Details

Time bar (total: 3.2m)

sample1.6s

Algorithm
intervals
Results
1.5s3388×body80valid

simplify794.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
793.0ms
(* (* (/ 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))))))

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize84.0ms

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)))

rewrite120.0ms

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
35.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
28.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
22.0ms
(/ (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)

series568.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
478.0ms
(/ (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)))))
49.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
42.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify1.9m

Counts
761 → 577
Calls
761 calls:
Slowest
1.1s
(* (/ (* (* (/ 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))))
885.0ms
(* (/ (/ 1 (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ 1 (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
884.0ms
(/ (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)))) (/ 1 (exp (* (fabs x) (fabs x)))))
874.0ms
(* (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
871.0ms
(/ (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 (sqrt PI)) 1))

prune10.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 0.3b

localize76.0ms

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

rewrite81.0ms

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
36.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
21.0ms
(* (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))))
17.0ms
(* (* (fabs x) (fabs x)) (fabs x))
5.0ms
(/ 3/4 (pow (fabs x) 5))

series689.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
557.0ms
(* (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))))
63.0ms
(/ 3/4 (pow (fabs x) 5))
36.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
32.0ms
(* (* (fabs x) (fabs x)) (fabs x))

simplify14.2s

Counts
139 → 157
Calls
139 calls:
Slowest
714.0ms
(* (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)))))
486.0ms
(* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
433.0ms
(* (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))))
383.0ms
(* (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)))))
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

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize77.0ms

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

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
35×times-frac
33×*-un-lft-identity
32×add-cube-cbrt
25×add-exp-log
22×add-cbrt-cube
20×pow1
19×associate-*l*
16×sqrt-prod
12×unpow-prod-down
8×associate-/r*
7×prod-exp cbrt-unprod
6×div-exp associate-/l*
5×pow-prod-up unswap-sqr
4×expm1-log1p-u cbrt-undiv associate-*r* pow-prod-down insert-posit16 log1p-expm1-u add-log-exp sqr-pow
3×div-inv
2×clear-num frac-2neg *-commutative fma-udef
1×pow2 distribute-rgt-in pow-to-exp distribute-lft-in pow-plus sqrt-div cube-unmult associate-*l/ pow-exp pow-sqr
Counts
4 → 141
Calls
4 calls:
Slowest
31.0ms
(* (fabs x) (* (fabs x) (fabs x)))
16.0ms
(/ 1/2 (* (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))))
10.0ms
(/ 3/4 (pow (fabs x) 5))

series741.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
563.0ms
(* (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))))
75.0ms
(/ 3/4 (pow (fabs x) 5))
59.0ms
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
43.0ms
(* (fabs x) (* (fabs x) (fabs x)))

simplify14.6s

Counts
133 → 153
Calls
133 calls:
Slowest
530.0ms
(* (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))))
483.0ms
(* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))))
475.0ms
(* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))))
413.0ms
(+ (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)))))
404.0ms
(* (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)))))

prune2.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

localize99.0ms

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
(/ 1/2 (* (fabs x) (fabs x)))
0.2b
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
35×times-frac
32×*-un-lft-identity
31×add-cube-cbrt
16×associate-*l* sqrt-prod
13×add-cbrt-cube add-exp-log
12×unpow-prod-down
8×associate-/r*
6×pow1 associate-/l*
5×div-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp unswap-sqr sqr-pow
3×cbrt-undiv associate-*r* fma-udef div-inv
2×clear-num frac-2neg prod-exp cbrt-unprod
1×distribute-rgt-in pow-to-exp distribute-lft-in sqrt-div pow-prod-down associate-*l/ pow-exp *-commutative
Counts
4 → 123
Calls
4 calls:
Slowest
22.0ms
(* (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))))))
21.0ms
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5))
13.0ms
(/ 1/2 (* (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)))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
1.1s
(* (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))))))
258.0ms
(fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x)))
132.0ms
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5))
31.0ms
(/ 1/2 (* (fabs x) (fabs x)))

simplify21.2s

Counts
112 → 135
Calls
112 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)))
480.0ms
(+ (/ (exp (pow (fabs x) 2)) (fabs x)) (* 3/4 (/ (exp (pow (fabs x) 2)) (pow (fabs x) 5))))
447.0ms
(+ (/ (exp (pow (fabs x) 2)) (fabs x)) (* 3/4 (/ (exp (pow (fabs x) 2)) (pow (fabs x) 5))))
401.0ms
(+ (/ (exp (pow (fabs x) 2)) (fabs x)) (* 3/4 (/ (exp (pow (fabs x) 2)) (pow (fabs x) 5))))
390.0ms
(/ (cbrt (exp (* (fabs x) (fabs x)))) (pow (cbrt (fabs x)) 5))

prune2.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.2b

regimes222.0ms

bsearch6.0ms

end0.0ms