Details

Time bar (total: 3.4m)

sample1.4s

Algorithm
intervals
Results
1.3s3870×body80valid

simplify785.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
785.0ms
(* (* (/ 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))))))

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.1b

localize60.0ms

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)))

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
42.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
32.0ms
(* (/ (/ 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)

series482.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
392.0ms
(/ (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)))))
45.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
45.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify1.9m

Counts
761 → 577
Calls
761 calls:
Slowest
941.0ms
(* (/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (fabs x)) (cbrt (fabs x)))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (fabs x)) (cbrt (fabs x)))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
904.0ms
(* (/ (* (* (/ 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))))
895.0ms
(/ (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)
889.0ms
(* (/ (/ 1 (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ 1 (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
871.0ms
(* (/ (* (* (/ 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))))

prune10.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.3b

localize62.0ms

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
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
0.3b
(* (* (fabs x) (fabs x)) (fabs x))

rewrite104.0ms

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
29.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
29.0ms
(* (* (fabs x) (fabs x)) (fabs x))
22.0ms
(* (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))))
19.0ms
(/ 3/4 (pow (fabs x) 5))

series677.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
542.0ms
(* (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))))
54.0ms
(/ 3/4 (pow (fabs x) 5))
51.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
30.0ms
(* (* (fabs x) (fabs x)) (fabs x))

simplify14.3s

Counts
139 → 157
Calls
139 calls:
Slowest
590.0ms
(/ (* (* 1/2 1/2) 1/2) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))))
459.0ms
(* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
418.0ms
(* (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))))
389.0ms
(* (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)))))
386.0ms
(* (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))))

prune3.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.3b

localize77.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (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)))) (sqrt (/ 1 PI)))
0.3b
(/ 3/4 (pow (fabs x) 5))
0.3b
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
0.3b
(* (* (fabs x) (fabs x)) (fabs x))

rewrite964.0ms

Algorithm
rewrite-expression-head
Rules
33×times-frac
32×add-sqr-sqrt
31×*-un-lft-identity add-cube-cbrt
28×pow1
27×add-exp-log
25×add-cbrt-cube
19×associate-*r*
13×sqrt-prod
12×unpow-prod-down
11×associate-*r/
9×prod-exp cbrt-unprod
8×associate-/r* frac-add
6×pow-plus sqrt-div div-exp pow-prod-down pow-prod-up associate-/l*
5×frac-times associate-*l/
4×expm1-log1p-u cbrt-undiv flip3-+ flip-+ insert-posit16 log1p-expm1-u add-log-exp sqr-pow
3×div-inv
2×pow2 clear-num frac-2neg associate-*l* pow-sqr *-commutative
1×pow-to-exp pow3 pow-exp unswap-sqr
Counts
4 → 150
Calls
4 calls:
Slowest
911.0ms
(* (* (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)))) (sqrt (/ 1 PI)))
30.0ms
(* (* (fabs x) (fabs x)) (fabs x))
14.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
5.0ms
(/ 3/4 (pow (fabs x) 5))

series599.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
439.0ms
(* (* (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)))) (sqrt (/ 1 PI)))
74.0ms
(/ 3/4 (pow (fabs x) 5))
44.0ms
(* (* (fabs x) (fabs x)) (fabs x))
41.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))

simplify16.4s

Counts
146 → 162
Calls
146 calls:
Slowest
1.2s
(* (* (* (* (exp (* (fabs x) (fabs x))) (exp (* (fabs x) (fabs x)))) (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))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7)))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))))) (* (* (sqrt (/ 1 PI)) (sqrt (/ 1 PI))) (sqrt (/ 1 PI))))
1.2s
(* (* (* (* (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))) (+ (+ (/ 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))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 15/8 (pow (fabs x) 7))))) (* (* (sqrt (/ 1 PI)) (sqrt (/ 1 PI))) (sqrt (/ 1 PI))))
840.0ms
(* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (pow (fabs x) 5)) (pow (fabs x) 7)) (sqrt PI))
607.0ms
(* (* (exp (* (fabs x) (fabs x))) (+ (* (+ (pow (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) 3) (pow (/ 3/4 (pow (fabs x) 5)) 3)) (pow (fabs x) 7)) (* (+ (* (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (- (* (/ 3/4 (pow (fabs x) 5)) (/ 3/4 (pow (fabs x) 5))) (* (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))))) 15/8))) (sqrt (/ 1 PI)))
455.0ms
(* (* (exp (* (fabs x) (fabs x))) (+ (* (+ (pow (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) 3) (pow (/ 3/4 (pow (fabs x) 5)) 3)) (pow (fabs x) 7)) (* (+ (* (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (- (* (/ 3/4 (pow (fabs x) 5)) (/ 3/4 (pow (fabs x) 5))) (* (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))))) 15/8))) (sqrt 1))

prune3.1s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.1b

localize98.0ms

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
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7))
0.3b
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5))
0.3b
(/ 1/2 (* (fabs x) (fabs x)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt times-frac
48×*-un-lft-identity
47×add-cube-cbrt
24×unpow-prod-down
16×associate-*l* sqrt-prod
15×associate-/r* add-cbrt-cube add-exp-log
9×associate-/l*
8×div-exp sqr-pow
6×pow1
4×expm1-log1p-u cbrt-undiv 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 prod-exp cbrt-unprod fma-udef
1×distribute-rgt-in distribute-lft-in sqrt-div pow-prod-down associate-*l/ *-commutative
Counts
4 → 160
Calls
4 calls:
Slowest
11.0ms
(/ 1/2 (* (fabs x) (fabs x)))
11.0ms
(* (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))))))
10.0ms
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7))
10.0ms
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5))

series971.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
644.0ms
(* (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))))))
154.0ms
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7))
143.0ms
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5))
29.0ms
(/ 1/2 (* (fabs x) (fabs x)))

simplify32.8s

Counts
167 → 172
Calls
167 calls:
Slowest
1.2s
(/ (* (* (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)))
744.0ms
(/ (cbrt (exp (* (fabs x) (fabs x)))) (pow (sqrt (fabs x)) 7))
383.0ms
(/ (* (* 1/2 1/2) 1/2) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))))
375.0ms
(/ (sqrt (exp (* (fabs x) (fabs x)))) (pow (sqrt (fabs x)) 5))

prune3.2s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.1b

regimes557.0ms

bsearch10.0ms

end0.0ms