Details

Time bar (total: 6.8s)

sample392.0ms

Algorithm
intervals
Results
330.0ms3247×body80valid

simplify67.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (65.0ms)

IterNodesCost
09061
140658
2226736
3500135

prune17.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.4b

Counts
2 → 2

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)

rewrite20.0ms

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:
5.0ms
(pow (/ 1.0 (fabs x)) 3)
5.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)
5.0ms
(pow (/ 1.0 (fabs x)) 6)

series123.0ms

Counts
4 → 10
Calls
4 calls:
37.0ms
(pow (/ 1.0 (fabs x)) 3)
34.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)
52.0ms
(pow (/ 1.0 (fabs x)) 6)

simplify76.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
0545752
12496663
25001647

prune623.0ms

Filtered
133 candidates to 82 candidates (61.7%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New12112133
Fresh011
Picked101
Done000
Total12213135

Merged error: 0.6b

Counts
135 → 13

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (+ (/ 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))))
0.7b
(pow (/ 1.0 (fabs x)) 3)
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite101.0ms

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:
85.0ms
(* (+ (/ 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))))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
5.0ms
(pow (/ 1.0 (fabs x)) 4)
2.0ms
(sqrt PI)

series620.0ms

Counts
4 → 10
Calls
4 calls:
547.0ms
(* (+ (/ 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))))
38.0ms
(pow (/ 1.0 (fabs x)) 3)
35.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify47.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09942448
150012114

prune769.0ms

Filtered
143 candidates to 92 candidates (64.3%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New13112143
Fresh8412
Picked101
Done000
Total14016156

Merged error: 0.0b

Counts
156 → 16

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
44×add-sqr-sqrt
43×add-cube-cbrt *-un-lft-identity
39×unpow-prod-down
26×cube-prod
13×add-exp-log
10×add-cbrt-cube
9×pow-unpow
8×pow1
6×pow-exp
5×div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp rem-cube-cbrt
3×pow-to-exp pow-pow div-exp sqrt-prod sqr-pow
2×cbrt-undiv cube-div cube-mult unpow3
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 141
Calls
4 calls:
5.0ms
(pow (/ 1.0 (fabs x)) 3)
5.0ms
(pow (/ 1.0 (fabs x)) 3)
5.0ms
(pow (/ 1.0 (fabs x)) 4)
2.0ms
(sqrt PI)

series106.0ms

Counts
4 → 10
Calls
4 calls:
33.0ms
(pow (/ 1.0 (fabs x)) 3)
33.0ms
(pow (/ 1.0 (fabs x)) 3)
39.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify65.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0460889
11940764
25001733

prune758.0ms

Filtered
151 candidates to 85 candidates (56.3%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New1456151
Fresh6915
Picked101
Done000
Total15215167

Merged error: 0.0b

Counts
167 → 15

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 1.875 (/ 1 (pow (fabs x) 7)))
0.3b
(/ 1 (pow (fabs x) 3))
0.3b
(/ 1 (pow (fabs x) 5))
0.5b
(* (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))))

rewrite43.0ms

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:
11.0ms
(* 1.875 (/ 1 (pow (fabs x) 7)))
6.0ms
(/ 1 (pow (fabs x) 3))
9.0ms
(/ 1 (pow (fabs x) 5))
10.0ms
(* (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))))

series559.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* 1.875 (/ 1 (pow (fabs x) 7)))
35.0ms
(/ 1 (pow (fabs x) 3))
55.0ms
(/ 1 (pow (fabs x) 5))
399.0ms
(* (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))))

simplify85.0ms

Algorithm
egg-herbie
Counts
223 → 223
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
07101857
139031488
250011482

prune822.0ms

Filtered
223 candidates to 105 candidates (47.1%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New2194223
Fresh5914
Picked101
Done000
Total22513238

Merged error: 0.0b

Counts
238 → 13

regimes419.0ms

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04229
14229

end0.0ms

sample938.0ms

Algorithm
intervals
Results
819.0ms8115×body80valid