Details

Time bar (total: 45.5s)

sample1.3s

Algorithm
intervals
Results
1.2s3582×body80valid

simplify808.0ms

Calls
1 calls:
Slowest
808.0ms
(* (* (/ 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: 1.3b

localize63.0ms

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)))
0.5b
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (fma (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ 1 (fabs x))) 3/4 (fma 15/8 (* (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ 1 (fabs x))) (/ (/ 1 (fabs x)) (fabs x))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x))))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
68×add-exp-log
57×times-frac
52×pow1
45×associate-*l*
44×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
35×associate-*r*
33×add-cbrt-cube
25×div-exp
24×pow-div
20×prod-exp
17×div-inv
12×rec-exp pow-flip inv-pow
10×pow-prod-up cbrt-unprod
9×cbrt-undiv
7×pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l/ *-commutative
2×pow2 frac-times pow-plus associate-*r/ fma-udef
1×distribute-rgt-in distribute-lft-in pow1/2
Calls
4 calls:
Slowest
20.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (fma (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ 1 (fabs x))) 3/4 (fma 15/8 (* (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ 1 (fabs x))) (/ (/ 1 (fabs x)) (fabs x))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x))))))
17.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
15.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

series510.0ms

Calls
4 calls:
Slowest
427.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (fma (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ 1 (fabs x))) 3/4 (fma 15/8 (* (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ 1 (fabs x))) (/ (/ 1 (fabs x)) (fabs x))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x))))))
41.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
41.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify16.0s

Calls
161 calls:
Slowest
1.2s
(* (* (* (/ (/ 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))))
809.0ms
(* (* (* (/ (/ 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))))
785.0ms
(* (/ (* (* (exp (* (fabs x) (fabs x))) (exp (* (fabs x) (fabs x)))) (exp (* (fabs x) (fabs x)))) (* (* (sqrt PI) (sqrt PI)) (sqrt PI))) (* (* (fma (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ 1 (fabs x))) 3/4 (fma 15/8 (* (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ 1 (fabs x))) (/ (/ 1 (fabs x)) (fabs x))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x))))) (fma (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ 1 (fabs x))) 3/4 (fma 15/8 (* (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ 1 (fabs x))) (/ (/ 1 (fabs x)) (fabs x))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x)))))) (fma (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ 1 (fabs x))) 3/4 (fma 15/8 (* (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ 1 (fabs x))) (/ (/ 1 (fabs x)) (fabs x))) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x)))))))
624.0ms
(* (/ (* (* (/ 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))))
607.0ms
(* (/ (* (* (/ 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))))

prune3.5s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 0.4b

localize69.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (/ 15/8 (pow (fabs x) 7)) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x))))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))))
0.3b
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
0.3b
(/ 15/8 (pow (fabs x) 7))
0.2b
(/ 3/4 (pow (fabs x) 5))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1 add-exp-log
14×add-cbrt-cube
13×associate-/r*
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×unpow-prod-down pow-div
5×prod-exp div-inv
4×expm1-log1p-u times-frac div-exp cbrt-unprod insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×clear-num frac-2neg associate-*l* pow-prod-down pow-flip inv-pow
2×pow2 cbrt-undiv rec-exp pow-plus pow-prod-up
1×sqrt-div associate-*r* associate-*l/ associate-*r/ *-commutative associate-/l/
Calls
4 calls:
Slowest
43.0ms
(* (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (/ 15/8 (pow (fabs x) 7)) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x))))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))))
14.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
2.0ms
(/ 15/8 (pow (fabs x) 7))
2.0ms
(/ 3/4 (pow (fabs x) 5))

series612.0ms

Calls
4 calls:
Slowest
439.0ms
(* (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (/ 15/8 (pow (fabs x) 7)) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x))))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))))
76.0ms
(/ 15/8 (pow (fabs x) 7))
61.0ms
(/ 3/4 (pow (fabs x) 5))
36.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))

simplify4.8s

Calls
63 calls:
Slowest
515.0ms
(/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))))
415.0ms
(* (* (* (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (/ 15/8 (pow (fabs x) 7)) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x))))) (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (/ 15/8 (pow (fabs x) 7)) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x)))))) (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (/ 15/8 (pow (fabs x) 7)) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x)))))) (* (* (* (sqrt (/ 1 PI)) (sqrt (/ 1 PI))) (sqrt (/ 1 PI))) (* (* (exp (* (fabs x) (fabs x))) (exp (* (fabs x) (fabs x)))) (exp (* (fabs x) (fabs x))))))
412.0ms
(* (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (/ 15/8 (pow (fabs x) 7)) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x))))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))))
405.0ms
(/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))))
363.0ms
(* (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (/ 15/8 (pow (fabs x) 7)) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x))))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))))

prune1.9s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (* 15/8 (/ 1 (pow (fabs x) 7))) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x))))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))))
0.3b
(/ 1 (pow (fabs x) 7))
0.3b
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
0.2b
(* 15/8 (/ 1 (pow (fabs x) 7)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log
18×pow1
14×add-cbrt-cube
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×associate-/r*
6×pow-div
5×rec-exp associate-*r* prod-exp div-inv
4×expm1-log1p-u times-frac div-exp cbrt-unprod insert-posit16 log1p-expm1-u pow-flip associate-/l* inv-pow add-log-exp
3×unpow-prod-down associate-*l* pow-prod-down
2×pow2 cbrt-undiv clear-num frac-2neg pow-plus associate-*r/ *-commutative pow-prod-up
1×pow-to-exp sqrt-div associate-*l/ pow-exp un-div-inv associate-/l/
Calls
4 calls:
Slowest
23.0ms
(* (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (* 15/8 (/ 1 (pow (fabs x) 7))) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x))))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))))
7.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
2.0ms
(/ 1 (pow (fabs x) 7))
1.0ms
(* 15/8 (/ 1 (pow (fabs x) 7)))

series690.0ms

Calls
4 calls:
Slowest
491.0ms
(* (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (* 15/8 (/ 1 (pow (fabs x) 7))) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x))))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))))
88.0ms
(* 15/8 (/ 1 (pow (fabs x) 7)))
74.0ms
(/ 1 (pow (fabs x) 7))
37.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))

simplify5.0s

Calls
64 calls:
Slowest
466.0ms
(/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))))
423.0ms
(/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))))
413.0ms
(* (* (* (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (* 15/8 (/ 1 (pow (fabs x) 7))) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x))))) (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (* 15/8 (/ 1 (pow (fabs x) 7))) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x)))))) (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (* 15/8 (/ 1 (pow (fabs x) 7))) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x)))))) (* (* (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x))))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x))))))
402.0ms
(* (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (* 15/8 (/ 1 (pow (fabs x) 7))) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x))))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))))
398.0ms
(* (* (* (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (* 15/8 (/ 1 (pow (fabs x) 7))) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x))))) (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (* 15/8 (/ 1 (pow (fabs x) 7))) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x)))))) (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (* 15/8 (/ 1 (pow (fabs x) 7))) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x)))))) (* (* (* (sqrt (/ 1 PI)) (sqrt (/ 1 PI))) (sqrt (/ 1 PI))) (* (* (exp (* (fabs x) (fabs x))) (exp (* (fabs x) (fabs x)))) (exp (* (fabs x) (fabs x))))))

prune2.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (* 15/8 (pow (fabs x) -7)) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x))))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))))
0.3b
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
0.2b
(* 15/8 (pow (fabs x) -7))
0.2b
(/ 3/4 (pow (fabs x) 5))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1 add-exp-log
14×add-cbrt-cube
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×associate-/r* associate-*r*
6×unpow-prod-down pow-div
5×prod-exp
4×expm1-log1p-u times-frac div-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv associate-/l* add-log-exp
3×associate-*l* pow-prod-down pow-flip inv-pow
2×pow2 cbrt-undiv rec-exp clear-num frac-2neg pow-plus *-commutative pow-prod-up
1×sqrt-div associate-*l/ associate-*r/ associate-/l/
Calls
4 calls:
Slowest
28.0ms
(* (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (* 15/8 (pow (fabs x) -7)) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x))))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))))
6.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))
2.0ms
(* 15/8 (pow (fabs x) -7))
1.0ms
(/ 3/4 (pow (fabs x) 5))

series629.0ms

Calls
4 calls:
Slowest
439.0ms
(* (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (* 15/8 (pow (fabs x) -7)) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x))))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))))
83.0ms
(* 15/8 (pow (fabs x) -7))
61.0ms
(/ 3/4 (pow (fabs x) 5))
46.0ms
(/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))

simplify5.3s

Calls
63 calls:
Slowest
506.0ms
(/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))))
442.0ms
(* (* (* (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (* 15/8 (pow (fabs x) -7)) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x))))) (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (* 15/8 (pow (fabs x) -7)) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x)))))) (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (* 15/8 (pow (fabs x) -7)) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x)))))) (* (* (* (sqrt (/ 1 PI)) (sqrt (/ 1 PI))) (sqrt (/ 1 PI))) (* (* (exp (* (fabs x) (fabs x))) (exp (* (fabs x) (fabs x)))) (exp (* (fabs x) (fabs x))))))
427.0ms
(* (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (* 15/8 (pow (fabs x) -7)) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x))))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))))
422.0ms
(sqrt (pow (fabs x) 5))
391.0ms
(* (* (* (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (* 15/8 (pow (fabs x) -7)) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x))))) (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (* 15/8 (pow (fabs x) -7)) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x)))))) (fma (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) 1/2 (+ (* 15/8 (pow (fabs x) -7)) (+ (/ 3/4 (pow (fabs x) 5)) (/ 1 (fabs x)))))) (* (* (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x))))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x))))))

prune1.8s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.4b

regimes276.0ms

bsearch10.0ms

end0.0ms