Details

Time bar (total: 4.5m)

sample1.5s

Algorithm
intervals
Results
1.5s3316×body80valid

simplify857.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
856.0ms
(* (* (/ 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))))))

prune40.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize74.0ms

Local error

Found 4 expressions with local error:

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

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
969×add-exp-log
723×times-frac
576×div-exp
497×add-sqr-sqrt
361×*-un-lft-identity
328×add-cube-cbrt
305×prod-exp
247×add-cbrt-cube
144×pow1
129×associate-*l*
120×cbrt-undiv
98×swap-sqr
96×rec-exp 1-exp
87×associate-*r*
75×cbrt-unprod
74×pow-div
69×div-inv
55×unswap-sqr
37×pow-flip inv-pow
35×pow-prod-up
13×pow-prod-down
11×pow-sqr
7×frac-times associate-*r/
5×associate-*l/
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow2 pow-plus *-commutative sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2 cube-unmult
Counts
4 → 706
Calls
4 calls:
Slowest
54.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
38.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
27.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series158.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
71.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
50.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
37.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify2.0m

Counts
861 → 716
Calls
861 calls:
Slowest
1.3s
(* (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ (/ 1 (fabs x)) (fabs x))) (* (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ (/ 1 (fabs x)) (fabs x))) (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ (/ 1 (fabs x)) (fabs x)))))
889.0ms
(* (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
862.0ms
(* (/ (* (* (/ 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))))
853.0ms
(* (/ (/ (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)))))
846.0ms
(* (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))

prune12.8s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.2b

localize89.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.5b
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.4b
(fma (/ 1 (fabs x)) (fma (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 3/4 (* 15/8 (pow (fabs x) -6))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x))))
0.4b
(/ (fma (/ 1 (fabs x)) (fma (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 3/4 (* 15/8 (pow (fabs x) -6))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x)))) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
464×times-frac
305×add-sqr-sqrt
240×*-un-lft-identity
224×add-cube-cbrt
108×add-exp-log
63×div-exp
49×swap-sqr
45×add-cbrt-cube
43×associate-*r* associate-*l*
39×sqrt-prod
37×div-inv
36×pow1
25×prod-exp unswap-sqr
22×associate-/r*
21×cbrt-undiv
16×pow-div
10×rec-exp 1-exp
9×cbrt-unprod
8×pow-flip inv-pow
5×pow-prod-up
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-prod-down pow-sqr associate-/l*
1×pow2 frac-times rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow-plus pow1/2 associate-*l/ associate-*r/ associate-/r/ *-commutative fma-udef
Counts
4 → 357
Calls
4 calls:
Slowest
44.0ms
(* (/ (/ 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 (pow (fabs x) -6))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x)))) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
2.0ms
(sqrt PI)
0.0ms
(fma (/ 1 (fabs x)) (fma (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 3/4 (* 15/8 (pow (fabs x) -6))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x))))

series735.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
464.0ms
(/ (fma (/ 1 (fabs x)) (fma (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 3/4 (* 15/8 (pow (fabs x) -6))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x)))) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
224.0ms
(fma (/ 1 (fabs x)) (fma (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 3/4 (* 15/8 (pow (fabs x) -6))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x))))
46.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify1.4m

Counts
468 → 367
Calls
468 calls:
Slowest
1.1s
(* (/ (/ (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)))))
943.0ms
(* (/ (/ 1 (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ 1 (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
885.0ms
(* (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
784.0ms
(* (/ (* (* (/ 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))))
747.0ms
(* (* (* (/ (/ 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))))

prune7.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize96.0ms

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

rewrite107.0ms

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
39.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
32.0ms
(* (* (fabs x) (fabs x)) (fabs x))
22.0ms
(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
11.0ms
(/ 15/8 (pow (fabs x) 7))

series759.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
554.0ms
(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
108.0ms
(/ 15/8 (pow (fabs x) 7))
54.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
42.0ms
(* (* (fabs x) (fabs x)) (fabs x))

simplify14.5s

Counts
139 → 157
Calls
139 calls:
Slowest
483.0ms
(* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
436.0ms
(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
420.0ms
(* (sqrt (/ 1 (sqrt PI))) (sqrt (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))
417.0ms
(* (sqrt (sqrt (/ 1 PI))) (sqrt (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))
408.0ms
(* (sqrt (sqrt (/ 1 PI))) (sqrt (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))

prune3.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize76.0ms

Local error

Found 4 expressions with local error:

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

rewrite100.0ms

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
37.0ms
(* (sqrt (sqrt (/ 1 PI))) (* (sqrt (sqrt (/ 1 PI))) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))
32.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
17.0ms
(* (sqrt (sqrt (/ 1 PI))) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
10.0ms
(/ 15/8 (pow (fabs x) 7))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
817.0ms
(* (sqrt (sqrt (/ 1 PI))) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
533.0ms
(* (sqrt (sqrt (/ 1 PI))) (* (sqrt (sqrt (/ 1 PI))) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))
98.0ms
(/ 15/8 (pow (fabs x) 7))
58.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))

simplify19.5s

Counts
152 → 174
Calls
152 calls:
Slowest
597.0ms
(* (* (* (sqrt (sqrt (/ 1 PI))) (sqrt (sqrt (/ 1 PI)))) (sqrt (sqrt (/ 1 PI)))) (* (* (* (sqrt (sqrt (/ 1 PI))) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x)))) (* (sqrt (sqrt (/ 1 PI))) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))) (* (sqrt (sqrt (/ 1 PI))) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))))
569.0ms
(* (* (sqrt (sqrt (/ 1 PI))) (/ (exp (* (fabs x) (fabs x))) (fabs x))) (sqrt (sqrt (/ 1 PI))))
518.0ms
(* (sqrt (sqrt 1)) (* (sqrt (sqrt (/ 1 PI))) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))
516.0ms
(* (sqrt (sqrt (/ 1 PI))) (* (sqrt (sqrt (/ 1 PI))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
510.0ms
(+ (log (sqrt (sqrt (/ 1 PI)))) (log (* (sqrt (sqrt (/ 1 PI))) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))))

prune3.3s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.1b

regimes317.0ms

bsearch4.0ms

end0.0ms