Details

Time bar (total: 3.1m)

sample1.4s

Algorithm
intervals
Results
1.4s2926×body80valid

simplify862.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
862.0ms
(* (* (/ 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))))))

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize76.0ms

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)))

rewrite105.0ms

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
37.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
26.0ms
(* (/ (/ 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)

series543.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
450.0ms
(/ (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)))
38.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify1.9m

Counts
761 → 577
Calls
761 calls:
Slowest
899.0ms
(* (/ (/ 1 (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ 1 (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
897.0ms
(/ (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))))) (/ (sqrt PI) (sqrt (exp (* (fabs x) (fabs x))))))
887.0ms
(* (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))))) (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))))))
829.0ms
(* (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
822.0ms
(* (* (* (/ (/ 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))))

prune10.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.3b

localize81.0ms

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
(/ 3/4 (pow (fabs x) 5))
0.3b
(* (* (fabs x) (fabs x)) (fabs x))
0.2b
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))

rewrite70.0ms

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
26.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
23.0ms
(* (* (fabs x) (fabs x)) (fabs x))
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))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
5.0ms
(/ 3/4 (pow (fabs x) 5))

series676.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
512.0ms
(* (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))))
83.0ms
(/ 3/4 (pow (fabs x) 5))
42.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
38.0ms
(* (* (fabs x) (fabs x)) (fabs x))

simplify13.7s

Counts
139 → 157
Calls
139 calls:
Slowest
743.0ms
(* (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)))))
484.0ms
(* (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))))
467.0ms
(* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
434.0ms
(* (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))))
381.0ms
(* (* (* (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)))))

prune2.8s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.3b

localize46.0ms

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
(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))

rewrite25.0ms

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
13.0ms
(* (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))
0.0ms
(fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x)))
0.0ms
(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))))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
600.0ms
(* (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))))))
398.0ms
(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))))
221.0ms
(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))

simplify20.9s

Counts
99 → 122
Calls
99 calls:
Slowest
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)))
797.0ms
(+ (/ (exp (pow (fabs x) 2)) (fabs x)) (* 3/4 (/ (exp (pow (fabs x) 2)) (pow (fabs x) 5))))
520.0ms
(+ (/ (exp (pow (fabs x) 2)) (fabs x)) (* 3/4 (/ (exp (pow (fabs x) 2)) (pow (fabs x) 5))))
478.0ms
(+ (/ (exp (pow (fabs x) 2)) (fabs x)) (* 3/4 (/ (exp (pow (fabs x) 2)) (pow (fabs x) 5))))
355.0ms
(/ (sqrt (exp (* (fabs x) (fabs x)))) (* (cbrt (pow (fabs x) 7)) (cbrt (pow (fabs x) 7))))

prune2.4s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.3b

localize79.0ms

Local error

Found 4 expressions with local error:

5.3b
(exp (log (fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))
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)) (exp (log (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)) (exp (log (fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x))))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
16×*-un-lft-identity associate-*l* sqrt-prod
15×add-cube-cbrt
11×times-frac
7×pow1
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u exp-prod fma-udef insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×log-prod associate-*r* exp-sum
1×distribute-rgt-in distribute-lft-in sqrt-div pow-prod-down associate-*l/ prod-exp log-pow *-commutative cbrt-unprod div-inv rem-exp-log
Counts
4 → 80
Calls
4 calls:
Slowest
21.0ms
(* (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)) (exp (log (fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x))))))))
6.0ms
(exp (log (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)))
0.0ms
(fma 15/8 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7)) (exp (log (fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x))))))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
643.0ms
(* (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)) (exp (log (fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x))))))))
361.0ms
(fma 15/8 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7)) (exp (log (fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x))))))
237.0ms
(exp (log (fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))
227.0ms
(fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x)))

simplify11.9s

Counts
51 → 92
Calls
51 calls:
Slowest
580.0ms
(exp (sqrt (log (fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x))))))
563.0ms
(exp (log (* (cbrt (fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x)))) (cbrt (fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))))
546.0ms
(+ (/ (exp (pow (fabs x) 2)) (fabs x)) (* 3/4 (/ (exp (pow (fabs x) 2)) (pow (fabs x) 5))))
532.0ms
(+ (/ (exp (pow (fabs x) 2)) (fabs x)) (* 3/4 (/ (exp (pow (fabs x) 2)) (pow (fabs x) 5))))
513.0ms
(exp (* (cbrt (log (fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x))))) (cbrt (log (fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))))

prune1.9s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 0.3b

regimes345.0ms

bsearch4.0ms

end0.0ms