Details

Time bar (total: 32.8s)

sample556.0ms

Algorithm
intervals
Results
478.0ms3039×body80valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: done (2.0s)

IterNodesCost
031103
190103
240165
3202351
done500149

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.1b

localize65.0ms

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)
1.1b
(pow (/ 1.0 (fabs x)) 6)

rewrite43.0ms

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:
13.0ms
(pow (/ 1.0 (fabs x)) 3)
14.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)
7.0ms
(pow (/ 1.0 (fabs x)) 6)

series201.0ms

Counts
4 → 10
Calls
4 calls:
63.0ms
(pow (/ 1.0 (fabs x)) 3)
72.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)
66.0ms
(pow (/ 1.0 (fabs x)) 6)

simplify1.7s

Counts
133 → 133
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02081438
15311292
217371182
done50001175

prune983.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize51.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (* (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)))))
0.7b
(pow (/ 1.0 (fabs x)) 3)
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite66.0ms

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:
20.0ms
(/ (* (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)))))
25.0ms
(pow (/ 1.0 (fabs x)) 3)
13.0ms
(pow (/ 1.0 (fabs x)) 4)
3.0ms
(sqrt PI)

series704.0ms

Counts
4 → 10
Calls
4 calls:
577.0ms
(/ (* (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)))))
67.0ms
(pow (/ 1.0 (fabs x)) 3)
60.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify2.0s

Counts
169 → 169
Iterations

Useful iterations: done (2.0s)

IterNodesCost
03135223
18154837
228334276
done50004274

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 0.75 (pow (fabs x) 5))
0.3b
(/ 1.875 (pow (fabs x) 7))
0.3b
(* (* 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
(/ 0.5 (pow (fabs x) 3))

rewrite5.9s

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:
13.0ms
(/ 0.75 (pow (fabs x) 5))
7.0ms
(/ 1.875 (pow (fabs x) 7))
5.8s
(* (* 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)))))
17.0ms
(/ 0.5 (pow (fabs x) 3))

series1.2s

Counts
4 → 12
Calls
4 calls:
88.0ms
(/ 0.75 (pow (fabs x) 5))
80.0ms
(/ 1.875 (pow (fabs x) 7))
997.0ms
(* (* 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)))))
67.0ms
(/ 0.5 (pow (fabs x) 3))

simplify2.9s

Counts
216 → 216
Iterations

Useful iterations: 2 (1.4s)

IterNodesCost
04275100
110834668
245974216
done50004216

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1.875 (pow (fabs x) 7))
0.3b
(/ 0.5 (pow (fabs x) 3))
0.4b
(/ (* 1.0 (* (+ (+ (+ (/ 0.5 (pow (fabs x) 3)) (/ 0.75 (pow (fabs x) 5))) (/ 1.0 (fabs x))) (/ 1.875 (pow (fabs x) 7))) (exp (pow (fabs x) 2)))) (sqrt PI))
1.0b
(sqrt PI)

rewrite6.6s

Algorithm
rewrite-expression-head
Rules
63×times-frac
51×add-sqr-sqrt
50×add-cube-cbrt *-un-lft-identity
25×associate-/r*
24×unpow-prod-down
22×add-exp-log
17×add-cbrt-cube
12×cube-prod
9×div-exp frac-add sqrt-prod
8×sqr-pow
7×associate-*r/ associate-*l/ associate-/l/ associate-/l*
5×pow1 cbrt-undiv
4×expm1-log1p-u cube-mult unpow3 log1p-expm1-u add-log-exp
3×frac-2neg flip3-+ prod-exp clear-num cbrt-unprod flip-+ div-inv
2×pow-to-exp pow-exp
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 167
Calls
4 calls:
8.0ms
(/ 1.875 (pow (fabs x) 7))
8.0ms
(/ 0.5 (pow (fabs x) 3))
6.6s
(/ (* 1.0 (* (+ (+ (+ (/ 0.5 (pow (fabs x) 3)) (/ 0.75 (pow (fabs x) 5))) (/ 1.0 (fabs x))) (/ 1.875 (pow (fabs x) 7))) (exp (pow (fabs x) 2)))) (sqrt PI))
1.0ms
(sqrt PI)

series844.0ms

Counts
4 → 10
Calls
4 calls:
94.0ms
(/ 1.875 (pow (fabs x) 7))
52.0ms
(/ 0.5 (pow (fabs x) 3))
697.0ms
(/ (* 1.0 (* (+ (+ (+ (/ 0.5 (pow (fabs x) 3)) (/ 0.75 (pow (fabs x) 5))) (/ 1.0 (fabs x))) (/ 1.875 (pow (fabs x) 7))) (exp (pow (fabs x) 2)))) (sqrt PI))
0.0ms
(sqrt PI)

simplify1.8s

Counts
177 → 177
Iterations

Useful iterations: done (1.8s)

IterNodesCost
03083446
17163161
227652835
done50002828

prune1.2s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.1b

regimes234.0ms

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02938
13738
done3738

end0.0ms

sample877.0ms

Algorithm
intervals
Results
751.0ms3534×body80valid