Details

Time bar (total: 4.8s)

sample81.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
11.0ms245×body80nan

simplify5.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

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))

rewrite50.0ms

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))))
17.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
27.0ms
(/ (- 1.0 x) (+ 1.0 x))

series156.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
99.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
53.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify36.0ms

Counts
100 → 100

prune236.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize19.0ms

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
(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
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

rewrite265.0ms

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))))))
45.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
48.0ms
(/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3)))
162.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

series268.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
139.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
48.0ms
(/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3)))
73.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

simplify94.0ms

Counts
187 → 187

prune511.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite213.0ms

Algorithm
rewrite-expression-head
Rules
1144×times-frac
1015×*-un-lft-identity
954×sqrt-prod
704×add-sqr-sqrt
461×add-cube-cbrt
164×distribute-lft-out
113×distribute-lft-out-- difference-of-squares
46×associate-/l*
37×sqrt-div
36×associate-/r/
18×flip3-+ flip-+ div-inv
14×associate-/r*
11×add-exp-log add-cbrt-cube
7×rem-sqrt-square
5×pow1
4×cbrt-undiv div-exp add-log-exp
3×div-sub associate-/l/
2×frac-2neg clear-num
1×flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 734
Calls
4 calls:
1.0ms
(atan (sqrt (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))))
64.0ms
(sqrt (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x))))
25.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))
54.0ms
(/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(atan (sqrt (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))))
94.0ms
(sqrt (/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x))))
94.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))
34.0ms
(/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))

simplify152.0ms

Counts
746 → 746

prune943.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes19.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
720.0ms8060×body80nan
410.0ms8000×body80valid