Details

Time bar (total: 4.7m)

sample1.3s

Algorithm
intervals
Results
1.2s3379×body80valid

simplify763.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
762.0ms
(* (* (/ 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

localize102.0ms

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))))

rewrite202.0ms

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
92.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))))
51.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
25.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series143.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
56.0ms
(* (/ (/ 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
851.0ms
(* (/ (* (* (/ 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))))
820.0ms
(* (/ (* (* (/ 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) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
806.0ms
(* (/ (/ (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)))))
789.0ms
(* (* (* (/ (/ 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)))))

prune12.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.2b

localize81.0ms

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))))
0.3b
(/ (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)))))

rewrite52.0ms

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
31.0ms
(* (/ (/ 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)))))
1.0ms
(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))))

series690.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
401.0ms
(/ (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)))))
246.0ms
(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))))
43.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify1.3m

Counts
468 → 367
Calls
468 calls:
Slowest
971.0ms
(* (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))))
943.0ms
(* (/ (/ (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)))))
918.0ms
(* (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
843.0ms
(* (* (* (/ (/ 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))))
801.0ms
(* (/ (* (* (/ 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))))

prune6.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

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
29.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
13.0ms
(* (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))))
11.0ms
(/ 3/4 (pow (fabs x) 5))
5.0ms
(/ 15/8 (pow (fabs x) 7))

series806.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
582.0ms
(* (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))))
92.0ms
(/ 15/8 (pow (fabs x) 7))
79.0ms
(/ 3/4 (pow (fabs x) 5))
54.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))

simplify18.2s

Counts
169 → 174
Calls
169 calls:
Slowest
765.0ms
(* (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)))))
441.0ms
(* (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))))
378.0ms
(+ (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)))))
377.0ms
(* (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 (/ (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)))))

prune3.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

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

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
105×add-sqr-sqrt
89×times-frac
61×*-un-lft-identity
60×add-cube-cbrt
53×sqrt-prod
49×associate-*r*
34×unpow-prod-down
30×add-exp-log
22×add-cbrt-cube associate-*l*
18×unswap-sqr
14×sqr-pow
9×div-exp
8×pow1 associate-/r* prod-exp
6×cbrt-unprod associate-/l*
5×cbrt-undiv
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
2×pow-to-exp clear-num frac-2neg pow-prod-down pow-exp *-commutative fma-udef
1×distribute-rgt-in distribute-lft-in sqrt-div associate-*l/ associate-*r/
Counts
4 → 199
Calls
4 calls:
Slowest
28.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
20.0ms
(* (sqrt 15/8) (/ (sqrt 15/8) (pow (fabs x) 7)))
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))) (* (sqrt 15/8) (/ (sqrt 15/8) (pow (fabs x) 7)))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
5.0ms
(/ 3/4 (pow (fabs x) 5))

series819.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
581.0ms
(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (* (sqrt 15/8) (/ (sqrt 15/8) (pow (fabs x) 7)))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
146.0ms
(* (sqrt 15/8) (/ (sqrt 15/8) (pow (fabs x) 7)))
51.0ms
(/ 3/4 (pow (fabs x) 5))
41.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))

simplify29.5s

Counts
201 → 211
Calls
201 calls:
Slowest
844.0ms
(* (sqrt (sqrt 15/8)) (/ (sqrt (sqrt 15/8)) (pow (sqrt (fabs x)) 7)))
542.0ms
(* (sqrt (sqrt 15/8)) (/ (sqrt (sqrt 15/8)) (pow (sqrt (fabs x)) 7)))
515.0ms
(* (sqrt (sqrt 15/8)) (/ (sqrt (sqrt 15/8)) (pow (sqrt (fabs x)) 7)))
507.0ms
(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (* (sqrt 15/8) (/ (sqrt 15/8) (pow (fabs x) 7)))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
503.0ms
(* (sqrt (sqrt 15/8)) (/ (sqrt (sqrt 15/8)) (pow (sqrt (fabs x)) 7)))

prune4.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes231.0ms

bsearch6.0ms

end0.0ms