Details

Time bar (total: 12.1s)

sample312.0ms

Algorithm
intervals
Results
257.0ms3272×body80valid

simplify929.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (189.0ms)

IterNodesCost
031103
190103
238165
3195451
done500151

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize33.0ms

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)

rewrite15.0ms

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)

series116.0ms

Counts
4 → 10
Calls
4 calls:
32.0ms
(pow (/ 1.0 (fabs x)) 3)
38.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)
46.0ms
(pow (/ 1.0 (fabs x)) 6)

simplify776.0ms

Counts
133 → 133
Iterations

Useful iterations: done (772.0ms)

IterNodesCost
02071440
15251295
217021185
done50011177

prune617.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b
(fma (/ 1.0 (fabs x)) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0)) (fma (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3) (/ 1.0 (fabs x))))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
28×add-cube-cbrt *-un-lft-identity
27×times-frac
26×unpow-prod-down
13×cube-prod
10×add-exp-log
7×pow1 add-cbrt-cube
6×pow-unpow
4×expm1-log1p-u pow-exp log1p-expm1-u add-log-exp
3×sqrt-prod div-inv
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 fma-udef
Counts
4 → 103
Calls
4 calls:
0.0ms
(fma (/ 1.0 (fabs x)) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0)) (fma (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3) (/ 1.0 (fabs x))))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
3.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)

series269.0ms

Counts
4 → 10
Calls
4 calls:
199.0ms
(fma (/ 1.0 (fabs x)) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0)) (fma (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3) (/ 1.0 (fabs x))))
37.0ms
(pow (/ 1.0 (fabs x)) 3)
34.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify724.0ms

Counts
113 → 113
Iterations

Useful iterations: 2 (250.0ms)

IterNodesCost
01871631
14741511
214071334
done50001334

prune535.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 0.75 (pow (fabs x) 5))
0.3b
(/ 1.875 (pow (fabs x) 7))
0.4b
(/ (+ (+ (/ 1.0 (fabs x)) (/ 0.75 (pow (fabs x) 5))) (+ (/ 1.875 (pow (fabs x) 7)) (/ 0.5 (pow (fabs x) 3)))) (/ (sqrt PI) (* 1.0 (exp (* (fabs x) (fabs x))))))
1.0b
(sqrt PI)

rewrite806.0ms

Algorithm
rewrite-expression-head
Rules
295×*-un-lft-identity
220×times-frac
121×distribute-lft-out
76×add-sqr-sqrt
75×add-cube-cbrt
30×sqrt-prod
24×unpow-prod-down associate-/r*
22×add-exp-log
17×add-cbrt-cube
15×frac-add
14×associate-/l*
12×div-inv
11×div-exp associate-/l/
8×sqr-pow
7×cbrt-undiv flip3-+ flip-+
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×pow-to-exp pow-exp
1×rem-sqrt-square sqrt-pow1 pow1/2 prod-exp associate-/r/ cbrt-unprod
Counts
4 → 237
Calls
4 calls:
3.0ms
(/ 0.75 (pow (fabs x) 5))
3.0ms
(/ 1.875 (pow (fabs x) 7))
787.0ms
(/ (+ (+ (/ 1.0 (fabs x)) (/ 0.75 (pow (fabs x) 5))) (+ (/ 1.875 (pow (fabs x) 7)) (/ 0.5 (pow (fabs x) 3)))) (/ (sqrt PI) (* 1.0 (exp (* (fabs x) (fabs x))))))
1.0ms
(sqrt PI)

series536.0ms

Counts
4 → 10
Calls
4 calls:
52.0ms
(/ 0.75 (pow (fabs x) 5))
62.0ms
(/ 1.875 (pow (fabs x) 7))
421.0ms
(/ (+ (+ (/ 1.0 (fabs x)) (/ 0.75 (pow (fabs x) 5))) (+ (/ 1.875 (pow (fabs x) 7)) (/ 0.5 (pow (fabs x) 3)))) (/ (sqrt PI) (* 1.0 (exp (* (fabs x) (fabs x))))))
0.0ms
(sqrt PI)

simplify1.1s

Counts
247 → 247
Iterations

Useful iterations: done (1.1s)

IterNodesCost
03748139
19357650
232797244
done50007241

prune936.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1.875 (pow (fabs x) 7))
0.4b
(/ (+ (+ (/ 1.0 (fabs x)) (/ 0.75 (pow (fabs x) 5))) (+ (/ 1.875 (pow (fabs x) 7)) (/ 0.5 (pow (fabs x) 3)))) (/ (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (* 1.0 (exp (* (fabs x) (fabs x))))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite800.0ms

Algorithm
rewrite-expression-head
Rules
157×*-un-lft-identity
94×times-frac
66×distribute-lft-out
39×add-sqr-sqrt
37×add-cube-cbrt
25×add-exp-log
24×add-cbrt-cube
15×frac-add
12×unpow-prod-down div-exp associate-/r*
11×div-inv associate-/l/ associate-/l*
10×cbrt-undiv
7×flip3-+ flip-+
6×pow1 sqrt-prod
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp sqr-pow
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×pow-to-exp pow-exp associate-/r/
Counts
4 → 164
Calls
4 calls:
3.0ms
(/ 1.875 (pow (fabs x) 7))
788.0ms
(/ (+ (+ (/ 1.0 (fabs x)) (/ 0.75 (pow (fabs x) 5))) (+ (/ 1.875 (pow (fabs x) 7)) (/ 0.5 (pow (fabs x) 3)))) (/ (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (* 1.0 (exp (* (fabs x) (fabs x))))))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series491.0ms

Counts
4 → 8
Calls
4 calls:
63.0ms
(/ 1.875 (pow (fabs x) 7))
427.0ms
(/ (+ (+ (/ 1.0 (fabs x)) (/ 0.75 (pow (fabs x) 5))) (+ (/ 1.875 (pow (fabs x) 7)) (/ 0.5 (pow (fabs x) 3)))) (/ (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (* 1.0 (exp (* (fabs x) (fabs x))))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify1.3s

Counts
172 → 172
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02816160
17795257
233344771
done50014768

prune710.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 0.0b

regimes282.0ms

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02842
13242
done3242

end0.0ms

sample691.0ms

Algorithm
intervals
Results
590.0ms7530×body80valid