Details

Time bar (total: 3.2m)

sample1.8s

Algorithm
intervals
Results
1.2s3575×body80valid

simplify848.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
847.0ms
(* (* (/ 1 (sqrt PI)) (exp (* (fabs x) (fabs x)))) (+ (+ (+ (/ 1 (fabs x)) (* (/ 1 2) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))))) (* (/ 3 4) (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))))) (* (/ 15 8) (* (* (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))))))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize62.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.6b
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.6b
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.3b
(/ (fma (/ 1 (fabs x)) (fma (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 3/4 (* 15/8 (* (/ (/ 1 (fabs x)) (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x)))) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
790×times-frac
529×add-sqr-sqrt
400×*-un-lft-identity
368×add-cube-cbrt
208×add-exp-log
123×div-exp
98×swap-sqr
86×associate-*r* associate-*l*
81×add-cbrt-cube
69×div-inv
67×pow1
50×prod-exp unswap-sqr
39×cbrt-undiv sqrt-prod
32×pow-div
22×associate-/r*
20×rec-exp 1-exp
18×cbrt-unprod
16×pow-flip inv-pow
10×pow-prod-up
6×pow-prod-down pow-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
2×pow2 frac-times pow-plus associate-*l/ associate-*r/ *-commutative
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/r/
Counts
4 → 567
Calls
4 calls:
Slowest
33.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
31.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
15.0ms
(/ (fma (/ 1 (fabs x)) (fma (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 3/4 (* 15/8 (* (/ (/ 1 (fabs x)) (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x)))) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
1.0ms
(sqrt PI)

series521.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
429.0ms
(/ (fma (/ 1 (fabs x)) (fma (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 3/4 (* 15/8 (* (/ (/ 1 (fabs x)) (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x)))) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
60.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
32.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify1.9m

Counts
761 → 577
Calls
761 calls:
Slowest
1.1s
(* (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ (/ 1 (fabs x)) (fabs x))) (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))))
935.0ms
(/ (fma (/ 1 (fabs x)) (fma (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 3/4 (* 15/8 (* (/ (/ 1 (fabs x)) (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x)))) (/ (sqrt (cbrt PI)) (cbrt (exp (* (fabs x) (fabs x))))))
890.0ms
(* (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ (/ 1 (fabs x)) (fabs x))))
880.0ms
(* (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ (/ 1 (fabs x)) (fabs x))))
873.0ms
(/ (cbrt (fma (/ 1 (fabs x)) (fma (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 3/4 (* 15/8 (* (/ (/ 1 (fabs x)) (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x))))) (/ (sqrt PI) (cbrt (exp (* (fabs x) (fabs x))))))

prune10.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 15/8 (pow (fabs x) 7))
0.3b
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
0.3b
(* (* (fabs x) (fabs x)) (fabs x))
0.3b
(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
35×times-frac
33×*-un-lft-identity
32×add-cube-cbrt
25×pow1 add-exp-log
22×add-cbrt-cube
17×associate-*l*
16×sqrt-prod
12×unpow-prod-down
8×associate-/r*
7×prod-exp cbrt-unprod
6×pow-plus div-exp associate-*r* pow-prod-up associate-/l*
5×unswap-sqr
4×expm1-log1p-u cbrt-undiv pow-prod-down insert-posit16 log1p-expm1-u add-log-exp sqr-pow
3×div-inv
2×pow2 clear-num frac-2neg pow-sqr *-commutative fma-udef
1×distribute-rgt-in pow-to-exp distribute-lft-in sqrt-div pow3 associate-*l/ pow-exp
Counts
4 → 145
Calls
4 calls:
Slowest
37.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
19.0ms
(* (* (fabs x) (fabs x)) (fabs x))
12.0ms
(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
10.0ms
(/ 15/8 (pow (fabs x) 7))

series671.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
526.0ms
(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
77.0ms
(/ 15/8 (pow (fabs x) 7))
42.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
25.0ms
(* (* (fabs x) (fabs x)) (fabs x))

simplify14.5s

Counts
139 → 157
Calls
139 calls:
Slowest
531.0ms
(* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
514.0ms
(/ (* (* 1/2 1/2) 1/2) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))))
500.0ms
(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
423.0ms
(* (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
414.0ms
(* (sqrt 1) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))

prune2.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 15/8 (pow (fabs x) 7))
0.3b
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
0.3b
(* (* (fabs x) (fabs x)) (fabs x))
0.3b
(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
35×times-frac
33×*-un-lft-identity
32×add-cube-cbrt
25×pow1 add-exp-log
22×add-cbrt-cube
17×associate-*l*
16×sqrt-prod
12×unpow-prod-down
8×associate-/r*
7×prod-exp cbrt-unprod
6×pow-plus div-exp associate-*r* pow-prod-up associate-/l*
5×unswap-sqr
4×expm1-log1p-u cbrt-undiv pow-prod-down insert-posit16 log1p-expm1-u add-log-exp sqr-pow
3×div-inv
2×pow2 clear-num frac-2neg pow-sqr *-commutative fma-udef
1×distribute-rgt-in pow-to-exp distribute-lft-in sqrt-div pow3 associate-*l/ pow-exp
Counts
4 → 145
Calls
4 calls:
Slowest
28.0ms
(* (* (fabs x) (fabs x)) (fabs x))
24.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
12.0ms
(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
5.0ms
(/ 15/8 (pow (fabs x) 7))

series685.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
528.0ms
(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
83.0ms
(/ 15/8 (pow (fabs x) 7))
46.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
27.0ms
(* (* (fabs x) (fabs x)) (fabs x))

simplify13.5s

Counts
139 → 157
Calls
139 calls:
Slowest
453.0ms
(* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
413.0ms
(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
403.0ms
(* (sqrt (sqrt (/ 1 PI))) (sqrt (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))
362.0ms
(* (sqrt (sqrt (/ 1 PI))) (sqrt (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))
356.0ms
(* (sqrt (sqrt (/ 1 PI))) (sqrt (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))

prune2.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize74.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (sqrt (/ 1 PI))) (* (sqrt (sqrt (/ 1 PI))) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))
0.3b
(* (sqrt (sqrt (/ 1 PI))) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
0.3b
(/ 15/8 (pow (fabs x) 7))
0.3b
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
65×sqrt-prod
52×add-sqr-sqrt
44×times-frac
42×*-un-lft-identity
41×add-cube-cbrt
38×associate-*l*
25×add-exp-log
22×add-cbrt-cube
12×unpow-prod-down
11×pow1
10×sqrt-div
8×associate-/r*
7×prod-exp cbrt-unprod
6×div-exp fma-udef associate-/l*
5×distribute-rgt-in distribute-lft-in unswap-sqr
4×expm1-log1p-u cbrt-undiv associate-*r* pow-prod-down associate-*l/ insert-posit16 log1p-expm1-u div-inv add-log-exp sqr-pow
2×clear-num frac-2neg *-commutative
1×frac-times pow-to-exp pow-exp associate-*r/
Counts
4 → 162
Calls
4 calls:
Slowest
60.0ms
(* (sqrt (sqrt (/ 1 PI))) (* (sqrt (sqrt (/ 1 PI))) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))
17.0ms
(* (sqrt (sqrt (/ 1 PI))) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
16.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
10.0ms
(/ 15/8 (pow (fabs x) 7))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
818.0ms
(* (sqrt (sqrt (/ 1 PI))) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
549.0ms
(* (sqrt (sqrt (/ 1 PI))) (* (sqrt (sqrt (/ 1 PI))) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))
79.0ms
(/ 15/8 (pow (fabs x) 7))
48.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))

simplify20.5s

Counts
152 → 174
Calls
152 calls:
Slowest
1.1s
(* (* (* (sqrt (sqrt (/ 1 PI))) (sqrt (sqrt (/ 1 PI)))) (sqrt (sqrt (/ 1 PI)))) (* (* (* (sqrt (sqrt (/ 1 PI))) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x)))) (* (sqrt (sqrt (/ 1 PI))) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))) (* (sqrt (sqrt (/ 1 PI))) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))))
501.0ms
(* (sqrt (sqrt 1)) (* (sqrt (sqrt (/ 1 PI))) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))
501.0ms
(+ (log (sqrt (sqrt (/ 1 PI)))) (log (* (sqrt (sqrt (/ 1 PI))) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))))
498.0ms
(* (* (* (sqrt (sqrt (/ 1 PI))) (sqrt (sqrt (/ 1 PI)))) (sqrt (sqrt (/ 1 PI)))) (* (* (* (sqrt (sqrt (/ 1 PI))) (sqrt (sqrt (/ 1 PI)))) (sqrt (sqrt (/ 1 PI)))) (* (* (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x)))) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))))
485.0ms
(* (sqrt (sqrt (/ 1 PI))) (* (sqrt (sqrt (/ 1 PI))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))

prune3.2s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes246.0ms

bsearch4.0ms

end0.0ms