Details

Time bar (total: 7.4s)

sample82.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
10.0ms243×body80nan

simplify57.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0911
11611
21911
32111
done2111

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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))))
18.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
25.0ms
(/ (- 1.0 x) (+ 1.0 x))

series168.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
111.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
52.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify817.0ms

Counts
100 → 100
Iterations

Useful iterations: done (812.0ms)

IterNodesCost
01621425
13481350
212551262
done50001258

prune373.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize42.0ms

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))))

rewrite400.0ms

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))))))
61.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
89.0ms
(/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3)))
226.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

series383.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
216.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
65.0ms
(/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3)))
86.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

simplify2.4s

Counts
187 → 187
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02454533
18084051
239353779
done50013773

prune833.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes94.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
11111
done1111

end0.0ms

sample1.6s

Algorithm
intervals
Results
635.0ms8000×body80valid
574.0ms7917×body80nan