Details

Time bar (total: 5.3m)

sample1.5s

Algorithm
intervals
Results
1.4s3769×body80valid

simplify802.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
802.0ms
(* (* (/ 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))))))

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.1b

localize62.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.5b
(/ (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)))))
0.4b
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.4b
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))

rewrite115.0ms

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
38.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
30.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
19.0ms
(/ (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)))))
2.0ms
(sqrt PI)

series506.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
410.0ms
(/ (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)))))
53.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
42.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify1.9m

Counts
761 → 577
Calls
761 calls:
Slowest
944.0ms
(/ (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 (/ (sqrt PI) (exp (* (fabs x) (fabs x))))))
879.0ms
(* (/ (* (* (/ 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))))
861.0ms
(* (/ (/ 1 (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ 1 (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
846.0ms
(* (/ (* (* (/ 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))))
813.0ms
(* (/ (/ (sqrt 1) (* (cbrt (fabs x)) (cbrt (fabs x)))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ (sqrt 1) (* (cbrt (fabs x)) (cbrt (fabs x)))) (* (cbrt (fabs x)) (cbrt (fabs x)))))

prune10.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.2b

localize86.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (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
(/ 3/4 (pow (fabs x) 5))
0.3b
(/ 15/8 (pow (fabs x) 7))
0.3b
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt times-frac
48×*-un-lft-identity
47×add-cube-cbrt
25×add-exp-log
24×unpow-prod-down
19×add-cbrt-cube
16×associate-*l* sqrt-prod
15×associate-/r*
9×div-exp associate-/l*
8×sqr-pow
6×pow1
5×cbrt-undiv
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp unswap-sqr
3×clear-num frac-2neg associate-*r*
2×pow-to-exp pow-exp fma-udef
1×distribute-rgt-in distribute-lft-in sqrt-div pow-prod-down associate-*l/ *-commutative
Counts
4 → 162
Calls
4 calls:
Slowest
22.0ms
(/ 3/4 (pow (fabs x) 5))
21.0ms
(* (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))))
14.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
9.0ms
(/ 15/8 (pow (fabs x) 7))

series726.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
556.0ms
(* (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))))
81.0ms
(/ 15/8 (pow (fabs x) 7))
52.0ms
(/ 3/4 (pow (fabs x) 5))
36.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))

simplify18.8s

Counts
169 → 174
Calls
169 calls:
Slowest
792.0ms
(/ (* (* 15/8 15/8) 15/8) (* (* (pow (fabs x) 7) (pow (fabs x) 7)) (pow (fabs x) 7)))
424.0ms
(* (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))))
418.0ms
(* (sqrt (/ (sqrt 1) (sqrt 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)))))
381.0ms
(* (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))))
369.0ms
(* (* (* (sqrt (/ 1 PI)) (sqrt (/ 1 PI))) (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)))))

prune3.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

localize88.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (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 2))) (pow (fabs x) (/ 7 2)))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
0.4b
(/ (/ 15/8 (pow (fabs x) (/ 7 2))) (pow (fabs x) (/ 7 2)))
0.3b
(/ 15/8 (pow (fabs x) (/ 7 2)))
0.3b
(/ 3/4 (pow (fabs x) 5))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
396×times-frac
218×add-sqr-sqrt
210×*-un-lft-identity
209×add-cube-cbrt
174×unpow-prod-down
58×sqr-pow
42×add-exp-log
31×associate-/l*
27×div-exp
21×associate-/r*
16×associate-*l* sqrt-prod
15×add-cbrt-cube
12×div-inv
9×pow-to-exp pow-exp
6×pow1
5×cbrt-undiv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×clear-num frac-2neg associate-*r*
2×fma-udef
1×distribute-rgt-in distribute-lft-in sqrt-div pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod associate-/l/
Counts
4 → 371
Calls
4 calls:
Slowest
12.0ms
(/ (/ 15/8 (pow (fabs x) (/ 7 2))) (pow (fabs x) (/ 7 2)))
11.0ms
(* (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 2))) (pow (fabs x) (/ 7 2)))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
7.0ms
(/ 3/4 (pow (fabs x) 5))
5.0ms
(/ 15/8 (pow (fabs x) (/ 7 2)))

series773.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
523.0ms
(* (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 2))) (pow (fabs x) (/ 7 2)))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
115.0ms
(/ 15/8 (pow (fabs x) (/ 7 2)))
71.0ms
(/ (/ 15/8 (pow (fabs x) (/ 7 2))) (pow (fabs x) (/ 7 2)))
65.0ms
(/ 3/4 (pow (fabs x) 5))

simplify2.2m

Counts
548 → 383
Calls
548 calls:
Slowest
732.0ms
(/ (/ (sqrt 15/8) (pow (* (cbrt (fabs x)) (cbrt (fabs x))) (/ 7 2))) (pow 1 (/ 7 2)))
692.0ms
(/ (/ 15/8 (pow (fabs x) (/ 7 2))) (pow (cbrt (fabs x)) (/ 7 2)))
674.0ms
(/ (/ 15/8 (pow (fabs x) (/ 7 2))) (pow (sqrt (fabs x)) (/ 7 2)))
657.0ms
(/ (/ (cbrt 15/8) (pow (cbrt (fabs x)) (/ 7 2))) (pow (cbrt (fabs x)) (/ 7 2)))
651.0ms
(/ (/ 15/8 (pow (fabs x) (/ 7 2))) (pow (cbrt (fabs x)) (/ 7 2)))

prune8.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.2b

localize76.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt (/ 1 PI)) (fma (/ 1/2 (* (fabs x) (fabs x))) (/ (exp (* (fabs x) (fabs x))) (fabs x)) (fma 15/8 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7)) (fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x))))))
0.3b
(fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x)))
0.3b
(fma 15/8 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7)) (fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
0.3b
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
32×times-frac
30×*-un-lft-identity
29×add-cube-cbrt
16×associate-*l* sqrt-prod
12×unpow-prod-down
8×add-cbrt-cube add-exp-log
7×associate-/r*
6×pow1
4×expm1-log1p-u fma-udef insert-posit16 log1p-expm1-u add-log-exp unswap-sqr sqr-pow
3×div-exp associate-*r* associate-/l*
2×div-inv
1×distribute-rgt-in pow-to-exp cbrt-undiv clear-num frac-2neg distribute-lft-in sqrt-div pow-prod-down associate-*l/ pow-exp prod-exp *-commutative cbrt-unprod
Counts
4 → 110
Calls
4 calls:
Slowest
12.0ms
(* (sqrt (/ 1 PI)) (fma (/ 1/2 (* (fabs x) (fabs x))) (/ (exp (* (fabs x) (fabs x))) (fabs x)) (fma 15/8 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7)) (fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x))))))
11.0ms
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7))
1.0ms
(fma 15/8 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7)) (fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
0.0ms
(fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x)))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
659.0ms
(* (sqrt (/ 1 PI)) (fma (/ 1/2 (* (fabs x) (fabs x))) (/ (exp (* (fabs x) (fabs x))) (fabs x)) (fma 15/8 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7)) (fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x))))))
397.0ms
(fma 15/8 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7)) (fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
246.0ms
(fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x)))
122.0ms
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7))

simplify21.1s

Counts
99 → 122
Calls
99 calls:
Slowest
1.2s
(/ (* (* (exp (* (fabs x) (fabs x))) (exp (* (fabs x) (fabs x)))) (exp (* (fabs x) (fabs x)))) (* (* (pow (fabs x) 7) (pow (fabs x) 7)) (pow (fabs x) 7)))
687.0ms
(* (sqrt (/ (sqrt 1) (sqrt PI))) (sqrt (fma (/ 1/2 (* (fabs x) (fabs x))) (/ (exp (* (fabs x) (fabs x))) (fabs x)) (fma 15/8 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7)) (fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))))
522.0ms
(+ (/ (exp (pow (fabs x) 2)) (fabs x)) (* 3/4 (/ (exp (pow (fabs x) 2)) (pow (fabs x) 5))))
489.0ms
(+ (/ (exp (pow (fabs x) 2)) (fabs x)) (* 3/4 (/ (exp (pow (fabs x) 2)) (pow (fabs x) 5))))
458.0ms
(+ (/ (exp (pow (fabs x) 2)) (fabs x)) (* 3/4 (/ (exp (pow (fabs x) 2)) (pow (fabs x) 5))))

prune2.0s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.2b

regimes205.0ms

bsearch8.0ms

end0.0ms