Details

Time bar (total: 19.5s)

sample139.0ms

Algorithm
intervals
Results
25.0ms256×body80valid
17.0ms276×body80nan

simplify81.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0911
11611
21911
32111
done2111

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

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))))

rewrite78.0ms

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:
19.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
45.0ms
(/ (- 1.0 x) (+ 1.0 x))
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

series177.0ms

Counts
3 → 9
Calls
3 calls:
128.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
38.0ms
(/ (- 1.0 x) (+ 1.0 x))
10.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify2.1s

Counts
106 → 106
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01731505
13721422
29201333
323331320
done50001300

prune349.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize26.0ms

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)))

rewrite71.0ms

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:
8.0ms
(sqrt (+ 1.0 x))
20.0ms
(sqrt (- 1.0 x))
6.0ms
(atan (fabs (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
31.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

series212.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(sqrt (+ 1.0 x))
38.0ms
(sqrt (- 1.0 x))
3.0ms
(atan (fabs (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))
128.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

simplify2.2s

Counts
149 → 149
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01972270
13742032
28611954
320131918
done50011906

prune556.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite718.0ms

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:
88.0ms
(/ (sqrt (- (pow 1.0 3) (pow x 3))) (sqrt (fma 1.0 1.0 (* x (+ x 1.0)))))
69.0ms
(sqrt (- (pow 1.0 3) (pow x 3)))
1.0ms
(atan (fabs (/ (/ (sqrt (- (pow 1.0 3) (pow x 3))) (sqrt (fma 1.0 1.0 (* x (+ x 1.0))))) (sqrt (+ 1.0 x)))))
199.0ms
(/ (/ (sqrt (- (pow 1.0 3) (pow x 3))) (sqrt (fma 1.0 1.0 (* x (+ x 1.0))))) (sqrt (+ 1.0 x)))

series399.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (sqrt (- (pow 1.0 3) (pow x 3))) (sqrt (fma 1.0 1.0 (* x (+ x 1.0)))))
86.0ms
(sqrt (- (pow 1.0 3) (pow x 3)))
10.0ms
(atan (fabs (/ (/ (sqrt (- (pow 1.0 3) (pow x 3))) (sqrt (fma 1.0 1.0 (* x (+ x 1.0))))) (sqrt (+ 1.0 x)))))
197.0ms
(/ (/ (sqrt (- (pow 1.0 3) (pow x 3))) (sqrt (fma 1.0 1.0 (* x (+ x 1.0))))) (sqrt (+ 1.0 x)))

simplify3.0s

Counts
1682 → 1682
Iterations

Useful iterations: done (2.8s)

IterNodesCost
0109877410
1229168723
2453067846
done500167844

prune5.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite99.0ms

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:
42.0ms
(sqrt (/ (- 1.0 x) (+ x 1.0)))
48.0ms
(/ (- 1.0 x) (+ x 1.0))
1.0ms
(atan (fabs (sqrt (/ (- 1.0 x) (+ x 1.0)))))

series188.0ms

Counts
3 → 9
Calls
3 calls:
123.0ms
(sqrt (/ (- 1.0 x) (+ x 1.0)))
60.0ms
(/ (- 1.0 x) (+ x 1.0))
6.0ms
(atan (fabs (sqrt (/ (- 1.0 x) (+ x 1.0)))))

simplify1.8s

Counts
106 → 106
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01751520
13721437
29371333
324001320
done50011312

prune385.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes20.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01927
12127
done2127

end0.0ms

sample1.7s

Algorithm
intervals
Results
814.0ms8000×body80valid
445.0ms7937×body80nan