Details

Time bar (total: 24.7s)

sample429.0ms

Algorithm
intervals
Results
346.0ms3772×body80valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: done (1.4s)

IterNodesCost
031103
190103
240165
3202351
done500149

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize33.0ms

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)

rewrite24.0ms

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:
6.0ms
(pow (/ 1.0 (fabs x)) 3)
6.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)
6.0ms
(pow (/ 1.0 (fabs x)) 6)

series121.0ms

Counts
4 → 10
Calls
4 calls:
33.0ms
(pow (/ 1.0 (fabs x)) 3)
34.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)
54.0ms
(pow (/ 1.0 (fabs x)) 6)

simplify1.1s

Counts
133 → 133
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02081438
15311292
217371182
done50001175

prune592.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (fma (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3) (* (/ 1.0 (fabs x)) (+ (* (/ 15.0 8.0) (/ 1.0 (pow (fabs x) 6))) (fma (pow (/ 1.0 (fabs x)) 4) (/ 3.0 4.0) 1)))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
0.8b
(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
85×times-frac
55×add-sqr-sqrt
54×add-cube-cbrt *-un-lft-identity
26×unpow-prod-down
22×associate-/r*
21×sqrt-prod
20×add-exp-log
19×add-cbrt-cube
13×cube-prod
8×div-exp
7×pow1 cbrt-undiv
6×pow-unpow div-inv
4×expm1-log1p-u pow-exp log1p-expm1-u add-log-exp
2×pow-to-exp pow-pow prod-exp cbrt-unprod rem-cube-cbrt sqr-pow
1×cube-div cube-mult rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 unpow3 clear-num associate-/r/ associate-/l*
Counts
4 → 159
Calls
4 calls:
21.0ms
(/ (* (fma (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3) (* (/ 1.0 (fabs x)) (+ (* (/ 15.0 8.0) (/ 1.0 (pow (fabs x) 6))) (fma (pow (/ 1.0 (fabs x)) 4) (/ 3.0 4.0) 1)))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
6.0ms
(pow (/ 1.0 (fabs x)) 3)
6.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)

series473.0ms

Counts
4 → 10
Calls
4 calls:
403.0ms
(/ (* (fma (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3) (* (/ 1.0 (fabs x)) (+ (* (/ 15.0 8.0) (/ 1.0 (pow (fabs x) 6))) (fma (pow (/ 1.0 (fabs x)) 4) (/ 3.0 4.0) 1)))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
36.0ms
(pow (/ 1.0 (fabs x)) 3)
34.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify1.3s

Counts
169 → 169
Iterations

Useful iterations: done (1.3s)

IterNodesCost
03135223
18154837
228334276
done50004274

prune760.0ms

Pruning

10 alts after pruning (9 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
(/ 0.5 (pow (fabs x) 3))
0.3b
(* (* 1.0 (sqrt (/ 1 PI))) (* (exp (pow (fabs x) 2)) (+ (+ (+ (/ 0.5 (pow (fabs x) 3)) (/ 0.75 (pow (fabs x) 5))) (/ 1.0 (fabs x))) (/ 1.875 (pow (fabs x) 7)))))
0.3b
(/ 1.875 (pow (fabs x) 7))

rewrite3.6s

Algorithm
rewrite-expression-head
Rules
78×times-frac
61×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
36×unpow-prod-down
29×add-exp-log associate-*r/
26×associate-/r*
22×add-cbrt-cube
18×frac-add
16×pow1
12×cube-prod sqr-pow
9×div-exp associate-/l*
8×sqrt-div pow-prod-down prod-exp cbrt-unprod
7×frac-times
6×flip3-+ flip-+
4×distribute-rgt-in expm1-log1p-u cube-mult distribute-lft-in unpow3 log1p-expm1-u add-log-exp
3×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
1×associate-*r* associate-*l* associate-*l/ *-commutative
Counts
4 → 204
Calls
4 calls:
7.0ms
(/ 0.75 (pow (fabs x) 5))
8.0ms
(/ 0.5 (pow (fabs x) 3))
3.6s
(* (* 1.0 (sqrt (/ 1 PI))) (* (exp (pow (fabs x) 2)) (+ (+ (+ (/ 0.5 (pow (fabs x) 3)) (/ 0.75 (pow (fabs x) 5))) (/ 1.0 (fabs x))) (/ 1.875 (pow (fabs x) 7)))))
7.0ms
(/ 1.875 (pow (fabs x) 7))

series598.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ 0.75 (pow (fabs x) 5))
39.0ms
(/ 0.5 (pow (fabs x) 3))
440.0ms
(* (* 1.0 (sqrt (/ 1 PI))) (* (exp (pow (fabs x) 2)) (+ (+ (+ (/ 0.5 (pow (fabs x) 3)) (/ 0.75 (pow (fabs x) 5))) (/ 1.0 (fabs x))) (/ 1.875 (pow (fabs x) 7)))))
64.0ms
(/ 1.875 (pow (fabs x) 7))

simplify1.8s

Counts
216 → 216
Iterations

Useful iterations: 2 (753.0ms)

IterNodesCost
04275100
110834668
246064216
done50004216

prune997.0ms

Pruning

13 alts after pruning (12 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
(/ 0.5 (pow (fabs x) 3))
0.3b
(/ 1.875 (pow (fabs x) 7))
0.3b
(* (* (* 1.0 (sqrt (/ 1 PI))) (exp (pow (fabs x) 2))) (+ (+ (+ (/ 0.5 (pow (fabs x) 3)) (/ 0.75 (pow (fabs x) 5))) (/ 1.0 (fabs x))) (/ 1.875 (pow (fabs x) 7))))

rewrite3.6s

Algorithm
rewrite-expression-head
Rules
82×times-frac
79×*-un-lft-identity
62×add-sqr-sqrt add-cube-cbrt
36×unpow-prod-down
26×add-exp-log associate-/r*
19×add-cbrt-cube
18×frac-add
15×associate-*r/
13×pow1
12×cube-prod sqr-pow
9×div-exp associate-*l/ distribute-lft-out associate-/l*
8×sqrt-div
7×frac-times associate-*r*
6×flip3-+ pow-prod-down prod-exp cbrt-unprod flip-+
4×expm1-log1p-u cube-mult unpow3 log1p-expm1-u add-log-exp
3×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
1×distribute-rgt-in distribute-lft-in associate-*l* *-commutative
Counts
4 → 205
Calls
4 calls:
7.0ms
(/ 0.75 (pow (fabs x) 5))
8.0ms
(/ 0.5 (pow (fabs x) 3))
7.0ms
(/ 1.875 (pow (fabs x) 7))
3.6s
(* (* (* 1.0 (sqrt (/ 1 PI))) (exp (pow (fabs x) 2))) (+ (+ (+ (/ 0.5 (pow (fabs x) 3)) (/ 0.75 (pow (fabs x) 5))) (/ 1.0 (fabs x))) (/ 1.875 (pow (fabs x) 7))))

series586.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ 0.75 (pow (fabs x) 5))
37.0ms
(/ 0.5 (pow (fabs x) 3))
68.0ms
(/ 1.875 (pow (fabs x) 7))
427.0ms
(* (* (* 1.0 (sqrt (/ 1 PI))) (exp (pow (fabs x) 2))) (+ (+ (+ (/ 0.5 (pow (fabs x) 3)) (/ 0.75 (pow (fabs x) 5))) (/ 1.0 (fabs x))) (/ 1.875 (pow (fabs x) 7))))

simplify1.9s

Counts
217 → 217
Iterations

Useful iterations: 2 (740.0ms)

IterNodesCost
04194965
110784530
248154147
done50004147

prune1.1s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.1b

regimes192.0ms

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02938
13738
done3738

end0.0ms

sample4.0s

Algorithm
intervals
Results
3.4s38769×body80valid