Details

Time bar (total: 15.6s)

sample326.0ms

Algorithm
intervals
Results
254.0ms3370×body80valid

simplify70.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
09061
140658
2226736
3500135

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)
1.3b
(pow (/ 1.0 (fabs x)) 6)

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
39×unpow-prod-down
37×add-sqr-sqrt
36×add-cube-cbrt *-un-lft-identity times-frac
13×add-exp-log cube-prod
9×pow-unpow
8×pow1
7×add-cbrt-cube
6×pow-exp
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×pow-to-exp pow-pow div-exp sqrt-prod sqr-pow
2×rem-cube-cbrt
1×cbrt-undiv cube-div cube-mult rem-sqrt-square sqrt-pow1 pow1/2 unpow3
Counts
4 → 123
Calls
4 calls:
7.0ms
(pow (/ 1.0 (fabs x)) 3)
6.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)
7.0ms
(pow (/ 1.0 (fabs x)) 6)

series106.0ms

Counts
4 → 10
Calls
4 calls:
29.0ms
(pow (/ 1.0 (fabs x)) 3)
30.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)
47.0ms
(pow (/ 1.0 (fabs x)) 6)

simplify78.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
0545752
12496663
25001647

prune644.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (+ (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3))) (* (/ 1.0 (fabs x)) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite667.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
29×add-exp-log add-cube-cbrt *-un-lft-identity
27×times-frac
26×unpow-prod-down
17×associate-*l/
16×add-cbrt-cube
13×cube-prod prod-exp
11×frac-times
10×frac-add
9×pow1
6×pow-unpow flip3-+ pow-exp flip-+
5×associate-*r/ div-exp cbrt-unprod
4×expm1-log1p-u pow-to-exp log1p-expm1-u add-log-exp
3×associate-*l* sqrt-prod div-inv
2×cbrt-undiv pow-pow rem-cube-cbrt sqr-pow
1×cube-div cube-mult rem-sqrt-square sqrt-pow1 pow1/2 unpow3 associate-*r* pow-prod-down *-commutative
Counts
4 → 133
Calls
4 calls:
648.0ms
(* (+ (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3))) (* (/ 1.0 (fabs x)) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
7.0ms
(pow (/ 1.0 (fabs x)) 3)
6.0ms
(pow (/ 1.0 (fabs x)) 4)
2.0ms
(sqrt PI)

series551.0ms

Counts
4 → 10
Calls
4 calls:
488.0ms
(* (+ (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3))) (* (/ 1.0 (fabs x)) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
29.0ms
(pow (/ 1.0 (fabs x)) 3)
34.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify45.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09942448
150012114

prune772.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1.0 (fabs x)) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)))
0.3b
(* (+ (/ 1.0 (/ 2.0 (/ 1.0 (pow (fabs x) 3)))) (* (/ 1.0 (fabs x)) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
1.0b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite822.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
28×add-sqr-sqrt
24×*-un-lft-identity
22×add-cube-cbrt
19×times-frac
18×associate-*l/ add-cbrt-cube
16×associate-*l*
15×prod-exp
13×frac-times unpow-prod-down
10×pow1 frac-add
8×flip3-+ flip-+
7×associate-*r/ cbrt-unprod
5×div-exp associate-*r*
4×expm1-log1p-u pow-exp log1p-expm1-u add-log-exp
3×pow-to-exp pow-unpow sqrt-prod
2×cbrt-undiv pow-prod-down *-commutative div-inv unswap-sqr
1×distribute-rgt-in rem-sqrt-square pow-pow distribute-lft-in sqrt-pow1 pow1/2 distribute-lft-out sqr-pow
Counts
4 → 126
Calls
4 calls:
72.0ms
(* (/ 1.0 (fabs x)) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)))
735.0ms
(* (+ (/ 1.0 (/ 2.0 (/ 1.0 (pow (fabs x) 3)))) (* (/ 1.0 (fabs x)) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
9.0ms
(pow (/ 1.0 (fabs x)) 4)
2.0ms
(sqrt PI)

series690.0ms

Counts
4 → 10
Calls
4 calls:
158.0ms
(* (/ 1.0 (fabs x)) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)))
500.0ms
(* (+ (/ 1.0 (/ 2.0 (/ 1.0 (pow (fabs x) 3)))) (* (/ 1.0 (fabs x)) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
31.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify56.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
010162947
150012606

prune865.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)
0.3b
(* (+ (/ 1.0 (/ 2.0 (/ 1.0 (pow (fabs x) 3)))) (/ (* 1.0 (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1))) (fabs x))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
1.0b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite1000.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
16×*-un-lft-identity
15×add-sqr-sqrt
14×add-cube-cbrt
13×unpow-prod-down prod-exp add-cbrt-cube
9×times-frac
8×pow1
7×associate-*l/
5×cbrt-unprod
4×expm1-log1p-u div-exp associate-*l* pow-exp log1p-expm1-u add-log-exp
3×frac-times pow-to-exp pow-unpow sqrt-prod
2×flip3-+ frac-add flip-+
1×cbrt-undiv rem-sqrt-square pow-pow sqrt-pow1 pow1/2 associate-*r/ associate-*r* pow-prod-down *-commutative fma-udef div-inv distribute-lft-out sqr-pow
Counts
4 → 88
Calls
4 calls:
0.0ms
(fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)
989.0ms
(* (+ (/ 1.0 (/ 2.0 (/ 1.0 (pow (fabs x) 3)))) (/ (* 1.0 (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1))) (fabs x))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
6.0ms
(pow (/ 1.0 (fabs x)) 4)
2.0ms
(sqrt PI)

series577.0ms

Counts
4 → 10
Calls
4 calls:
51.0ms
(fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)
495.0ms
(* (+ (/ 1.0 (/ 2.0 (/ 1.0 (pow (fabs x) 3)))) (/ (* 1.0 (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1))) (fabs x))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
31.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify71.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
06191706
125041441
250011436

prune524.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes382.0ms

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04229
14229

end0.0ms

sample7.1s

Algorithm
intervals
Results
5.9s78267×body80valid