Details

Time bar (total: 10.4s)

sample94.0ms

Algorithm
intervals
Results
17.0ms256×body80valid
10.0ms245×body80nan

simplify62.0ms

Counts
1 → 1
Iterations
IterNodes
done21
321
219
116
09

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite51.0ms

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-cbrt-cube add-exp-log associate-/l*
4×pow1 associate-/r* associate-/r/
3×add-log-exp
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv clear-num frac-2neg sqrt-pow1 flip3-- pow1/2 sqrt-div div-sub div-exp flip--
Counts
3 → 91
Calls
3 calls:
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
16.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
21.0ms
(/ (- 1.0 x) (+ 1.0 x))

series141.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
92.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
44.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify738.0ms

Counts
100 → 100
Iterations
IterNodes
done5001
21250
1348
0162

prune445.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
85×sqrt-prod
78×*-un-lft-identity
60×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-cbrt-cube add-exp-log
4×add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ flip3-- pow1/2 associate-/r/ flip-+ flip-- associate-/l/
1×cbrt-undiv sqrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 128
Calls
4 calls:
37.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
11.0ms
(sqrt (- 1.0 x))
11.0ms
(sqrt (+ 1.0 x))
1.0ms
(atan (fabs (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))

series201.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
41.0ms
(sqrt (- 1.0 x))
36.0ms
(sqrt (+ 1.0 x))
5.0ms
(atan (fabs (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))))

simplify643.0ms

Counts
140 → 140
Iterations
IterNodes
done5000
21146
1344
0184

prune594.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
28×times-frac
24×sqrt-prod
23×add-sqr-sqrt
22×add-cube-cbrt
8×distribute-lft-out
7×associate-/l*
6×difference-of-squares
5×add-cbrt-cube add-exp-log
4×pow1 associate-/r* sqrt-div
3×add-log-exp
2×flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp flip-+ div-inv
Counts
3 → 78
Calls
3 calls:
8.0ms
(sqrt (- (* 1.0 1.0) (* x x)))
0.0ms
(atan (fabs (/ (sqrt (- (* 1.0 1.0) (* x x))) (+ x 1.0))))
19.0ms
(/ (sqrt (- (* 1.0 1.0) (* x x))) (+ x 1.0))

series247.0ms

Counts
3 → 9
Calls
3 calls:
110.0ms
(sqrt (- (* 1.0 1.0) (* x x)))
8.0ms
(atan (fabs (/ (sqrt (- (* 1.0 1.0) (* x x))) (+ x 1.0))))
128.0ms
(/ (sqrt (- (* 1.0 1.0) (* x x))) (+ x 1.0))

simplify886.0ms

Counts
87 → 87
Iterations
IterNodes
done5002
21645
1383
0167

prune595.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (sqrt (+ x 1.0)))
0.0b
(cbrt (sqrt (+ 1.0 x)))
0.0b
(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
0.0b
(/ (/ (sqrt (- 1.0 x)) (* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))) (cbrt (sqrt (+ 1.0 x))))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
209×cbrt-prod
198×*-un-lft-identity
175×sqrt-prod
160×add-sqr-sqrt
150×cbrt-div sqrt-div
116×add-cube-cbrt
90×associate-/r/
75×flip3-+ flip-+
48×frac-times
29×distribute-lft-out
24×associate-*l/ associate-*r/
20×associate-/l*
15×add-exp-log
14×swap-sqr
12×div-inv
11×pow1 distribute-lft-out-- difference-of-squares
10×associate-/r* associate-*r* associate-*l*
9×unswap-sqr
8×add-cbrt-cube pow1/3
5×cbrt-undiv div-exp
4×add-log-exp
2×pow-prod-down prod-exp pow-sqr pow-prod-up cbrt-unprod
1×pow2 clear-num frac-2neg pow-plus *-commutative associate-/l/
Counts
4 → 352
Calls
4 calls:
8.0ms
(cbrt (sqrt (+ x 1.0)))
9.0ms
(cbrt (sqrt (+ 1.0 x)))
47.0ms
(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
81.0ms
(/ (/ (sqrt (- 1.0 x)) (* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))) (cbrt (sqrt (+ 1.0 x))))

series554.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(cbrt (sqrt (+ x 1.0)))
141.0ms
(cbrt (sqrt (+ 1.0 x)))
161.0ms
(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
125.0ms
(/ (/ (sqrt (- 1.0 x)) (* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))) (cbrt (sqrt (+ 1.0 x))))

simplify659.0ms

Counts
364 → 364
Iterations
IterNodes
done5001
11266
0525

prune1.9s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes30.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done14
114
012

end0.0ms

sample2.1s

Algorithm
intervals
Results
933.0ms8043×body80nan
790.0ms8000×body80valid