Details

Time bar (total: 3.7s)

sample47.0ms

Algorithm
intervals
Results
22.0ms97×body1280valid
6.0ms179×body80valid
6.0ms39×body640valid
3.0ms26×body320valid
1.0ms14×body160valid

simplify63.0ms

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: 32.0b

localize5.0ms

Local error

Found 1 expressions with local error:

3.4b
(- (exp (* a x)) 1.0)

rewrite6.0ms

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)

series37.0ms

Counts
1 → 3
Calls
1 calls:
37.0ms
(- (exp (* a x)) 1.0)

simplify81.0ms

Algorithm
egg-herbie
Counts
31 → 31
Iterations

Useful iterations: 3 (77.0ms)

IterNodesCost
0162253
1526172
22608161
35002125

prune70.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.7b

localize16.0ms

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)))
14.7b
(* (pow a 2) (pow x 2))
18.4b
(* (pow a 3) (pow x 3))

rewrite28.0ms

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))
14.0ms
(* (pow a 3) (pow x 3))

series297.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
98.0ms
(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
34.0ms
(* (pow a 2) (pow x 2))
59.0ms
(* (pow a 3) (pow x 3))

simplify77.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
0369802
11845699
25001656

prune355.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.7b

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)))
14.7b
(* (pow a 2) (pow x 2))

rewrite14.0ms

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:
0.0ms
(fma 1/6 (pow (* x a) 3) (* a x))
2.0ms
(pow (* x a) 3)
0.0ms
(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
9.0ms
(* (pow a 2) (pow x 2))

series247.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(fma 1/6 (pow (* x a) 3) (* a x))
45.0ms
(pow (* x a) 3)
89.0ms
(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (pow (* x a) 3) (* a x)))
31.0ms
(* (pow a 2) (pow x 2))

simplify47.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0278558
11355418
25001407

prune266.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
22×fma-def
18×*-un-lft-identity times-frac
16×add-sqr-sqrt add-cube-cbrt
10×pow1 add-exp-log
7×add-cbrt-cube
6×pow-unpow add-log-exp
5×unpow-prod-down sqr-pow
4×expm1-log1p-u pow-pow pow-exp log1p-expm1-u unpow2
2×pow-to-exp pow-prod-down prod-exp fma-udef rem-cube-cbrt
1×+-commutative cube-mult associate-+r+ flip3-+ unpow3 cube-prod sum-log cbrt-unprod flip-+ div-inv distribute-lft-out
Counts
4 → 91
Calls
4 calls:
0.0ms
(fma 1/6 (pow (* x a) 3) (* a x))
2.0ms
(pow (* x a) 2)
5.0ms
(pow (* x a) 3)
17.0ms
(+ (/ (pow (* x a) 2) 2) (fma 1/6 (pow (* x a) 3) (* a x)))

series227.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(fma 1/6 (pow (* x a) 3) (* a x))
22.0ms
(pow (* x a) 2)
40.0ms
(pow (* x a) 3)
83.0ms
(+ (/ (pow (* x a) 2) 2) (fma 1/6 (pow (* x a) 3) (* a x)))

simplify45.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0229397
11124364
25002359

prune270.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes167.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 21.4b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02114
12114

end0.0ms

sample1.3s

Algorithm
intervals
Results
601.0ms2716×body1280valid
203.0ms1317×body640valid
199.0ms5473×body80valid
80.0ms738×body320valid
29.0ms392×body160valid