Details

Time bar (total: 40.4s)

sample1.3s

Algorithm
intervals
Results
1.1s3566×body80valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: done (2.0s)

IterNodesCost
031103
190103
240165
3202351
done500149

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize43.0ms

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)
1.2b
(pow (/ 1.0 (fabs x)) 6)

rewrite45.0ms

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:
7.0ms
(pow (/ 1.0 (fabs x)) 3)
24.0ms
(pow (/ 1.0 (fabs x)) 4)
3.0ms
(sqrt PI)
7.0ms
(pow (/ 1.0 (fabs x)) 6)

series189.0ms

Counts
4 → 10
Calls
4 calls:
61.0ms
(pow (/ 1.0 (fabs x)) 3)
68.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)
59.0ms
(pow (/ 1.0 (fabs x)) 6)

simplify1.7s

Counts
133 → 133
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02081438
15311292
217371182
done50001175

prune990.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.4b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 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)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
37×times-frac
36×add-cube-cbrt *-un-lft-identity
26×unpow-prod-down
15×add-exp-log
13×cube-prod associate-*l*
12×add-cbrt-cube
9×pow1
6×pow-unpow
4×expm1-log1p-u pow-exp log1p-expm1-u div-inv add-log-exp
3×div-exp associate-*r* sqrt-prod
2×cbrt-undiv frac-times pow-to-exp pow-pow flip3-+ associate-*r/ prod-exp cbrt-unprod flip-+ rem-cube-cbrt unswap-sqr sqr-pow
1×cube-div distribute-rgt-in cube-mult rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 unpow3 pow-prod-down associate-*l/ *-commutative
Counts
4 → 133
Calls
4 calls:
91.0ms
(* (/ 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)))
14.0ms
(pow (/ 1.0 (fabs x)) 3)
8.0ms
(pow (/ 1.0 (fabs x)) 4)
2.0ms
(sqrt PI)

series374.0ms

Counts
4 → 10
Calls
4 calls:
261.0ms
(* (/ 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)))
61.0ms
(pow (/ 1.0 (fabs x)) 3)
52.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify2.5s

Counts
143 → 143
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02302594
17172399
229902167
done50022161

prune1.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
85×times-frac
55×add-sqr-sqrt
54×add-cube-cbrt *-un-lft-identity
25×associate-/r*
21×sqrt-prod add-cbrt-cube
19×add-exp-log
13×unpow-prod-down cube-prod
8×cbrt-undiv div-exp
6×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
3×pow-unpow
2×frac-2neg pow-exp prod-exp clear-num cbrt-unprod rem-cube-cbrt
1×cube-div cube-mult pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 unpow3 associate-/r/ sqr-pow
Counts
4 → 158
Calls
4 calls:
5.0ms
(/ (fma 1.0 (+ (/ 0.75 (pow (fabs x) 4)) (/ 1.875 (pow (fabs x) 6))) 1.0) (fabs x))
50.0ms
(/ (* (fma (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3) (/ (fma 1.0 (+ (/ 0.75 (pow (fabs x) 4)) (/ 1.875 (pow (fabs x) 6))) 1.0) (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
14.0ms
(pow (/ 1.0 (fabs x)) 3)
3.0ms
(sqrt PI)

series976.0ms

Counts
4 → 10
Calls
4 calls:
258.0ms
(/ (fma 1.0 (+ (/ 0.75 (pow (fabs x) 4)) (/ 1.875 (pow (fabs x) 6))) 1.0) (fabs x))
652.0ms
(/ (* (fma (/ 1.0 2.0) (pow (/ 1.0 (fabs x)) 3) (/ (fma 1.0 (+ (/ 0.75 (pow (fabs x) 4)) (/ 1.875 (pow (fabs x) 6))) 1.0) (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
65.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify2.0s

Counts
168 → 168
Iterations

Useful iterations: 2 (931.0ms)

IterNodesCost
03095224
17724938
227004368
done50004368

prune1.3s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.875 (pow (fabs x) 7))
0.3b
(* (* (sqrt (/ 1 PI)) (exp (pow (fabs x) 2))) (+ (+ (+ (/ 1.0 (fabs x)) (/ 0.75 (pow (fabs x) 5))) (/ 1.875 (pow (fabs x) 7))) (/ 0.5 (pow (fabs x) 3))))
0.3b
(/ 0.5 (pow (fabs x) 3))
0.3b
(/ 0.75 (pow (fabs x) 5))

rewrite3.1s

Algorithm
rewrite-expression-head
Rules
82×times-frac
79×*-un-lft-identity
62×add-sqr-sqrt add-cube-cbrt
36×unpow-prod-down
26×associate-/r*
23×add-exp-log
18×frac-add
15×add-cbrt-cube
12×cube-prod sqr-pow
9×pow1 div-exp associate-*l/ distribute-lft-out associate-/l*
8×sqrt-div
7×frac-times associate-*r/ associate-*r*
6×flip3-+ flip-+
4×expm1-log1p-u cube-mult unpow3 log1p-expm1-u add-log-exp
3×cbrt-undiv pow-to-exp frac-2neg pow-prod-down pow-exp prod-exp clear-num cbrt-unprod div-inv
1×distribute-rgt-in distribute-lft-in associate-*l* *-commutative
Counts
4 → 202
Calls
4 calls:
8.0ms
(/ 1.875 (pow (fabs x) 7))
3.1s
(* (* (sqrt (/ 1 PI)) (exp (pow (fabs x) 2))) (+ (+ (+ (/ 1.0 (fabs x)) (/ 0.75 (pow (fabs x) 5))) (/ 1.875 (pow (fabs x) 7))) (/ 0.5 (pow (fabs x) 3))))
9.0ms
(/ 0.5 (pow (fabs x) 3))
8.0ms
(/ 0.75 (pow (fabs x) 5))

series880.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ 1.875 (pow (fabs x) 7))
642.0ms
(* (* (sqrt (/ 1 PI)) (exp (pow (fabs x) 2))) (+ (+ (+ (/ 1.0 (fabs x)) (/ 0.75 (pow (fabs x) 5))) (/ 1.875 (pow (fabs x) 7))) (/ 0.5 (pow (fabs x) 3))))
63.0ms
(/ 0.5 (pow (fabs x) 3))
66.0ms
(/ 0.75 (pow (fabs x) 5))

simplify2.8s

Counts
214 → 214
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
04044633
110284200
242803923
done50003923

prune1.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes321.0ms

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02938
13738
done3738

end0.0ms

sample16.9s

Algorithm
intervals
Results
15.4s57200×body80valid