Details

Time bar (total: 23.4s)

sample124.0ms

Algorithm
intervals
Results
24.0ms256×body80valid
17.0ms276×body80nan

simplify129.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0911
12011
22111
done2111

prune41.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b
(/ (- 1.0 x) (+ 1.0 x))
0.0b
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
45×add-sqr-sqrt
41×times-frac
26×sqrt-prod
24×add-cube-cbrt
11×distribute-lft-out
9×distribute-lft-out-- difference-of-squares
5×add-exp-log add-cbrt-cube associate-/l*
4×pow1 associate-/r* associate-/r/
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv flip3-- frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp clear-num flip--
Counts
3 → 97
Calls
3 calls:
25.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
80.0ms
(/ (- 1.0 x) (+ 1.0 x))
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

series388.0ms

Counts
3 → 9
Calls
3 calls:
181.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
195.0ms
(/ (- 1.0 x) (+ 1.0 x))
12.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify2.2s

Counts
106 → 106
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01731505
18941422
done50011319

prune408.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1.0 x))
0.0b
(sqrt (- 1.0 x))
0.0b
(atan (fabs (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
0.0b
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
85×sqrt-prod
78×*-un-lft-identity
62×add-sqr-sqrt
56×times-frac
40×add-cube-cbrt
10×distribute-lft-out
9×distribute-lft-out-- difference-of-squares
8×sqrt-div associate-/l*
7×associate-/r*
6×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv sqrt-undiv frac-2neg div-exp clear-num hypot-def div-inv
Counts
4 → 137
Calls
4 calls:
22.0ms
(sqrt (+ 1.0 x))
10.0ms
(sqrt (- 1.0 x))
1.0ms
(atan (fabs (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
35.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

series222.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (+ 1.0 x))
36.0ms
(sqrt (- 1.0 x))
5.0ms
(atan (fabs (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
144.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

simplify1.9s

Counts
149 → 149
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01972270
19892020
done50001914

prune529.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (pow 1.0 3) (pow x 3)))
0.0b
(/ (sqrt (- (pow 1.0 3) (pow x 3))) (sqrt (fma 1.0 1.0 (* (+ x 1.0) x))))
0.0b
(atan (fabs (/ (/ (sqrt (- (pow 1.0 3) (pow x 3))) (sqrt (fma 1.0 1.0 (* (+ x 1.0) x)))) (sqrt (+ 1.0 x)))))
0.0b
(/ (/ (sqrt (- (pow 1.0 3) (pow x 3))) (sqrt (fma 1.0 1.0 (* (+ x 1.0) x)))) (sqrt (+ 1.0 x)))

rewrite685.0ms

Algorithm
rewrite-expression-head
Rules
2851×sqrt-prod
2716×times-frac
2320×add-sqr-sqrt
1881×*-un-lft-identity
975×add-cube-cbrt
896×difference-of-squares
672×unpow-prod-down cube-prod
448×sqr-pow
280×distribute-lft-out--
200×associate-/l*
173×distribute-lft-out
56×difference-cubes
13×associate-/r*
11×add-exp-log add-cbrt-cube
10×div-inv
6×sqrt-div
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×sqrt-undiv associate-/l/
2×flip3-- frac-2neg clear-num associate-/r/ flip--
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 1670
Calls
4 calls:
69.0ms
(sqrt (- (pow 1.0 3) (pow x 3)))
102.0ms
(/ (sqrt (- (pow 1.0 3) (pow x 3))) (sqrt (fma 1.0 1.0 (* (+ x 1.0) x))))
1.0ms
(atan (fabs (/ (/ (sqrt (- (pow 1.0 3) (pow x 3))) (sqrt (fma 1.0 1.0 (* (+ x 1.0) x)))) (sqrt (+ 1.0 x)))))
204.0ms
(/ (/ (sqrt (- (pow 1.0 3) (pow x 3))) (sqrt (fma 1.0 1.0 (* (+ x 1.0) x)))) (sqrt (+ 1.0 x)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (- (pow 1.0 3) (pow x 3)))
124.0ms
(/ (sqrt (- (pow 1.0 3) (pow x 3))) (sqrt (fma 1.0 1.0 (* (+ x 1.0) x))))
10.0ms
(atan (fabs (/ (/ (sqrt (- (pow 1.0 3) (pow x 3))) (sqrt (fma 1.0 1.0 (* (+ x 1.0) x)))) (sqrt (+ 1.0 x)))))
232.0ms
(/ (/ (sqrt (- (pow 1.0 3) (pow x 3))) (sqrt (fma 1.0 1.0 (* (+ x 1.0) x)))) (sqrt (+ 1.0 x)))

simplify1.6s

Counts
1682 → 1682
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0110077410
done500172138

prune6.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (/ (/ (- (pow 1.0 3) (pow x 3)) (fma 1.0 1.0 (* (+ x 1.0) x))) (+ 1.0 x)))
0.0b
(/ (/ (- (pow 1.0 3) (pow x 3)) (fma 1.0 1.0 (* (+ x 1.0) x))) (+ 1.0 x))
0.0b
(atan (fabs (sqrt (/ (/ (- (pow 1.0 3) (pow x 3)) (fma 1.0 1.0 (* (+ x 1.0) x))) (+ 1.0 x)))))
0.0b
(/ (- (pow 1.0 3) (pow x 3)) (fma 1.0 1.0 (* (+ x 1.0) x)))

rewrite538.0ms

Algorithm
rewrite-expression-head
Rules
1385×times-frac
1205×add-sqr-sqrt
1083×*-un-lft-identity
496×difference-of-squares
455×add-cube-cbrt
372×unpow-prod-down cube-prod
322×sqrt-prod
248×sqr-pow
159×distribute-lft-out
155×distribute-lft-out--
104×associate-/l*
31×difference-cubes
12×div-inv
11×add-exp-log add-cbrt-cube
7×associate-/r*
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp associate-/r/ log1p-expm1-u add-log-exp
3×rem-sqrt-square div-sub associate-/l/
2×frac-2neg flip3-+ clear-num flip-+
1×flip3-- sqrt-pow1 pow1/2 sqrt-div flip--
Counts
4 → 885
Calls
4 calls:
141.0ms
(sqrt (/ (/ (- (pow 1.0 3) (pow x 3)) (fma 1.0 1.0 (* (+ x 1.0) x))) (+ 1.0 x)))
138.0ms
(/ (/ (- (pow 1.0 3) (pow x 3)) (fma 1.0 1.0 (* (+ x 1.0) x))) (+ 1.0 x))
1.0ms
(atan (fabs (sqrt (/ (/ (- (pow 1.0 3) (pow x 3)) (fma 1.0 1.0 (* (+ x 1.0) x))) (+ 1.0 x)))))
128.0ms
(/ (- (pow 1.0 3) (pow x 3)) (fma 1.0 1.0 (* (+ x 1.0) x)))

series509.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(sqrt (/ (/ (- (pow 1.0 3) (pow x 3)) (fma 1.0 1.0 (* (+ x 1.0) x))) (+ 1.0 x)))
93.0ms
(/ (/ (- (pow 1.0 3) (pow x 3)) (fma 1.0 1.0 (* (+ x 1.0) x))) (+ 1.0 x))
7.0ms
(atan (fabs (sqrt (/ (/ (- (pow 1.0 3) (pow x 3)) (fma 1.0 1.0 (* (+ x 1.0) x))) (+ 1.0 x)))))
217.0ms
(/ (- (pow 1.0 3) (pow x 3)) (fma 1.0 1.0 (* (+ x 1.0) x)))

simplify1.7s

Counts
897 → 897
Iterations

Useful iterations: done (1.6s)

IterNodesCost
084736640
done500035179

prune3.8s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes22.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01927
12127
done2127

end0.0ms

sample1.8s

Algorithm
intervals
Results
871.0ms8000×body80valid
513.0ms7937×body80nan