Details

Time bar (total: 33.1s)

sample1.3s

Algorithm
intervals
Results
1.2s3481×body80valid

simplify1.2s

Counts
1 → 1

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize84.0ms

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 (* (* (/ (/ 1 (fabs x)) (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))) 15/8)) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x))))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
652×times-frac
454×add-sqr-sqrt
325×*-un-lft-identity
293×add-cube-cbrt
204×add-exp-log
120×div-exp
98×swap-sqr
86×associate-*r* associate-*l*
76×add-cbrt-cube
67×pow1
64×div-inv
50×prod-exp unswap-sqr
36×cbrt-undiv
32×pow-div
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×sqrt-prod
2×pow2 frac-times pow-plus associate-*l/ associate-*r/ *-commutative
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 469
Calls
4 calls:
Slowest
29.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
23.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
1.0ms
(sqrt PI)
0.0ms
(fma (/ 1 (fabs x)) (fma (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 3/4 (* (* (/ (/ 1 (fabs x)) (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))) 15/8)) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x))))

series342.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
246.0ms
(fma (/ 1 (fabs x)) (fma (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) 3/4 (* (* (/ (/ 1 (fabs x)) (fabs x)) (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))) 15/8)) (fma 1/2 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) (/ 1 (fabs x))))
53.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
44.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify1.0s

Counts
626 → 479

prune8.7s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.2b

localize99.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.3b
(/ 15/8 (pow (fabs x) 7))
0.3b
(/ (+ (+ (/ 1 (fabs x)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 15/8 (pow (fabs x) 7)) (/ 3/4 (pow (fabs x) 5)))) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
0.3b
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))

rewrite696.0ms

Algorithm
rewrite-expression-head
Rules
567×*-un-lft-identity
402×times-frac
299×distribute-lft-out
177×add-sqr-sqrt
176×add-cube-cbrt
93×sqrt-prod
59×div-inv
30×associate-/r*
22×add-exp-log
20×add-cbrt-cube
15×frac-add associate-/l*
12×unpow-prod-down
11×associate-/l/
9×div-exp
7×cbrt-undiv flip3-+ flip-+
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp sqr-pow
3×clear-num frac-2neg prod-exp cbrt-unprod
1×pow-to-exp rem-sqrt-square sqrt-pow1 pow1/2 pow-exp associate-/r/
Counts
4 → 348
Calls
4 calls:
Slowest
637.0ms
(/ (+ (+ (/ 1 (fabs x)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 15/8 (pow (fabs x) 7)) (/ 3/4 (pow (fabs x) 5)))) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
29.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
10.0ms
(/ 15/8 (pow (fabs x) 7))
3.0ms
(sqrt PI)

series648.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
511.0ms
(/ (+ (+ (/ 1 (fabs x)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 15/8 (pow (fabs x) 7)) (/ 3/4 (pow (fabs x) 5)))) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
82.0ms
(/ 15/8 (pow (fabs x) 7))
54.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify977.0ms

Counts
584 → 358

prune6.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize74.0ms

Local error

Found 4 expressions with local error:

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

rewrite528.0ms

Algorithm
rewrite-expression-head
Rules
51×times-frac
46×add-sqr-sqrt
45×*-un-lft-identity add-cube-cbrt
33×associate-*r/
30×frac-add
24×unpow-prod-down
23×pow1 add-exp-log
19×associate-*l*
18×add-cbrt-cube
14×associate-/r* flip3-+ flip-+
13×sqrt-prod
12×sqrt-div
11×frac-times
8×sqr-pow
6×div-exp pow-prod-down prod-exp cbrt-unprod associate-/l*
5×pow-prod-up
4×distribute-rgt-in expm1-log1p-u distribute-lft-in insert-posit16 log1p-expm1-u add-log-exp
3×div-inv
2×pow-to-exp cbrt-undiv clear-num frac-2neg associate-*r* pow-exp *-commutative
1×pow2 pow-plus cube-unmult associate-*l/ pow-sqr unswap-sqr
Counts
4 → 184
Calls
4 calls:
Slowest
489.0ms
(* (sqrt (/ 1 PI)) (* (exp (* (fabs x) (fabs x))) (+ (+ (/ 1 (fabs x)) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))) (+ (/ 15/8 (pow (fabs x) 7)) (/ 3/4 (pow (fabs x) 5))))))
22.0ms
(* (fabs x) (* (fabs x) (fabs x)))
9.0ms
(/ 15/8 (pow (fabs x) 7))
5.0ms
(/ 3/4 (pow (fabs x) 5))

series644.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
486.0ms
(* (sqrt (/ 1 PI)) (* (exp (* (fabs x) (fabs x))) (+ (+ (/ 1 (fabs x)) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))) (+ (/ 15/8 (pow (fabs x) 7)) (/ 3/4 (pow (fabs x) 5))))))
70.0ms
(/ 15/8 (pow (fabs x) 7))
52.0ms
(/ 3/4 (pow (fabs x) 5))
36.0ms
(* (fabs x) (* (fabs x) (fabs x)))

simplify836.0ms

Counts
253 → 196

prune3.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize79.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
1.0b
(sqrt PI)
0.3b
(/ 15/8 (pow (fabs x) 7))
0.3b
(/ (+ (+ (/ 1 (fabs x)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 15/8 (pow (fabs x) 7)) (/ 3/4 (pow (fabs x) 5)))) (/ (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (exp (* (fabs x) (fabs x)))))

rewrite667.0ms

Algorithm
rewrite-expression-head
Rules
186×*-un-lft-identity
114×times-frac
104×distribute-lft-out
52×add-sqr-sqrt
50×add-cube-cbrt
28×div-inv
16×add-exp-log
15×add-cbrt-cube frac-add
14×associate-/r*
12×unpow-prod-down associate-/l*
11×associate-/l/
8×div-exp
7×flip3-+ flip-+
6×pow1 cbrt-undiv sqrt-prod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp sqr-pow
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×pow-to-exp pow-exp prod-exp associate-/r/ cbrt-unprod
Counts
4 → 190
Calls
4 calls:
Slowest
645.0ms
(/ (+ (+ (/ 1 (fabs x)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 15/8 (pow (fabs x) 7)) (/ 3/4 (pow (fabs x) 5)))) (/ (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (exp (* (fabs x) (fabs x)))))
17.0ms
(/ 15/8 (pow (fabs x) 7))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series624.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
537.0ms
(/ (+ (+ (/ 1 (fabs x)) (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))) (+ (/ 15/8 (pow (fabs x) 7)) (/ 3/4 (pow (fabs x) 5)))) (/ (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (exp (* (fabs x) (fabs x)))))
87.0ms
(/ 15/8 (pow (fabs x) 7))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify968.0ms

Counts
288 → 198

prune3.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes202.0ms

bsearch7.0ms

end0.0ms