Details

Time bar (total: 25.5s)

sample337.0ms

Algorithm
intervals
Results
266.0ms3409×body80valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: done (1.5s)

IterNodesCost
031103
190103
240165
3202351
done500149

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize34.0ms

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)

rewrite23.0ms

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)

series115.0ms

Counts
4 → 10
Calls
4 calls:
32.0ms
(pow (/ 1.0 (fabs x)) 3)
37.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)
46.0ms
(pow (/ 1.0 (fabs x)) 6)

simplify1.0s

Counts
133 → 133
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02081438
15311292
217371182
done50001175

prune582.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.4b

localize29.0ms

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)

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)

series466.0ms

Counts
4 → 10
Calls
4 calls:
400.0ms
(/ (* (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)))))
32.0ms
(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

prune735.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.875 (pow (fabs x) 7))
0.2b
(/ 0.5 (pow (fabs x) 3))
0.3b
(/ 0.75 (pow (fabs x) 5))
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)))))

rewrite3.8s

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:
8.0ms
(/ 1.875 (pow (fabs x) 7))
8.0ms
(/ 0.5 (pow (fabs x) 3))
7.0ms
(/ 0.75 (pow (fabs x) 5))
3.7s
(* (* 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)))))

series573.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(/ 1.875 (pow (fabs x) 7))
37.0ms
(/ 0.5 (pow (fabs x) 3))
54.0ms
(/ 0.75 (pow (fabs x) 5))
416.0ms
(* (* 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)))))

simplify1.8s

Counts
216 → 216
Iterations

Useful iterations: 2 (731.0ms)

IterNodesCost
04275100
110844668
246264216
done50004216

prune912.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite3.8s

Algorithm
rewrite-expression-head
Rules
117×times-frac
115×add-sqr-sqrt
79×add-cube-cbrt *-un-lft-identity
61×sqrt-prod
55×unpow-prod-down
47×associate-*r*
40×associate-*r/
34×add-exp-log
25×add-cbrt-cube
21×sqr-pow
18×pow1 frac-add
14×associate-/r* unswap-sqr
12×prod-exp
10×cbrt-unprod
9×div-exp pow-prod-down associate-/l*
8×sqrt-div
7×frac-times associate-*l*
6×flip3-+ flip-+
4×distribute-rgt-in expm1-log1p-u distribute-lft-in log1p-expm1-u add-log-exp
3×cbrt-undiv pow-to-exp pow-exp div-inv
2×frac-2neg clear-num *-commutative
1×associate-*l/
Counts
4 → 245
Calls
4 calls:
34.0ms
(* (sqrt 1.875) (/ (sqrt 1.875) (pow (fabs x) 7)))
9.0ms
(/ (sqrt 1.875) (pow (fabs x) 7))
8.0ms
(/ 0.75 (pow (fabs x) 5))
3.7s
(* (* 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))) (* (sqrt 1.875) (/ (sqrt 1.875) (pow (fabs x) 7))))))

series758.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(* (sqrt 1.875) (/ (sqrt 1.875) (pow (fabs x) 7)))
88.0ms
(/ (sqrt 1.875) (pow (fabs x) 7))
53.0ms
(/ 0.75 (pow (fabs x) 5))
499.0ms
(* (* 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))) (* (sqrt 1.875) (/ (sqrt 1.875) (pow (fabs x) 7))))))

simplify2.2s

Counts
257 → 257
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
04316295
111445492
249274921
done50004921

prune1.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

regimes227.0ms

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02938
13738
done3738

end0.0ms

sample4.3s

Algorithm
intervals
Results
3.6s46156×body80valid