Details

Time bar (total: 7.9s)

sample346.0ms

Algorithm
intervals
Results
281.0ms3682×body80valid

simplify68.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (66.0ms)

IterNodesCost
09061
140658
2226736
3500135

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.7b
(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)

simplify75.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
0545752
12496663
25001647

prune657.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.4b

localize41.0ms

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

rewrite49.0ms

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:
37.0ms
(* (/ 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)
4.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)

series245.0ms

Counts
4 → 10
Calls
4 calls:
174.0ms
(* (/ 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 (96.0ms)

IterNodesCost
07221344
136371199
250021192

prune812.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 2.0 (pow (/ 1.0 (fabs x)) 3))
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)

rewrite803.0ms

Algorithm
rewrite-expression-head
Rules
186×times-frac
116×*-un-lft-identity
115×add-sqr-sqrt
114×add-cube-cbrt
65×unpow-prod-down cube-prod
34×add-exp-log
32×associate-/r*
18×add-cbrt-cube
13×prod-exp
11×div-inv
9×div-exp
8×pow1
7×associate-*l/
6×pow-exp
5×cube-mult unpow3 cbrt-unprod sqr-pow
4×expm1-log1p-u pow-to-exp associate-*l* log1p-expm1-u add-log-exp
3×cbrt-undiv frac-times pow-unpow sqrt-prod associate-/l*
2×cube-div flip3-+ frac-add flip-+ rem-cube-cbrt
1×rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 associate-*r/ associate-*r* pow-prod-down clear-num associate-/r/ *-commutative distribute-lft-out
Counts
4 → 245
Calls
4 calls:
11.0ms
(/ 2.0 (pow (/ 1.0 (fabs x)) 3))
775.0ms
(* (+ (/ 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)

series667.0ms

Counts
4 → 10
Calls
4 calls:
107.0ms
(/ 2.0 (pow (/ 1.0 (fabs x)) 3))
527.0ms
(* (+ (/ 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))))
33.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify137.0ms

Algorithm
egg-herbie
Counts
255 → 255
Iterations

Useful iterations: 2 (106.0ms)

IterNodesCost
08983088
147712560
250012559

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (pow (fabs x) 5))
0.3b
(/ 1 (pow (fabs x) 7))
0.3b
(/ 1 (pow (fabs x) 3))
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))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
62×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
36×unpow-prod-down
35×add-exp-log
26×associate-/r*
18×div-exp
15×add-cbrt-cube
12×cube-prod sqr-pow
9×pow1 pow-to-exp rec-exp 1-exp pow-exp associate-/l*
4×expm1-log1p-u cube-mult unpow3 log1p-expm1-u add-log-exp
3×cbrt-undiv pow-flip frac-2neg associate-*l* pow-prod-down prod-exp clear-num cbrt-unprod div-inv inv-pow
2×associate-*r/
1×sqrt-div associate-*r* *-commutative
Counts
4 → 206
Calls
4 calls:
4.0ms
(/ 1 (pow (fabs x) 5))
4.0ms
(/ 1 (pow (fabs x) 7))
5.0ms
(/ 1 (pow (fabs x) 3))
19.0ms
(* (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))))

series548.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ 1 (pow (fabs x) 5))
67.0ms
(/ 1 (pow (fabs x) 7))
35.0ms
(/ 1 (pow (fabs x) 3))
397.0ms
(* (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))))

simplify74.0ms

Algorithm
egg-herbie
Counts
218 → 218
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05671797
131081458
250011455

prune758.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes202.0ms

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04430
14430

end0.0ms

sample889.0ms

Algorithm
intervals
Results
759.0ms9964×body80valid