Details

Time bar (total: 12.8s)

sample166.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
18.0ms257×body80nan

simplify40.0ms

Counts
1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize66.0ms

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))

rewrite253.0ms

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:
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
40.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
200.0ms
(/ (- 1.0 x) (+ 1.0 x))

series193.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
102.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
86.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify2.1s

Counts
100 → 100

prune305.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite409.0ms

Algorithm
rewrite-expression-head
Rules
184×*-un-lft-identity
91×times-frac
79×add-sqr-sqrt
55×distribute-lft-out
51×associate-*l*
44×unpow-prod-down cube-prod
36×add-cube-cbrt
19×distribute-lft-out-- difference-of-squares
11×add-exp-log sum-cubes add-cbrt-cube
9×pow1 associate-/r*
6×flip3-+ flip-+
5×sqrt-div associate-/l*
4×frac-times associate-*r/ associate-/r/ add-log-exp
3×associate-*r*
2×cbrt-undiv sqrt-pow1 div-exp pow-prod-down associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×distribute-rgt-in flip3-- frac-2neg distribute-lft-in pow1/2 div-sub clear-num sqrt-prod *-commutative flip--
Counts
4 → 175
Calls
4 calls:
1.0ms
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
69.0ms
(/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3)))
66.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
261.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

series375.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
83.0ms
(/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3)))
183.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
96.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

simplify1.6s

Counts
187 → 187

prune747.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
80×sqrt-prod
74×*-un-lft-identity
56×times-frac
55×add-sqr-sqrt
38×add-cube-cbrt
10×distribute-lft-out
8×associate-/l* distribute-lft-out-- difference-of-squares
7×associate-/r*
6×sqrt-div
5×add-exp-log add-cbrt-cube
4×pow1
3×add-log-exp
2×flip3-+ associate-/r/ flip-+ associate-/l/
1×cbrt-undiv rem-sqrt-square sqrt-undiv flip3-- frac-2neg sqrt-pow1 pow1/2 div-exp clear-num flip-- div-inv
Counts
3 → 111
Calls
3 calls:
7.0ms
(sqrt (+ 1.0 x))
10.0ms
(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
30.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

series169.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(sqrt (+ 1.0 x))
3.0ms
(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
135.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

simplify2.3s

Counts
120 → 120

prune328.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes30.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.6s

end0.0ms

sample2.0s

Algorithm
intervals
Results
914.0ms8084×body80nan
702.0ms8000×body80valid