Details

Time bar (total: 28.7s)

sample134.0ms

Algorithm
intervals
Results
38.0ms199×body80valid
27.0ms22×body640valid
21.0ms21×body1280valid
16.0ms256×pre80true
5.0ms8×body320valid
2.0ms6×body160valid

simplify818.0ms

Counts
1 → 1

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize46.0ms

Local error

Found 3 expressions with local error:

1.9b
(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
0.1b
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
0.0b
(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
51×*-un-lft-identity
31×add-sqr-sqrt times-frac
23×add-cube-cbrt
10×distribute-lft-out
9×associate-/l*
7×associate-/r* add-cbrt-cube add-exp-log
4×distribute-lft-out-- difference-of-squares associate-/l/
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv clear-num frac-2neg flip3-+ div-exp associate-/r/ flip-+ div-inv
1×flip3-- div-sub fma-udef flip--
Counts
3 → 95
Calls
3 calls:
Slowest
20.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
18.0ms
(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
0.0ms
(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series449.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
197.0ms
(fma (/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha)))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
131.0ms
(/ (+ beta alpha) (+ 2.0 (fma 2 i (+ beta alpha))))
121.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))

simplify1.4s

Counts
104 → 104

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.1b

localize45.0ms

Local error

Found 4 expressions with local error:

1.9b
(fma (/ 1 (/ (+ 2.0 (fma 2 i (+ beta alpha))) (+ beta alpha))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
0.5b
(/ 1 (/ (+ 2.0 (fma 2 i (+ beta alpha))) (+ beta alpha)))
0.1b
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
0.0b
(/ (+ 2.0 (fma 2 i (+ beta alpha))) (+ beta alpha))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
175×*-un-lft-identity
161×times-frac
91×add-sqr-sqrt
83×add-cube-cbrt
42×distribute-lft-out
29×associate-/r*
19×add-exp-log
13×add-cbrt-cube
12×associate-/l*
11×associate-/r/
9×div-exp
7×div-inv
6×flip3-+ flip-+
5×pow1 cbrt-undiv
4×expm1-log1p-u insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp difference-of-squares associate-/l/
3×clear-num frac-2neg
2×rec-exp 1-exp
1×flip3-- div-sub fma-udef pow-flip flip-- inv-pow
Counts
4 → 210
Calls
4 calls:
Slowest
30.0ms
(/ 1 (/ (+ 2.0 (fma 2 i (+ beta alpha))) (+ beta alpha)))
18.0ms
(/ (+ 2.0 (fma 2 i (+ beta alpha))) (+ beta alpha))
16.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
4.0ms
(fma (/ 1 (/ (+ 2.0 (fma 2 i (+ beta alpha))) (+ beta alpha))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series641.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
263.0ms
(/ 1 (/ (+ 2.0 (fma 2 i (+ beta alpha))) (+ beta alpha)))
145.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
119.0ms
(/ (+ 2.0 (fma 2 i (+ beta alpha))) (+ beta alpha))
113.0ms
(fma (/ 1 (/ (+ 2.0 (fma 2 i (+ beta alpha))) (+ beta alpha))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

simplify809.0ms

Counts
222 → 222

prune3.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.1b

localize87.0ms

Local error

Found 4 expressions with local error:

8.2b
(fma (/ (/ (+ beta alpha) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
0.4b
(/ (+ beta alpha) (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))))
0.2b
(/ (/ (+ beta alpha) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))))
0.1b
(/ (- beta alpha) (fma 2 i (+ beta alpha)))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
510×*-un-lft-identity
505×times-frac
288×sqrt-prod
238×add-sqr-sqrt
230×add-cube-cbrt
136×distribute-lft-out
43×associate-/l*
20×sqrt-div associate-/r/
17×associate-/r*
13×add-cbrt-cube add-exp-log
11×flip3-+ flip-+ div-inv
5×cbrt-undiv div-exp associate-/l/
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp difference-of-squares
3×clear-num frac-2neg
1×flip3-- div-sub fma-udef flip--
Counts
4 → 409
Calls
4 calls:
Slowest
60.0ms
(/ (/ (+ beta alpha) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))))
38.0ms
(/ (+ beta alpha) (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))))
13.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
1.0ms
(fma (/ (/ (+ beta alpha) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series652.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
231.0ms
(fma (/ (/ (+ beta alpha) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
170.0ms
(/ (+ beta alpha) (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))))
131.0ms
(/ (- beta alpha) (fma 2 i (+ beta alpha)))
120.0ms
(/ (/ (+ beta alpha) (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (sqrt (+ 2.0 (fma 2 i (+ beta alpha)))))

simplify1.8s

Counts
421 → 421

prune7.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.1b

localize93.0ms

Local error

Found 4 expressions with local error:

7.7b
(fma (* (/ (+ beta alpha) (sqrt (* (cbrt (+ 2.0 (fma 2 i (+ beta alpha)))) (cbrt (+ 2.0 (fma 2 i (+ beta alpha))))))) (/ (/ 1 (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (sqrt (cbrt (+ 2.0 (fma 2 i (+ beta alpha))))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)
0.7b
(cbrt (+ 2.0 (fma 2 i (+ beta alpha))))
0.7b
(cbrt (+ 2.0 (fma 2 i (+ beta alpha))))
0.7b
(cbrt (+ 2.0 (fma 2 i (+ beta alpha))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-div
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 flip-+ distribute-lft-out
1×fma-udef
Counts
4 → 62
Calls
4 calls:
Slowest
3.0ms
(cbrt (+ 2.0 (fma 2 i (+ beta alpha))))
3.0ms
(cbrt (+ 2.0 (fma 2 i (+ beta alpha))))
3.0ms
(cbrt (+ 2.0 (fma 2 i (+ beta alpha))))
0.0ms
(fma (* (/ (+ beta alpha) (sqrt (* (cbrt (+ 2.0 (fma 2 i (+ beta alpha)))) (cbrt (+ 2.0 (fma 2 i (+ beta alpha))))))) (/ (/ 1 (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (sqrt (cbrt (+ 2.0 (fma 2 i (+ beta alpha))))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
343.0ms
(cbrt (+ 2.0 (fma 2 i (+ beta alpha))))
329.0ms
(cbrt (+ 2.0 (fma 2 i (+ beta alpha))))
310.0ms
(cbrt (+ 2.0 (fma 2 i (+ beta alpha))))
239.0ms
(fma (* (/ (+ beta alpha) (sqrt (* (cbrt (+ 2.0 (fma 2 i (+ beta alpha)))) (cbrt (+ 2.0 (fma 2 i (+ beta alpha))))))) (/ (/ 1 (sqrt (+ 2.0 (fma 2 i (+ beta alpha))))) (sqrt (cbrt (+ 2.0 (fma 2 i (+ beta alpha))))))) (/ (- beta alpha) (fma 2 i (+ beta alpha))) 1.0)

simplify1.1s

Counts
74 → 74

prune1.6s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 13.1b

regimes587.0ms

Accuracy

0% (0.4b remaining)

Error of 12.8b against oracle of 12.3b and baseline of 12.8b

bsearch8.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.1s6320×body80valid
1.0s554×body1280valid
472.0ms8000×pre80true
383.0ms550×body640valid
206.0ms377×body320valid
64.0ms199×body160valid