Details

Time bar (total: 4.8s)

sample282.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
8.0ms244×body80nan

simplify25.0ms

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 (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.0b

Counts
2 → 1

localize10.0ms

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))

rewrite27.0ms

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))

series156.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
96.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
57.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify44.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0388859
11145822
25002804

prune214.0ms

Filtered
119 candidates to 85 candidates (28.6%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1172119
Fresh000
Picked101
Done000
Total1182120

Merged error: 0b

Counts
120 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(atan (sqrt (/ 1 (/ (+ 1.0 x) (- 1.0 x)))))
0.0b
(sqrt (/ 1 (/ (+ 1.0 x) (- 1.0 x))))
0.0b
(/ (+ 1.0 x) (- 1.0 x))
0.0b
(/ 1 (/ (+ 1.0 x) (- 1.0 x)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
342×times-frac
333×*-un-lft-identity
241×add-sqr-sqrt
154×add-cube-cbrt
96×sqrt-prod
67×associate-/r*
49×distribute-lft-out
46×associate-/r/
39×distribute-lft-out-- difference-of-squares
32×sqrt-div
20×associate-/l*
17×add-exp-log
11×add-cbrt-cube div-inv
9×flip3-- flip--
8×div-exp
7×pow1
6×clear-num associate-/l/
5×rem-sqrt-square frac-2neg
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-pow1 flip3-+ flip-+ remove-double-div
2×rec-exp pow-flip 1-exp inv-pow
1×pow1/2
Counts
4 → 348
Calls
4 calls:
1.0ms
(atan (sqrt (/ 1 (/ (+ 1.0 x) (- 1.0 x)))))
21.0ms
(sqrt (/ 1 (/ (+ 1.0 x) (- 1.0 x))))
11.0ms
(/ (+ 1.0 x) (- 1.0 x))
14.0ms
(/ 1 (/ (+ 1.0 x) (- 1.0 x)))

series172.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan (sqrt (/ 1 (/ (+ 1.0 x) (- 1.0 x)))))
95.0ms
(sqrt (/ 1 (/ (+ 1.0 x) (- 1.0 x))))
34.0ms
(/ (+ 1.0 x) (- 1.0 x))
40.0ms
(/ 1 (/ (+ 1.0 x) (- 1.0 x)))

simplify103.0ms

Algorithm
egg-herbie
Counts
360 → 360
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
07803335
130903013
250012668

prune411.0ms

Filtered
360 candidates to 160 candidates (55.6%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New3591360
Fresh101
Picked011
Done000
Total3602362

Merged error: 0b

Counts
362 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (pow 1.0 3) (pow x 3)) (* (- 1.0 x) (fma x (- x 1.0) (* 1.0 1.0))))
0.0b
(sqrt (/ 1 (/ (+ (pow 1.0 3) (pow x 3)) (* (- 1.0 x) (fma x (- x 1.0) (* 1.0 1.0))))))
0.0b
(/ 1 (/ (+ (pow 1.0 3) (pow x 3)) (* (- 1.0 x) (fma x (- x 1.0) (* 1.0 1.0)))))
0.0b
(* (- 1.0 x) (fma x (- x 1.0) (* 1.0 1.0)))

rewrite303.0ms

Algorithm
rewrite-expression-head
Rules
1936×times-frac
1870×*-un-lft-identity
1018×add-sqr-sqrt
662×add-cube-cbrt
516×pow-unpow sum-cubes
428×sqrt-prod
425×associate-*l*
306×associate-/r*
259×distribute-lft-out
258×unpow-prod-down
255×associate-*r*
138×sqrt-div
87×unswap-sqr
85×*-commutative distribute-lft-out-- difference-of-squares
74×associate-/r/
35×associate-/l*
32×add-exp-log
20×associate-*l/ add-cbrt-cube
14×div-exp
11×div-inv
10×flip3-- flip--
9×pow1
7×cbrt-undiv rem-sqrt-square
6×clear-num associate-/l/
5×frac-2neg prod-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rec-exp sqrt-pow1 flip3-+ 1-exp cbrt-unprod flip-+ remove-double-div
2×pow-flip fma-udef inv-pow
1×distribute-rgt-in distribute-lft-in pow1/2 pow-prod-down
Counts
4 → 1369
Calls
4 calls:
26.0ms
(/ (+ (pow 1.0 3) (pow x 3)) (* (- 1.0 x) (fma x (- x 1.0) (* 1.0 1.0))))
81.0ms
(sqrt (/ 1 (/ (+ (pow 1.0 3) (pow x 3)) (* (- 1.0 x) (fma x (- x 1.0) (* 1.0 1.0))))))
43.0ms
(/ 1 (/ (+ (pow 1.0 3) (pow x 3)) (* (- 1.0 x) (fma x (- x 1.0) (* 1.0 1.0)))))
7.0ms
(* (- 1.0 x) (fma x (- x 1.0) (* 1.0 1.0)))

series368.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(/ (+ (pow 1.0 3) (pow x 3)) (* (- 1.0 x) (fma x (- x 1.0) (* 1.0 1.0))))
152.0ms
(sqrt (/ 1 (/ (+ (pow 1.0 3) (pow x 3)) (* (- 1.0 x) (fma x (- x 1.0) (* 1.0 1.0))))))
80.0ms
(/ 1 (/ (+ (pow 1.0 3) (pow x 3)) (* (- 1.0 x) (fma x (- x 1.0) (* 1.0 1.0)))))
52.0ms
(* (- 1.0 x) (fma x (- x 1.0) (* 1.0 1.0)))

simplify304.0ms

Algorithm
egg-herbie
Counts
1381 → 1381
Iterations

Useful iterations: 1 (50.0ms)

IterNodesCost
0287024725
1500122078

prune1.6s

Filtered
1381 candidates to 404 candidates (70.7%)
Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New138101381
Fresh000
Picked011
Done011
Total138121383

Merged error: 0b

Counts
1383 → 2

regimes15.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02313
12313

end0.0ms

sample697.0ms

Algorithm
intervals
Results
314.0ms8000×body80valid
192.0ms7941×body80nan