Details

Time bar (total: 22.8s)

sample258.0ms

Algorithm
intervals
Results
24.0ms256×body80valid
18.0ms240×body80nan

simplify43.0ms

Counts
1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

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))

rewrite338.0ms

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×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 → 91
Calls
3 calls:
38.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
51.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
230.0ms
(/ (- 1.0 x) (+ 1.0 x))

series386.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
265.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
81.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify1.9s

Counts
100 → 100

prune460.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite339.0ms

Algorithm
rewrite-expression-head
Rules
1144×times-frac
1018×*-un-lft-identity
958×sqrt-prod
706×add-sqr-sqrt
462×add-cube-cbrt
165×distribute-lft-out
113×distribute-lft-out-- difference-of-squares
46×associate-/l*
39×sqrt-div
36×associate-/r/
19×flip3-+ flip-+
18×div-inv
14×associate-/r*
11×add-exp-log add-cbrt-cube
8×rem-sqrt-square
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×div-sub associate-/l/
2×frac-2neg sqrt-pow1 pow1/2 clear-num
1×flip3-- flip--
Counts
4 → 743
Calls
4 calls:
15.0ms
(sqrt (+ 1.0 x))
90.0ms
(/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))
88.0ms
(sqrt (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x))))
34.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

series369.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(sqrt (+ 1.0 x))
43.0ms
(/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))
132.0ms
(sqrt (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x))))
146.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

simplify1.6s

Counts
755 → 755

prune1.5s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize67.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
3710×sqrt-prod
2886×times-frac
2821×*-un-lft-identity
1841×add-sqr-sqrt
973×add-cube-cbrt
672×distribute-lft-out
669×associate-*l*
420×unpow-prod-down cube-prod
252×distribute-lft-out-- difference-of-squares
105×sum-cubes
88×unswap-sqr
72×associate-/l*
69×associate-*r*
68×sqrt-div
50×associate-/r/
27×flip3-+ flip-+
25×div-inv
20×associate-/r*
13×add-exp-log add-cbrt-cube
10×pow1
6×sqrt-pow1
4×cbrt-undiv pow1/2 div-exp add-log-exp
3×pow-prod-down associate-/l/
2×rem-sqrt-square frac-2neg div-sub clear-num
1×frac-times sqrt-undiv sqrt-unprod associate-*r/ associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 1712
Calls
4 calls:
16.0ms
(sqrt (sqrt (+ 1.0 x)))
64.0ms
(/ (sqrt (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))) (sqrt (sqrt (+ 1.0 x))))
1.4s
(* (sqrt (/ (/ (- 1.0 x) (sqrt (+ (pow 1.0 3) (pow x 3)))) (sqrt (sqrt (+ 1.0 x))))) (sqrt (/ (sqrt (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))) (sqrt (sqrt (+ 1.0 x))))))
121.0ms
(/ (/ (- 1.0 x) (sqrt (+ (pow 1.0 3) (pow x 3)))) (sqrt (sqrt (+ 1.0 x))))

series1.3s

Counts
4 → 12
Calls
4 calls:
115.0ms
(sqrt (sqrt (+ 1.0 x)))
317.0ms
(/ (sqrt (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))) (sqrt (sqrt (+ 1.0 x))))
451.0ms
(* (sqrt (/ (/ (- 1.0 x) (sqrt (+ (pow 1.0 3) (pow x 3)))) (sqrt (sqrt (+ 1.0 x))))) (sqrt (/ (sqrt (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))) (sqrt (sqrt (+ 1.0 x))))))
381.0ms
(/ (/ (- 1.0 x) (sqrt (+ (pow 1.0 3) (pow x 3)))) (sqrt (sqrt (+ 1.0 x))))

simplify2.4s

Counts
1724 → 1724

prune8.2s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes26.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify28.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
548.0ms8000×body80valid
533.0ms8049×body80nan