Details

Time bar (total: 4.0m)

sample291.0ms

Algorithm
intervals
Results
237.0ms3126×body80valid

simplify75.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (73.0ms)

IterNodesCost
09061
140658
2226436
3500235

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: 1.3b

Counts
2 → 2

localize36.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow (/ 1.0 (fabs x)) 3)
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)
1.3b
(pow (/ 1.0 (fabs x)) 6)

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
39×unpow-prod-down
30×add-sqr-sqrt
29×add-cube-cbrt *-un-lft-identity
27×times-frac
13×add-exp-log
9×pow-unpow
8×pow1
7×add-cbrt-cube
6×pow-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp pow-pow div-exp sqrt-prod div-inv sqr-pow
2×rem-cube-cbrt
1×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 unpow3
Counts
4 → 108
Calls
4 calls:
4.0ms
(pow (/ 1.0 (fabs x)) 3)
4.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)
4.0ms
(pow (/ 1.0 (fabs x)) 6)

series125.0ms

Counts
4 → 10
Calls
4 calls:
35.0ms
(pow (/ 1.0 (fabs x)) 3)
39.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)
51.0ms
(pow (/ 1.0 (fabs x)) 6)

simplify63.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0496650
11909602
25002595

prune602.0ms

Filtered
118 candidates to 83 candidates (70.3%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New10711118
Fresh011
Picked101
Done000
Total10812120

Merged error: 0.3b

Counts
120 → 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)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
37×*-un-lft-identity
35×add-cube-cbrt
28×times-frac
26×unpow-prod-down
18×frac-times
15×add-exp-log
13×associate-*l*
12×add-cbrt-cube
10×flip3-+ flip-+
9×pow1 associate-*l/ associate-/r* associate-/l*
6×pow-unpow
4×expm1-log1p-u associate-*r* pow-exp log1p-expm1-u add-log-exp
3×distribute-rgt-in frac-2neg distribute-lft-in div-exp clear-num sqrt-prod div-inv
2×cbrt-undiv +-commutative pow-to-exp associate-+r+ pow-pow associate-*r/ prod-exp cbrt-unprod fma-udef rem-cube-cbrt unswap-sqr sqr-pow
1×rem-sqrt-square sqrt-pow1 pow1/2 unpow3 pow-prod-down *-commutative distribute-lft-out
Counts
4 → 147
Calls
4 calls:
53.0ms
(* (/ 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)))
7.0ms
(pow (/ 1.0 (fabs x)) 3)
4.0ms
(pow (/ 1.0 (fabs x)) 4)
2.0ms
(sqrt PI)

series260.0ms

Counts
4 → 10
Calls
4 calls:
185.0ms
(* (/ 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)))
34.0ms
(pow (/ 1.0 (fabs x)) 3)
40.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify53.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
08942120
150022010

prune871.0ms

Filtered
157 candidates to 114 candidates (72.6%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New14512157
Fresh7411
Picked101
Done000
Total15316169

Merged error: 0.1b

Counts
169 → 16

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (pow (fabs x) 6))
0.3b
(* (+ (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3))) (/ (* 1.0 (+ (fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1)) (fabs x))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite4.3s

Algorithm
rewrite-expression-head
Rules
26420×associate-/r*
22184×times-frac
21148×add-sqr-sqrt
21110×*-un-lft-identity
19430×add-cube-cbrt
17510×associate-*l/
17472×frac-add
16152×frac-times
15680×associate-/l*
10681×unpow-prod-down
4059×sqrt-prod
3378×associate-*r*
2532×associate-*l*
2454×clear-num
2453×frac-2neg
1676×associate-*r/
1664×associate-/l/
1095×div-inv
860×unswap-sqr
845×flip3-+ flip-+
839×distribute-lft-out
835×*-commutative
831×sqr-pow
821×unpow3
42×add-exp-log
18×add-cbrt-cube
17×prod-exp
13×pow1
11×div-exp
9×pow-exp
6×pow-to-exp pow-unpow pow-flip
5×cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv rec-exp 1-exp pow-prod-down associate-/r/
2×pow-pow rem-cube-cbrt
1×rem-sqrt-square distribute-rgt-out sqrt-pow1 pow1/2 inv-pow
Counts
4 → 17706
Calls
4 calls:
6.0ms
(/ 1 (pow (fabs x) 6))
788.0ms
(* (+ (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3))) (/ (* 1.0 (+ (fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1)) (fabs x))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
2.0ms
(sqrt PI)

series642.0ms

Counts
4 → 10
Calls
4 calls:
51.0ms
(/ 1 (pow (fabs x) 6))
554.0ms
(* (+ (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3))) (/ (* 1.0 (+ (fma 1.875 (/ 1 (pow (fabs x) 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1)) (fabs x))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
36.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify10.1s

Algorithm
egg-herbie
Counts
17716 → 17716
Iterations

Useful iterations: 0 (444.0ms)

IterNodesCost
0241881074770

prune1.8m

Filtered
17716 candidates to 11281 candidates (63.7%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New17707917716
Fresh12315
Picked101
Done000
Total177201217732

Merged error: 0.0b

Counts
17732 → 12

localize40.0ms

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

rewrite4.5s

Algorithm
rewrite-expression-head
Rules
26431×associate-/r*
22253×times-frac
21182×add-sqr-sqrt
21144×*-un-lft-identity
19464×add-cube-cbrt
17510×associate-*l/
17472×frac-add
16152×frac-times
15680×associate-/l*
10721×unpow-prod-down
4059×sqrt-prod
3378×associate-*r*
2532×associate-*l*
2454×clear-num
2453×frac-2neg
1676×associate-*r/
1664×associate-/l/
1099×div-inv
860×unswap-sqr
845×flip3-+ flip-+
839×distribute-lft-out
835×*-commutative
831×sqr-pow
825×unpow3
41×add-exp-log
18×add-cbrt-cube
17×prod-exp
11×pow1
10×div-exp
8×pow-exp
5×cbrt-unprod
4×expm1-log1p-u pow-to-exp log1p-expm1-u add-log-exp
3×cbrt-undiv pow-unpow pow-prod-down associate-/r/
2×rem-cube-cbrt
1×rem-sqrt-square distribute-rgt-out pow-pow sqrt-pow1 pow1/2
Counts
4 → 17738
Calls
4 calls:
8.0ms
(/ 2.0 (pow (/ 1.0 (fabs x)) 3))
797.0ms
(* (+ (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3))) (/ (* 1.0 (+ (fma 1.875 (pow (fabs x) (- 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1)) (fabs x))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
2.0ms
(sqrt PI)

series702.0ms

Counts
4 → 10
Calls
4 calls:
109.0ms
(/ 2.0 (pow (/ 1.0 (fabs x)) 3))
548.0ms
(* (+ (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3))) (/ (* 1.0 (+ (fma 1.875 (pow (fabs x) (- 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1)) (fabs x))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
44.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify10.2s

Algorithm
egg-herbie
Counts
17748 → 17748
Iterations

Useful iterations: 0 (457.0ms)

IterNodesCost
0241411075284

prune1.6m

Filtered
17748 candidates to 11315 candidates (63.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New17742617748
Fresh7411
Picked101
Done000
Total177501017760

Merged error: 0.0b

Counts
17760 → 10

regimes189.0ms

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04945
14945

end0.0ms

sample3.9s

Algorithm
intervals
Results
3.4s46998×body80valid