Details

Time bar (total: 10.9s)

sample333.0ms

Algorithm
intervals
Results
275.0ms3563×body80valid

simplify69.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
09061
140658
2226736
3500135

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize40.0ms

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)

rewrite16.0ms

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)

series118.0ms

Counts
4 → 10
Calls
4 calls:
32.0ms
(pow (/ 1.0 (fabs x)) 3)
39.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)
47.0ms
(pow (/ 1.0 (fabs x)) 6)

simplify79.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
0545752
12496663
25001647

prune650.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize40.0ms

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)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(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:
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)
3.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)

series247.0ms

Counts
4 → 10
Calls
4 calls:
175.0ms
(* (/ 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)
39.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify115.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
07221344
136371199
250021192

prune795.0ms

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
(/ (* (+ (fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1) 1.0) (fabs x))
0.3b
(* 0.75 (/ 1 (pow (fabs x) 4)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
53×add-sqr-sqrt
48×times-frac
40×*-un-lft-identity
37×add-cube-cbrt
32×add-exp-log
25×associate-*r*
24×unpow-prod-down
17×add-cbrt-cube
13×cube-prod
11×prod-exp
9×div-exp
8×pow1
7×unswap-sqr
6×sqr-pow
5×pow-exp
4×cbrt-undiv expm1-log1p-u pow-to-exp log1p-expm1-u div-inv add-log-exp
3×rec-exp pow-unpow 1-exp associate-*l* associate-/r* sqrt-prod cbrt-unprod
2×associate-*l/ associate-/l/ rem-cube-cbrt
1×cube-div cube-mult rem-sqrt-square pow-pow frac-2neg sqrt-pow1 flip3-+ pow1/2 unpow3 associate-*r/ pow-prod-down clear-num un-div-inv *-commutative flip-+ associate-/l*
Counts
4 → 148
Calls
4 calls:
5.0ms
(/ (* (+ (fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1) 1.0) (fabs x))
17.0ms
(* 0.75 (/ 1 (pow (fabs x) 4)))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series228.0ms

Counts
4 → 10
Calls
4 calls:
158.0ms
(/ (* (+ (fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1) 1.0) (fabs x))
37.0ms
(* 0.75 (/ 1 (pow (fabs x) 4)))
33.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify95.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
07471183
13866965
25001945

prune822.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (pow (exp (fabs x)) (/ (fabs x) 2)) (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)))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
0.3b
(/ (* 1.0 (fma 0.75 (/ 1 (pow (fabs x) 4)) (fma 1.875 (/ 1 (pow (fabs x) 6)) 1))) (fabs x))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
95×add-exp-log
74×prod-exp
33×add-cbrt-cube
23×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
21×times-frac
17×pow-exp
16×pow-to-exp
15×div-exp
14×cbrt-unprod
13×unpow-prod-down cube-prod
8×pow1
5×cbrt-undiv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-/r* sqrt-prod div-inv
2×rem-cube-cbrt
1×cube-div cube-mult rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 unpow3 associate-*r/ associate-*r* associate-*l* pow-prod-down associate-*l/ clear-num *-commutative associate-/l* sqr-pow
Counts
4 → 134
Calls
4 calls:
26.0ms
(* (* (pow (exp (fabs x)) (/ (fabs x) 2)) (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)))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
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)

series752.0ms

Counts
4 → 10
Calls
4 calls:
544.0ms
(* (* (pow (exp (fabs x)) (/ (fabs x) 2)) (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)))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
176.0ms
(/ (* 1.0 (fma 0.75 (/ 1 (pow (fabs x) 4)) (fma 1.875 (/ 1 (pow (fabs x) 6)) 1))) (fabs x))
32.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify112.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
08052658
137272117
250022049

prune508.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes215.0ms

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03826
13826

end0.0ms

sample5.5s

Algorithm
intervals
Results
4.8s61196×body80valid