Details

Time bar (total: 3.9m)

sample1.3s

Algorithm
intervals
Results
1.2s3467×body80valid

simplify1.1s

Counts
1 → 1
Calls
1 calls:
Slowest
1.1s
(* (* (/ 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))))))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize52.0ms

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)))))

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
53.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
24.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
20.0ms
(/ (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)

series544.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
437.0ms
(/ (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)))))
55.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
52.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify2.0m

Counts
761 → 577
Calls
761 calls:
Slowest
976.0ms
(/ (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))))) (/ (sqrt PI) (sqrt (exp (* (fabs x) (fabs x))))))
924.0ms
(* (/ (/ (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)))))
918.0ms
(* (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
906.0ms
(* (/ (/ 1 (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ 1 (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))
872.0ms
(* (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))) (/ (/ (sqrt 1) (sqrt (fabs x))) (* (cbrt (fabs x)) (cbrt (fabs x)))))

prune10.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

localize63.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt times-frac
48×*-un-lft-identity
47×add-cube-cbrt
25×add-exp-log
24×unpow-prod-down
19×add-cbrt-cube
16×associate-*l* sqrt-prod
15×associate-/r*
9×div-exp associate-/l*
8×sqr-pow
6×pow1
5×cbrt-undiv
4×expm1-log1p-u prod-exp cbrt-unprod 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 fma-udef
1×distribute-rgt-in distribute-lft-in sqrt-div pow-prod-down associate-*l/ *-commutative
Counts
4 → 162
Calls
4 calls:
Slowest
21.0ms
(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
17.0ms
(/ 15/8 (pow (fabs x) 7))
14.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
10.0ms
(/ 3/4 (pow (fabs x) 5))

series710.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
540.0ms
(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
74.0ms
(/ 15/8 (pow (fabs x) 7))
58.0ms
(/ 3/4 (pow (fabs x) 5))
37.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))

simplify18.8s

Counts
169 → 174
Calls
169 calls:
Slowest
739.0ms
(* (sqrt (/ 1 (sqrt PI))) (sqrt (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))
433.0ms
(/ (* (* 3/4 3/4) 3/4) (* (* (pow (fabs x) 5) (pow (fabs x) 5)) (pow (fabs x) 5)))
430.0ms
(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
378.0ms
(/ (* (* 15/8 15/8) 15/8) (* (* (pow (fabs x) 7) (pow (fabs x) 7)) (pow (fabs x) 7)))
372.0ms
(* (sqrt (sqrt (/ 1 PI))) (sqrt (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 15/8 (pow (fabs x) 7))) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))

prune3.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize89.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
194×times-frac
122×add-sqr-sqrt
114×*-un-lft-identity
113×add-cube-cbrt
48×unpow-prod-down
42×add-exp-log
29×associate-/r*
23×div-exp
22×add-cbrt-cube
16×associate-*l* sqrt-prod sqr-pow
13×associate-/l*
8×div-inv
7×pow1 cbrt-undiv
4×expm1-log1p-u pow-to-exp rec-exp 1-exp pow-exp prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×clear-num frac-2neg associate-*r*
2×fma-udef
1×distribute-rgt-in distribute-lft-in sqrt-div pow-prod-down associate-*l/ associate-/r/ *-commutative pow-flip inv-pow
Counts
4 → 247
Calls
4 calls:
Slowest
39.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
21.0ms
(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 1 (/ (pow (fabs x) 7) 15/8))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
14.0ms
(/ 1 (/ (pow (fabs x) 7) 15/8))
12.0ms
(/ (pow (fabs x) 7) 15/8)

series864.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
613.0ms
(* (sqrt (/ 1 PI)) (fma (exp (* (fabs x) (fabs x))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (/ 1 (/ (pow (fabs x) 7) 15/8))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
99.0ms
(/ (pow (fabs x) 7) 15/8)
89.0ms
(/ 1 (/ (pow (fabs x) 7) 15/8))
62.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))

simplify55.8s

Counts
301 → 259
Calls
301 calls:
Slowest
773.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (pow (sqrt (fabs x)) 7) 1))
759.0ms
(/ (sqrt 1) (/ (pow (* (cbrt (fabs x)) (cbrt (fabs x))) 7) 1))
690.0ms
(/ 1 (/ (cbrt (pow (fabs x) 7)) (sqrt 15/8)))
672.0ms
(/ (sqrt 1) (/ (pow (* (cbrt (fabs x)) (cbrt (fabs x))) 7) (* (cbrt 15/8) (cbrt 15/8))))
627.0ms
(/ 1 (/ (pow (* (cbrt (fabs x)) (cbrt (fabs x))) 7) 1))

prune4.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt times-frac
48×*-un-lft-identity
47×add-cube-cbrt
25×add-exp-log
24×unpow-prod-down
19×add-cbrt-cube
16×associate-*l* sqrt-prod
15×associate-/r*
9×div-exp associate-/l*
8×sqr-pow
6×pow1
5×cbrt-undiv
4×expm1-log1p-u prod-exp cbrt-unprod 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 fma-udef
1×distribute-rgt-in distribute-lft-in sqrt-div pow-prod-down associate-*l/ *-commutative
Counts
4 → 162
Calls
4 calls:
Slowest
21.0ms
(* (sqrt (/ 1 PI)) (fma (+ (/ 3/4 (pow (fabs x) 5)) (+ (/ 1/2 (* (fabs x) (* (fabs x) (fabs x)))) (/ 15/8 (pow (fabs x) 7)))) (exp (* (fabs x) (fabs x))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
20.0ms
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))
5.0ms
(/ 15/8 (pow (fabs x) 7))
5.0ms
(/ 3/4 (pow (fabs x) 5))

series710.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
529.0ms
(* (sqrt (/ 1 PI)) (fma (+ (/ 3/4 (pow (fabs x) 5)) (+ (/ 1/2 (* (fabs x) (* (fabs x) (fabs x)))) (/ 15/8 (pow (fabs x) 7)))) (exp (* (fabs x) (fabs x))) (/ (exp (* (fabs x) (fabs x))) (fabs x))))
70.0ms
(/ 15/8 (pow (fabs x) 7))
64.0ms
(/ 3/4 (pow (fabs x) 5))
47.0ms
(/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))

simplify16.7s

Counts
169 → 174
Calls
169 calls:
Slowest
353.0ms
(/ (* (* 3/4 3/4) 3/4) (* (* (pow (fabs x) 5) (pow (fabs x) 5)) (pow (fabs x) 5)))
329.0ms
(/ (* (* 15/8 15/8) 15/8) (* (* (pow (fabs x) 7) (pow (fabs x) 7)) (pow (fabs x) 7)))
299.0ms
(/ (* (cbrt 15/8) (cbrt 15/8)) (* (cbrt (pow (fabs x) 7)) (cbrt (pow (fabs x) 7))))
291.0ms
(* (sqrt (sqrt (/ 1 PI))) (sqrt (fma (+ (/ 3/4 (pow (fabs x) 5)) (+ (/ 1/2 (* (fabs x) (* (fabs x) (fabs x)))) (/ 15/8 (pow (fabs x) 7)))) (exp (* (fabs x) (fabs x))) (/ (exp (* (fabs x) (fabs x))) (fabs x)))))
288.0ms
(* (sqrt (/ 1 PI)) (/ (exp (* (fabs x) (fabs x))) (fabs x)))

prune3.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes544.0ms

bsearch4.0ms

end0.0ms