Details

Time bar (total: 4.1m)

sample1.3s

Algorithm
intervals
Results
1.2s3582×body80valid

simplify884.0ms

Calls
1 calls:
Slowest
884.0ms
(* (* (/ 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))))))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize64.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.6b
(/ (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)))))
0.5b
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.5b
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))

rewrite84.0ms

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/
Calls
4 calls:
Slowest
30.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
28.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
10.0ms
(/ (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)

series585.0ms

Calls
4 calls:
Slowest
484.0ms
(/ (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)))))
54.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
47.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify1.9m

Calls
761 calls:
Slowest
1.2s
(* (/ (* (* (/ 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))))
976.0ms
(/ (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 (/ (sqrt PI) (exp (* (fabs x) (fabs x))))))
973.0ms
(/ (sqrt (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))))) (/ 1 1))
912.0ms
(* (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
872.0ms
(* (/ (/ 1 (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ 1 (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))

prune10.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.4b

localize56.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (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)))
0.3b
(* (* (fabs x) (fabs x)) (fabs x))

rewrite63.0ms

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
Calls
4 calls:
Slowest
24.0ms
(* (* (fabs x) (fabs x)) (fabs x))
17.0ms
(* (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)))
5.0ms
(/ 15/8 (pow (fabs x) 7))

series719.0ms

Calls
4 calls:
Slowest
564.0ms
(* (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))))
82.0ms
(/ 15/8 (pow (fabs x) 7))
37.0ms
(* (* (fabs x) (fabs x)) (fabs x))
36.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))

simplify14.0s

Calls
139 calls:
Slowest
763.0ms
(* (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))))
454.0ms
(* (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))))
449.0ms
(* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
407.0ms
(+ (log (sqrt (/ 1 PI))) (log (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)))))
368.0ms
(* (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))

prune2.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.4b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (/ (pow (fabs x) 7) 15/8))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
0.3b
(/ (pow (fabs x) 7) 15/8)
0.3b
(/ 1 (/ (pow (fabs x) 7) 15/8))
0.3b
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
194×times-frac
122×add-sqr-sqrt
114×*-un-lft-identity
113×add-cube-cbrt
48×unpow-prod-down
42×add-exp-log
29×associate-/r*
23×div-exp
22×add-cbrt-cube
16×associate-*l* sqrt-prod sqr-pow
13×associate-/l*
8×div-inv
7×pow1 cbrt-undiv
4×expm1-log1p-u pow-to-exp rec-exp 1-exp pow-exp prod-exp cbrt-unprod 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/ associate-/r/ *-commutative pow-flip inv-pow
Calls
4 calls:
Slowest
19.0ms
(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (/ (pow (fabs x) 7) 15/8))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
14.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
7.0ms
(/ 1 (/ (pow (fabs x) 7) 15/8))
6.0ms
(/ (pow (fabs x) 7) 15/8)

series694.0ms

Calls
4 calls:
Slowest
506.0ms
(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (/ (pow (fabs x) 7) 15/8))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
73.0ms
(/ (pow (fabs x) 7) 15/8)
72.0ms
(/ 1 (/ (pow (fabs x) 7) 15/8))
42.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))

simplify54.8s

Calls
301 calls:
Slowest
703.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (pow (sqrt (fabs x)) 7) 1))
700.0ms
(/ 1 (/ (pow (* (cbrt (fabs x)) (cbrt (fabs x))) 7) 1))
672.0ms
(/ (sqrt 1) (/ (pow (* (cbrt (fabs x)) (cbrt (fabs x))) 7) 1))
606.0ms
(/ (sqrt 1) (/ (pow (sqrt (fabs x)) 7) 1))
603.0ms
(/ 1 (/ (pow (* (cbrt (fabs x)) (cbrt (fabs x))) 7) (* (cbrt 15/8) (cbrt 15/8))))

prune4.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.4b

localize83.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (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
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7))
0.3b
(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) 5))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
53×times-frac
46×*-un-lft-identity
45×add-cube-cbrt
24×unpow-prod-down
16×associate-*l* sqrt-prod
14×associate-/r*
10×add-cbrt-cube add-exp-log
8×sqr-pow
6×pow1 div-exp associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×associate-*r* fma-udef div-inv
2×pow-to-exp cbrt-undiv clear-num frac-2neg pow-exp
1×distribute-rgt-in distribute-lft-in sqrt-div pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
16.0ms
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7))
15.0ms
(* (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))))))
12.0ms
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5))
0.0ms
(fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x)))

series1.1s

Calls
4 calls:
Slowest
635.0ms
(* (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))))))
252.0ms
(fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x)))
127.0ms
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7))
120.0ms
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5))

simplify32.8s

Calls
154 calls:
Slowest
1.1s
(/ (* (* (exp (* (fabs x) (fabs x))) (exp (* (fabs x) (fabs x)))) (exp (* (fabs x) (fabs x)))) (* (* (pow (fabs x) 5) (pow (fabs x) 5)) (pow (fabs x) 5)))
1.1s
(/ (* (* (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)))
665.0ms
(/ (sqrt (exp (* (fabs x) (fabs x)))) (pow (fabs x) (/ 5 2)))
518.0ms
(+ (/ (exp (pow (fabs x) 2)) (fabs x)) (* 3/4 (/ (exp (pow (fabs x) 2)) (pow (fabs x) 5))))
515.0ms
(+ (/ (exp (pow (fabs x) 2)) (fabs x)) (* 3/4 (/ (exp (pow (fabs x) 2)) (pow (fabs x) 5))))

prune2.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

regimes371.0ms

bsearch5.0ms

end0.0ms