Details

Time bar (total: 8.4s)

sample327.0ms

Algorithm
intervals
Results
268.0ms3460×body80valid

simplify67.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (65.0ms)

IterNodesCost
09061
140658
2226736
3500135

prune16.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (/ 1.0 (fabs x)) 3)
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)
1.2b
(pow (/ 1.0 (fabs x)) 6)

rewrite15.0ms

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:
4.0ms
(pow (/ 1.0 (fabs x)) 3)
3.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)
4.0ms
(pow (/ 1.0 (fabs x)) 6)

series117.0ms

Counts
4 → 10
Calls
4 calls:
32.0ms
(pow (/ 1.0 (fabs x)) 3)
38.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)
47.0ms
(pow (/ 1.0 (fabs x)) 6)

simplify76.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
0545752
12496663
25001647

prune631.0ms

Filtered
133 candidates to 82 candidates (61.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ 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)))
0.7b
(pow (/ 1.0 (fabs x)) 3)
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
38×*-un-lft-identity
37×times-frac
36×add-cube-cbrt
26×unpow-prod-down
15×add-exp-log
13×cube-prod associate-*l*
12×add-cbrt-cube
9×pow1
6×pow-unpow
4×expm1-log1p-u associate-*r* pow-exp log1p-expm1-u div-inv add-log-exp
3×div-exp sqrt-prod
2×cbrt-undiv frac-times pow-to-exp pow-pow flip3-+ associate-*r/ prod-exp cbrt-unprod flip-+ rem-cube-cbrt unswap-sqr sqr-pow
1×cube-div distribute-rgt-in cube-mult rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 unpow3 pow-prod-down associate-*l/ *-commutative distribute-lft-out
Counts
4 → 134
Calls
4 calls:
38.0ms
(* (/ 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)))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
3.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)

series243.0ms

Counts
4 → 10
Calls
4 calls:
173.0ms
(* (/ 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)))
32.0ms
(pow (/ 1.0 (fabs x)) 3)
38.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify112.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
07221344
136371199
250021192

prune776.0ms

Filtered
144 candidates to 93 candidates (64.6%)
Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (+ (fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1) 1.0) (fabs x))
0.3b
(* (+ (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3))) (/ (* (+ (fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1) 1.0) (fabs x))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite816.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
25×*-un-lft-identity
24×add-sqr-sqrt
23×add-cube-cbrt
21×times-frac add-cbrt-cube
14×prod-exp
13×unpow-prod-down cube-prod
9×associate-*l/
8×pow1
6×div-exp cbrt-unprod
4×cbrt-undiv expm1-log1p-u associate-*l* pow-exp log1p-expm1-u add-log-exp
3×frac-times pow-to-exp pow-unpow flip3-+ associate-/r* sqrt-prod flip-+ div-inv
2×frac-add associate-/l/ rem-cube-cbrt
1×cube-div cube-mult rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 unpow3 associate-*r/ associate-*r* pow-prod-down clear-num *-commutative distribute-lft-out associate-/l* sqr-pow
Counts
4 → 121
Calls
4 calls:
6.0ms
(/ (* (+ (fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1) 1.0) (fabs x))
803.0ms
(* (+ (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3))) (/ (* (+ (fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1) 1.0) (fabs x))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series726.0ms

Counts
4 → 10
Calls
4 calls:
155.0ms
(/ (* (+ (fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1) 1.0) (fabs x))
534.0ms
(* (+ (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3))) (/ (* (+ (fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1) 1.0) (fabs x))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
36.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify122.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (99.0ms)

IterNodesCost
08192062
142441703
250011700

prune698.0ms

Filtered
131 candidates to 83 candidates (63.4%)
Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (fma (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3) (/ (* 1.0 (fma 0.75 (/ 1 (pow (fabs x) 4)) (fma 1.875 (/ 1 (pow (fabs x) 6)) 1))) (fabs x))) (* (pow (exp (fabs x)) (* 2 (/ (fabs x) 2))) (/ 1.0 (sqrt PI))))
0.3b
(/ (* 1.0 (fma 0.75 (/ 1 (pow (fabs x) 4)) (fma 1.875 (/ 1 (pow (fabs x) 6)) 1))) (fabs x))
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
24×add-sqr-sqrt
23×add-cube-cbrt *-un-lft-identity
21×times-frac add-cbrt-cube
14×prod-exp
13×unpow-prod-down cube-prod
8×pow1
6×div-exp cbrt-unprod
4×cbrt-undiv expm1-log1p-u pow-exp log1p-expm1-u add-log-exp
3×pow-to-exp pow-unpow associate-*l* associate-/r* sqrt-prod div-inv
2×associate-*r/ rem-cube-cbrt
1×cube-div cube-mult rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 unpow3 associate-*r* pow-prod-down clear-num *-commutative associate-/l* sqr-pow
Counts
4 → 112
Calls
4 calls:
17.0ms
(* (fma (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3) (/ (* 1.0 (fma 0.75 (/ 1 (pow (fabs x) 4)) (fma 1.875 (/ 1 (pow (fabs x) 6)) 1))) (fabs x))) (* (pow (exp (fabs x)) (* 2 (/ (fabs x) 2))) (/ 1.0 (sqrt PI))))
4.0ms
(/ (* 1.0 (fma 0.75 (/ 1 (pow (fabs x) 4)) (fma 1.875 (/ 1 (pow (fabs x) 6)) 1))) (fabs x))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series716.0ms

Counts
4 → 10
Calls
4 calls:
503.0ms
(* (fma (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3) (/ (* 1.0 (fma 0.75 (/ 1 (pow (fabs x) 4)) (fma 1.875 (/ 1 (pow (fabs x) 6)) 1))) (fabs x))) (* (pow (exp (fabs x)) (* 2 (/ (fabs x) 2))) (/ 1.0 (sqrt PI))))
177.0ms
(/ (* 1.0 (fma 0.75 (/ 1 (pow (fabs x) 4)) (fma 1.875 (/ 1 (pow (fabs x) 6)) 1))) (fabs x))
36.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify95.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
06581699
132361370
250011364

prune503.0ms

Filtered
122 candidates to 70 candidates (57.4%)
Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes239.0ms

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04027
14027

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.6s21445×body80valid