Details

Time bar (total: 44.5s)

sample1.4s

Algorithm
intervals
Results
1.2s3879×body80valid

simplify5.2s

Counts
1 → 1
Iterations
IterNodes
47662
31577
2409
195
031

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))
0.4b
(/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))
0.8b
(/ (fma (/ (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) 15/8 (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (fma (* (/ 1 (fabs x)) 3/4) (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1 (fabs x))))) (sqrt PI))
1.0b
(sqrt PI)

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
84×add-exp-log
80×times-frac
79×pow1
49×add-sqr-sqrt
48×*-un-lft-identity add-cbrt-cube add-cube-cbrt
37×div-exp
36×pow-div
29×associate-/l*
24×pow-plus prod-exp pow-prod-up
19×cbrt-undiv
18×pow-flip inv-pow
15×sqrt-prod
12×cbrt-unprod
8×pow2 associate-/r* pow-sqr
7×div-inv
6×rec-exp 1-exp
4×expm1-log1p-u pow3 insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×associate-/l/
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 212
Calls
4 calls:
30.0ms
(/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))
18.0ms
(/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))
4.0ms
(/ (fma (/ (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) 15/8 (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (fma (* (/ 1 (fabs x)) 3/4) (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1 (fabs x))))) (sqrt PI))
1.0ms
(sqrt PI)

series458.0ms

Counts
4 → 10
Calls
4 calls:
40.0ms
(/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))
46.0ms
(/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))
372.0ms
(/ (fma (/ (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) 15/8 (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (fma (* (/ 1 (fabs x)) 3/4) (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1 (fabs x))))) (sqrt PI))
0.0ms
(sqrt PI)

simplify2.0s

Counts
222 → 222
Iterations
IterNodes
34392
21156
1517
0236

prune4.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 0.6b

localize47.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (pow (fabs x) -4) (* (* (fabs x) (fabs x)) (fabs x)))
0.4b
(/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))
0.8b
(/ (fma (/ (pow (fabs x) -4) (* (* (fabs x) (fabs x)) (fabs x))) 15/8 (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (fma (* (/ 1 (fabs x)) 3/4) (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1 (fabs x))))) (sqrt PI))
1.0b
(sqrt PI)

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
69×add-exp-log
56×pow1 times-frac
39×add-sqr-sqrt
38×*-un-lft-identity add-cube-cbrt
36×add-cbrt-cube
28×div-exp
27×pow-div
23×associate-/l*
21×prod-exp
18×pow-plus pow-prod-up
15×sqrt-prod
13×cbrt-undiv
9×cbrt-unprod pow-flip inv-pow
8×associate-/r*
6×pow2 unpow-prod-down pow-sqr
5×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-to-exp rec-exp clear-num frac-2neg 1-exp pow3 pow-exp
2×sqr-pow
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 184
Calls
4 calls:
17.0ms
(/ (pow (fabs x) -4) (* (* (fabs x) (fabs x)) (fabs x)))
26.0ms
(/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))
5.0ms
(/ (fma (/ (pow (fabs x) -4) (* (* (fabs x) (fabs x)) (fabs x))) 15/8 (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (fma (* (/ 1 (fabs x)) 3/4) (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1 (fabs x))))) (sqrt PI))
1.0ms
(sqrt PI)

series481.0ms

Counts
4 → 10
Calls
4 calls:
77.0ms
(/ (pow (fabs x) -4) (* (* (fabs x) (fabs x)) (fabs x)))
40.0ms
(/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))
364.0ms
(/ (fma (/ (pow (fabs x) -4) (* (* (fabs x) (fabs x)) (fabs x))) 15/8 (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (fma (* (/ 1 (fabs x)) 3/4) (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1 (fabs x))))) (sqrt PI))
0.0ms
(sqrt PI)

simplify3.6s

Counts
194 → 194
Iterations
IterNodes
36667
21582
1645
0293

prune3.5s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 0.5b

localize79.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))
0.8b
(/ (fma (/ (pow (fabs x) -4) (* (* (fabs x) (fabs x)) (fabs x))) 15/8 (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (fma (* (/ 1 (fabs x)) 3/4) (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1 (fabs x))))) (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
43×pow1
34×times-frac
30×add-cbrt-cube
24×add-sqr-sqrt
22×*-un-lft-identity add-cube-cbrt
20×div-exp
18×pow-div
16×associate-/l*
13×prod-exp
12×pow-plus pow-prod-up
11×cbrt-undiv
9×pow-flip inv-pow
7×cbrt-unprod
6×sqrt-prod
4×pow2 expm1-log1p-u pow-sqr insert-posit16 log1p-expm1-u div-inv add-log-exp
3×rec-exp 1-exp
2×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 pow3
1×associate-/l/
Counts
4 → 133
Calls
4 calls:
18.0ms
(/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))
15.0ms
(/ (fma (/ (pow (fabs x) -4) (* (* (fabs x) (fabs x)) (fabs x))) 15/8 (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (fma (* (/ 1 (fabs x)) 3/4) (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1 (fabs x))))) (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series433.0ms

Counts
4 → 8
Calls
4 calls:
54.0ms
(/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))
378.0ms
(/ (fma (/ (pow (fabs x) -4) (* (* (fabs x) (fabs x)) (fabs x))) 15/8 (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (fma (* (/ 1 (fabs x)) 3/4) (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1 (fabs x))))) (* (sqrt (sqrt PI)) (sqrt (sqrt PI))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify2.5s

Counts
141 → 141
Iterations
IterNodes
34479
21168
1508
0223

prune2.8s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.5b

localize97.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (fma (/ (pow (fabs x) -4) (* (* (fabs x) (fabs x)) (fabs x))) 15/8 (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (fma (* (/ 1 (fabs x)) 3/4) (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1 (fabs x))))) (* (sqrt (sqrt PI)) (sqrt (expm1 (log1p (sqrt PI))))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)
1.0b
(expm1 (log1p (sqrt PI)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×add-cbrt-cube add-exp-log
8×*-un-lft-identity add-cube-cbrt
6×pow1 sqrt-prod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×times-frac associate-/l*
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp
1×expm1-log1p clear-num associate-/r* frac-2neg prod-exp cbrt-unprod div-inv expm1-udef
Counts
4 → 68
Calls
4 calls:
17.0ms
(/ (fma (/ (pow (fabs x) -4) (* (* (fabs x) (fabs x)) (fabs x))) 15/8 (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (fma (* (/ 1 (fabs x)) 3/4) (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1 (fabs x))))) (* (sqrt (sqrt PI)) (sqrt (expm1 (log1p (sqrt PI))))))
2.0ms
(sqrt PI)
2.0ms
(sqrt PI)
1.0ms
(expm1 (log1p (sqrt PI)))

series1.1s

Counts
4 → 6
Calls
4 calls:
1.1s
(/ (fma (/ (pow (fabs x) -4) (* (* (fabs x) (fabs x)) (fabs x))) 15/8 (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (fma (* (/ 1 (fabs x)) 3/4) (/ (/ 1 (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))) (/ 1 (fabs x))))) (* (sqrt (sqrt PI)) (sqrt (expm1 (log1p (sqrt PI))))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)
0.0ms
(expm1 (log1p (sqrt PI)))

simplify9.8s

Counts
74 → 74
Iterations
IterNodes
411546
31988
2550
1219
0113

prune1.5s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.5b

regimes286.0ms

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
227
127
022

end0.0ms

sample4.8s

Algorithm
intervals
Results
4.6s12440×body80valid