Details

Time bar (total: 5.7m)

sample1.3s

Algorithm
intervals
Results
1.2s3149×body80valid

simplify801.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
801.0ms
(* (* (/ 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: 0.9b

localize69.0ms

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
(/ (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)))))

rewrite110.0ms

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
33.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
30.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
15.0ms
(/ (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)

series1.0s

Counts
4 → 10
Calls
4 calls:
Slowest
850.0ms
(/ (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)))))
126.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
56.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify2.8m

Counts
791 → 577
Calls
791 calls:
Slowest
992.0ms
(* (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
974.0ms
(* (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
955.0ms
(/ (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) (exp (* (fabs x) (fabs x)))))
872.0ms
(* (/ (* (* (/ 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))))
849.0ms
(* (/ (/ (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)))))

prune10.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize71.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

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
30.0ms
(* (* (fabs x) (fabs x)) (fabs x))
14.0ms
(* (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))))
14.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
5.0ms
(/ 3/4 (pow (fabs x) 5))

series718.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
551.0ms
(* (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))))
65.0ms
(/ 3/4 (pow (fabs x) 5))
53.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
49.0ms
(* (* (fabs x) (fabs x)) (fabs x))

simplify31.7s

Counts
187 → 157
Calls
187 calls:
Slowest
891.0ms
(* (sqrt (/ 1 (cbrt 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))))
593.0ms
(* (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
532.0ms
(* (cbrt (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))))
531.0ms
(* (* (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))))
506.0ms
(* (sqrt (/ (cbrt 1) (sqrt 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))))

prune3.2s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b
(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
(* (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) 5))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
53×times-frac
46×*-un-lft-identity
45×add-cube-cbrt
24×unpow-prod-down
16×associate-*l* sqrt-prod
14×associate-/r*
10×add-cbrt-cube add-exp-log
8×sqr-pow
6×pow1 div-exp associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×associate-*r* fma-udef div-inv
2×pow-to-exp cbrt-undiv clear-num frac-2neg pow-exp
1×distribute-rgt-in distribute-lft-in sqrt-div pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 147
Calls
4 calls:
Slowest
30.0ms
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7))
18.0ms
(* (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) 5))
1.0ms
(fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
631.0ms
(* (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))))))
253.0ms
(fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x)))
162.0ms
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5))
132.0ms
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7))

simplify1.0m

Counts
208 → 159
Calls
208 calls:
Slowest
1.5s
(/ (* (* (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)))
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)))
820.0ms
(* 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)))
783.0ms
(* (sqrt (/ (sqrt 1) (cbrt 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))))))
694.0ms
(* (* (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7)) (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7)))

prune3.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize88.0ms

Local error

Found 4 expressions with local error:

5.1b
(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
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7))
0.3b
(* (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))))))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
32×*-un-lft-identity times-frac
31×add-cube-cbrt
16×associate-*l* sqrt-prod
12×unpow-prod-down
8×add-cbrt-cube add-exp-log
7×pow1 associate-/r*
4×expm1-log1p-u exp-prod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr sqr-pow
3×log-prod div-exp associate-*r* exp-sum fma-udef 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 log-pow *-commutative cbrt-unprod rem-exp-log
Counts
4 → 117
Calls
4 calls:
Slowest
10.0ms
(* (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))))))))
10.0ms
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7))
3.0ms
(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)))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
722.0ms
(* (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))))))))
228.0ms
(fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x)))
223.0ms
(exp (log (fma 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))
162.0ms
(/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7))

simplify53.5s

Counts
158 → 129
Calls
158 calls:
Slowest
1.2s
(/ (* (* (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)))
1.0s
(+ (/ (exp (pow (fabs x) 2)) (fabs x)) (* 3/4 (/ (exp (pow (fabs x) 2)) (pow (fabs x) 5))))
693.0ms
(/ (cbrt (exp (* (fabs x) (fabs x)))) (cbrt (pow (fabs x) 7)))
657.0ms
(* 3/4 (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 5)))
646.0ms
(* (* (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7)) (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (pow (fabs x) 7)))

prune2.6s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes227.0ms

bsearch4.0ms

end0.0ms