms

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)) (* x a))
9.0ms
(* (pow a 2) (pow x 2))

series95.0ms

Counts
2 → 6
Calls
2 calls:
63.0ms
(fma 1/2 (* (pow a 2) (pow x 2)) (* x a))
32.0ms
(* (pow a 2) (pow x 2))

simplify179.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0190337
1729280
24610269
35001269

prune137.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b
(* (* (fabs x) a) (* (fabs x) a))
5.4b
(fma 1/2 (* (* (fabs x) a) (* (fabs x) a)) (* x a))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
41×pow1
17×pow-prod-down
14×add-exp-log add-cbrt-cube
8×prod-exp cbrt-unprod
4×pow-sqr pow-prod-up
2×add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity pow-plus log1p-expm1-u add-log-exp
1×pow2 swap-sqr associate-*r* associate-*l* *-commutative fma-udef
Counts
2 → 46
Calls
2 calls:
10.0ms
(* (* (fabs x) a) (* (fabs x) a))
0.0ms
(fma 1/2 (* (* (fabs x) a) (* (fabs x) a)) (* x a))

series91.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(* (* (fabs x) a) (* (fabs x) a))
60.0ms
(fma 1/2 (* (* (fabs x) a) (* (fabs x) a)) (* x a))

simplify88.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 3 (80.0ms)

IterNodesCost
0133295
1592227
22999216
35001214

prune75.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes247.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.8b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02630
12630

end0.0ms

sample919.0ms

Algorithm
intervals
Results
427.0ms2729×body1280valid
129.0ms1294×body640valid
110.0ms5499×body80valid
52.0ms757×body320valid
17.0ms395×body160valid