Details

Time bar (total: 19.6s)

sample833.0ms

Algorithm
intervals
Results
758.0ms4008×body80valid

simplify67.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (64.0ms)

IterNodesCost
09061
140658
2226736
3500135

prune60.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.1b

localize36.0ms

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)

rewrite17.0ms

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:
6.0ms
(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)

series41.0ms

Counts
4 → 10
Calls
4 calls:
12.0ms
(pow (/ 1.0 (fabs x)) 3)
13.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)
16.0ms
(pow (/ 1.0 (fabs x)) 6)

simplify75.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
0545752
12496663
25001647

prune1.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

localize36.0ms

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)

rewrite53.0ms

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:
39.0ms
(* (/ 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)))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
4.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)

series87.0ms

Counts
4 → 10
Calls
4 calls:
63.0ms
(* (/ 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)))
12.0ms
(pow (/ 1.0 (fabs x)) 3)
13.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify109.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
07221344
136371199
250021192

prune2.2s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

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))))
0.3b
(/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite901.0ms

Algorithm
rewrite-expression-head
Rules
921×times-frac
437×*-un-lft-identity
436×add-sqr-sqrt
435×add-cube-cbrt
169×unpow-prod-down cube-prod
101×associate-/r*
40×add-exp-log
31×div-inv
21×add-cbrt-cube
14×div-exp
13×cube-mult unpow3 prod-exp sqr-pow
8×pow1
7×associate-*l/
6×pow-exp
5×cbrt-undiv cube-div associate-/r/ cbrt-unprod
4×expm1-log1p-u pow-to-exp associate-*l* log1p-expm1-u add-log-exp
3×frac-times pow-unpow sqrt-prod associate-/l*
2×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 *-commutative distribute-lft-out
Counts
4 → 523
Calls
4 calls:
826.0ms
(* (+ (/ 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))))
30.0ms
(/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series190.0ms

Counts
4 → 10
Calls
4 calls:
158.0ms
(* (+ (/ 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))))
20.0ms
(/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))
12.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify104.0ms

Algorithm
egg-herbie
Counts
533 → 533
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
018397144
150026633

prune6.0s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

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:
4.0ms
(/ 1 (pow (fabs x) 7))
14.0ms
(* 1.875 (/ 1 (pow (fabs x) 7)))
20.0ms
(* (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))))
5.0ms
(/ 1 (pow (fabs x) 3))

series176.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(/ 1 (pow (fabs x) 7))
23.0ms
(* 1.875 (/ 1 (pow (fabs x) 7)))
113.0ms
(* (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))))
19.0ms
(/ 1 (pow (fabs x) 3))

simplify76.0ms

Algorithm
egg-herbie
Counts
223 → 223
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06161836
132161465
250021459

prune2.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes508.0ms

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04430
14430

end0.0ms

sample3.9s

Algorithm
intervals
Results
3.7s19618×body80valid