Details

Time bar (total: 6.7s)

sample397.0ms

Algorithm
intervals
Results
336.0ms3260×body80valid

simplify68.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (66.0ms)

IterNodesCost
09061
140658
2226736
3500135

prune19.0ms

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: 1.2b

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)
2.0ms
(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)

simplify78.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
0545752
12496663
25001653

prune627.0ms

Filtered
133 candidates to 83 candidates (62.4%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New12211133
Fresh011
Picked101
Done000
Total12312135

Merged error: 0.3b

Counts
135 → 12

localize36.0ms

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)

rewrite34.0ms

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:
15.0ms
(* (/ 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)))
9.0ms
(pow (/ 1.0 (fabs x)) 3)
5.0ms
(pow (/ 1.0 (fabs x)) 4)
2.0ms
(sqrt PI)

series434.0ms

Counts
4 → 10
Calls
4 calls:
363.0ms
(* (/ 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)))
36.0ms
(pow (/ 1.0 (fabs x)) 3)
34.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify119.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (100.0ms)

IterNodesCost
07221344
136371199
250021192

prune737.0ms

Filtered
144 candidates to 93 candidates (64.6%)
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New13410144
Fresh6511
Picked011
Done000
Total14016156

Merged error: 0.1b

Counts
156 → 16

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 0.75 (/ 1 (pow (fabs x) 4)))
0.3b
(/ 1 (pow (fabs x) 4))
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
67×add-sqr-sqrt
66×times-frac
54×*-un-lft-identity
51×add-cube-cbrt
36×add-exp-log unpow-prod-down
25×associate-*r*
14×add-cbrt-cube
13×cube-prod div-exp
10×prod-exp sqr-pow
8×pow1 pow-exp
7×pow-to-exp associate-/r* unswap-sqr
6×rec-exp 1-exp
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×cbrt-undiv pow-unpow associate-*l* sqrt-prod associate-/l*
2×cbrt-unprod rem-cube-cbrt
1×cube-div cube-mult rem-sqrt-square pow-flip pow-pow frac-2neg sqrt-pow1 pow1/2 unpow3 associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
4 → 178
Calls
4 calls:
11.0ms
(* 0.75 (/ 1 (pow (fabs x) 4)))
5.0ms
(/ 1 (pow (fabs x) 4))
5.0ms
(pow (/ 1.0 (fabs x)) 3)
2.0ms
(sqrt PI)

series111.0ms

Counts
4 → 10
Calls
4 calls:
39.0ms
(* 0.75 (/ 1 (pow (fabs x) 4)))
35.0ms
(/ 1 (pow (fabs x) 4))
36.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify77.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
06161089
12913881
25001857

prune717.0ms

Filtered
188 candidates to 97 candidates (51.6%)
Pruning

17 alts after pruning (15 fresh and 2 done)

PrunedKeptTotal
New1871188
Fresh01414
Picked011
Done011
Total18717204

Merged error: 0.1b

Counts
204 → 17

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt (/ 1.0 (fabs x))) (* (sqrt (/ 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)

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
36×add-cube-cbrt *-un-lft-identity times-frac
26×unpow-prod-down
16×associate-*l* sqrt-prod
15×add-exp-log
13×cube-prod
12×pow1 sqrt-div add-cbrt-cube
9×frac-times associate-*r/
6×pow-unpow
4×distribute-rgt-in expm1-log1p-u distribute-lft-in flip3-+ pow-exp flip-+ log1p-expm1-u div-inv add-log-exp
3×pow-prod-down associate-*l/ prod-exp cbrt-unprod
2×pow-to-exp pow-pow div-exp rem-cube-cbrt sqr-pow
1×cbrt-undiv cube-div cube-mult rem-sqrt-square sqrt-pow1 pow1/2 unpow3 associate-*r* *-commutative
Counts
4 → 141
Calls
4 calls:
20.0ms
(* (sqrt (/ 1.0 (fabs x))) (* (sqrt (/ 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)
5.0ms
(pow (/ 1.0 (fabs x)) 4)
2.0ms
(sqrt PI)

series291.0ms

Counts
4 → 10
Calls
4 calls:
226.0ms
(* (sqrt (/ 1.0 (fabs x))) (* (sqrt (/ 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)
33.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify106.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
07291664
136531470
250011456

prune684.0ms

Filtered
151 candidates to 94 candidates (62.3%)
Pruning

17 alts after pruning (14 fresh and 3 done)

PrunedKeptTotal
New1465151
Fresh5914
Picked011
Done022
Total15117168

Merged error: 0.1b

Counts
168 → 17

regimes407.0ms

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04333
14333

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.3s12545×body80valid