Details

Time bar (total: 5.3s)

sample290.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
6.0ms244×body80nan

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0166
1196
2216
3216

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.0b

Counts
2 → 1

localize11.0ms

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))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
70×*-un-lft-identity
49×add-sqr-sqrt
41×times-frac
26×add-cube-cbrt sqrt-prod
14×sqrt-div
12×distribute-lft-out
10×associate-/l* distribute-lft-out-- difference-of-squares
8×associate-/r*
5×add-exp-log add-cbrt-cube
4×pow1 associate-/r/ associate-/l/
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square flip3-- frac-2neg flip3-+ clear-num flip-- flip-+ div-inv
1×cbrt-undiv sqrt-pow1 pow1/2 div-sub div-exp
Counts
3 → 110
Calls
3 calls:
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
9.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
11.0ms
(/ (- 1.0 x) (+ 1.0 x))

series162.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
100.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
59.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify45.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0388859
11145822
25002804

prune219.0ms

Filtered
119 candidates to 85 candidates (71.4%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1172119
Fresh000
Picked101
Done000
Total1182120

Merged error: 0b

Counts
120 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
1336×sqrt-prod
901×times-frac
820×*-un-lft-identity
595×add-sqr-sqrt
388×add-cube-cbrt
115×distribute-lft-out
101×distribute-lft-out-- difference-of-squares
66×sqrt-div
65×associate-/r*
45×associate-/r/
23×associate-/l*
15×flip3-- flip-- div-inv
8×add-exp-log add-cbrt-cube associate-/l/
5×pow1
4×expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
3×rem-sqrt-square flip3-+ flip-+
2×cbrt-undiv div-exp
1×sqrt-undiv sqrt-pow1 pow1/2
Counts
4 → 677
Calls
4 calls:
4.0ms
(atan (/ (sqrt (sqrt (- 1.0 x))) (sqrt (/ (+ 1.0 x) (sqrt (- 1.0 x))))))
12.0ms
(sqrt (/ (+ 1.0 x) (sqrt (- 1.0 x))))
10.0ms
(/ (+ 1.0 x) (sqrt (- 1.0 x)))
36.0ms
(/ (sqrt (sqrt (- 1.0 x))) (sqrt (/ (+ 1.0 x) (sqrt (- 1.0 x)))))

series451.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan (/ (sqrt (sqrt (- 1.0 x))) (sqrt (/ (+ 1.0 x) (sqrt (- 1.0 x))))))
252.0ms
(sqrt (/ (+ 1.0 x) (sqrt (- 1.0 x))))
96.0ms
(/ (+ 1.0 x) (sqrt (- 1.0 x)))
100.0ms
(/ (sqrt (sqrt (- 1.0 x))) (sqrt (/ (+ 1.0 x) (sqrt (- 1.0 x)))))

simplify179.0ms

Algorithm
egg-herbie
Counts
689 → 689
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
0107812552
1316912157
2500111468

prune1.1s

Filtered
689 candidates to 271 candidates (39.3%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New6890689
Fresh011
Picked011
Done000
Total6892691

Merged error: 0b

Counts
691 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite313.0ms

Algorithm
rewrite-expression-head
Rules
575×*-un-lft-identity
467×add-sqr-sqrt
364×associate-+r+
360×prod-diff
290×associate-*l*
275×add-cube-cbrt
188×associate-*r*
184×distribute-rgt-in distribute-lft-in
138×times-frac
88×pow-unpow sum-cubes
76×frac-times
72×swap-sqr
71×sqrt-prod
64×distribute-lft-out
63×associate-/r*
60×unswap-sqr
59×sqrt-div
56×*-commutative
50×distribute-lft-out--
44×unpow-prod-down
43×flip3-+ flip-+
38×associate-*l/
35×associate-/l*
34×difference-of-squares
14×associate-/l/
11×add-exp-log add-cbrt-cube
9×pow1
7×flip3-- frac-2neg clear-num flip--
6×associate-/r/
4×expm1-log1p-u associate-*r/ log1p-expm1-u add-log-exp
3×rem-sqrt-square div-inv
2×cbrt-undiv +-commutative sub-neg sqrt-pow1 div-exp pow-prod-down prod-exp cbrt-unprod
1×pow1/2 div-sub
Counts
4 → 740
Calls
4 calls:
16.0ms
(/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3)))
1.0ms
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
140.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
92.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

series290.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3)))
7.0ms
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
148.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
80.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

simplify218.0ms

Algorithm
egg-herbie
Counts
752 → 752
Iterations

Useful iterations: 1 (57.0ms)

IterNodesCost
0385716625
1500115214

prune1.1s

Filtered
752 candidates to 270 candidates (35.9%)
Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New7520752
Fresh000
Picked011
Done011
Total7522754

Merged error: 0b

Counts
754 → 2

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

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01411
11411

end0.0ms

sample720.0ms

Algorithm
intervals
Results
319.0ms8000×body80valid
203.0ms7849×body80nan