Details

Time bar (total: 14.5s)

sample321.0ms

Algorithm
intervals
Results
251.0ms3370×body80valid

simplify68.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (64.0ms)

IterNodesCost
09061
140658
2226736
3500135

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize36.0ms

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)

rewrite26.0ms

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:
9.0ms
(pow (/ 1.0 (fabs x)) 3)
6.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)
6.0ms
(pow (/ 1.0 (fabs x)) 6)

series115.0ms

Counts
4 → 10
Calls
4 calls:
35.0ms
(pow (/ 1.0 (fabs x)) 3)
33.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)
46.0ms
(pow (/ 1.0 (fabs x)) 6)

simplify77.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
0545752
12496663
25001647

prune636.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.3b

localize36.0ms

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)

rewrite678.0ms

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:
660.0ms
(* (+ (/ 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))))
6.0ms
(pow (/ 1.0 (fabs x)) 3)
6.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)

series575.0ms

Counts
4 → 10
Calls
4 calls:
506.0ms
(* (+ (/ 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))))
35.0ms
(pow (/ 1.0 (fabs x)) 3)
33.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify44.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09942448
150012114

prune764.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

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)

rewrite681.0ms

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:
662.0ms
(* (+ (/ 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))))
6.0ms
(pow (/ 1.0 (fabs x)) 3)
6.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)

series580.0ms

Counts
4 → 10
Calls
4 calls:
514.0ms
(* (+ (/ 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))))
32.0ms
(pow (/ 1.0 (fabs x)) 3)
34.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify44.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09942445
150012111

prune793.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (pow (fabs x) 3))
0.3b
(/ 1 (pow (fabs x) 5))
0.3b
(* 1.875 (/ 1 (pow (fabs x) 7)))
0.3b
(* (fma 0.5 (/ 1 (pow (fabs x) 3)) (fma 0.75 (/ 1 (pow (fabs x) 5)) (fma 1.0 (/ 1 (fabs x)) (* 1.875 (/ 1 (pow (fabs x) 7)))))) (* (exp (* 1/2 (pow (fabs x) 2))) (sqrt (/ 1 PI))))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
76×add-sqr-sqrt
64×*-un-lft-identity
61×add-cube-cbrt
46×add-exp-log
35×unpow-prod-down
26×associate-*r*
19×associate-/r*
18×div-exp add-cbrt-cube
13×prod-exp sqr-pow
12×cube-prod
11×pow1
9×pow-to-exp rec-exp 1-exp pow-exp
7×unswap-sqr
6×associate-*l* associate-/l*
5×cbrt-unprod
4×expm1-log1p-u cube-mult unpow3 pow-prod-down log1p-expm1-u add-log-exp
3×cbrt-undiv associate-*r/ div-inv
2×pow-flip frac-2neg clear-num *-commutative inv-pow
1×sqrt-div un-div-inv
Counts
4 → 211
Calls
4 calls:
9.0ms
(/ 1 (pow (fabs x) 3))
8.0ms
(/ 1 (pow (fabs x) 5))
22.0ms
(* 1.875 (/ 1 (pow (fabs x) 7)))
46.0ms
(* (fma 0.5 (/ 1 (pow (fabs x) 3)) (fma 0.75 (/ 1 (pow (fabs x) 5)) (fma 1.0 (/ 1 (fabs x)) (* 1.875 (/ 1 (pow (fabs x) 7)))))) (* (exp (* 1/2 (pow (fabs x) 2))) (sqrt (/ 1 PI))))

series540.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ 1 (pow (fabs x) 3))
53.0ms
(/ 1 (pow (fabs x) 5))
68.0ms
(* 1.875 (/ 1 (pow (fabs x) 7)))
384.0ms
(* (fma 0.5 (/ 1 (pow (fabs x) 3)) (fma 0.75 (/ 1 (pow (fabs x) 5)) (fma 1.0 (/ 1 (fabs x)) (* 1.875 (/ 1 (pow (fabs x) 7)))))) (* (exp (* 1/2 (pow (fabs x) 2))) (sqrt (/ 1 PI))))

simplify83.0ms

Algorithm
egg-herbie
Counts
223 → 223
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
07101836
138831467
250011461

prune907.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes330.0ms

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04529
14729
24729

end0.0ms

sample7.0s

Algorithm
intervals
Results
5.8s78267×body80valid