Details

Time bar (total: 3.6s)

sample281.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
6.0ms222×body80nan

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite23.0ms

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:
8.0ms
(/ (- 1.0 x) (+ 1.0 x))
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
10.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))

series156.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(/ (- 1.0 x) (+ 1.0 x))
7.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
115.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))

simplify42.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0354753
11071709
25001690

prune183.0ms

Filtered
100 candidates to 70 candidates (70.0%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New964100
Fresh000
Picked101
Done000
Total974101

Merged error: 0b

Counts
101 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
85×sqrt-prod
78×*-un-lft-identity
60×add-sqr-sqrt
56×times-frac
40×add-cube-cbrt
10×distribute-lft-out
9×distribute-lft-out-- difference-of-squares
8×sqrt-div associate-/l*
7×associate-/r*
6×pow1 add-exp-log add-cbrt-cube
4×add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv sqrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 128
Calls
4 calls:
3.0ms
(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
3.0ms
(sqrt (+ 1.0 x))
3.0ms
(sqrt (- 1.0 x))
10.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

series160.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
30.0ms
(sqrt (+ 1.0 x))
37.0ms
(sqrt (- 1.0 x))
91.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

simplify46.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03531256
110841184
250011121

prune224.0ms

Filtered
140 candidates to 80 candidates (57.1%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1400140
Fresh033
Picked011
Done000
Total1404144

Merged error: 0b

Counts
144 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
150×*-un-lft-identity
130×sqrt-prod
103×add-sqr-sqrt
101×times-frac
64×cbrt-prod
60×add-cube-cbrt
58×unpow-prod-down cube-prod
25×distribute-lft-out
20×distribute-lft-out-- difference-of-squares
10×associate-/r/
7×pow1
5×add-exp-log flip3-+ add-cbrt-cube flip-+ div-inv
4×add-log-exp
3×pow-unpow pow-pow sqrt-div
2×cube-div cube-mult rem-sqrt-square sqrt-pow1 pow1/2 unpow3 sqr-pow
1×pow-to-exp cbrt-div pow1/3 pow-exp sqrt-pow2 rem-cbrt-cube rem-cube-cbrt
Counts
4 → 198
Calls
4 calls:
1.0ms
(atan (cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)))
8.0ms
(sqrt (/ (- 1.0 x) (+ x 1.0)))
13.0ms
(cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))
12.0ms
(pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)

series381.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan (cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)))
93.0ms
(sqrt (/ (- 1.0 x) (+ x 1.0)))
91.0ms
(cbrt (pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3))
195.0ms
(pow (sqrt (/ (- 1.0 x) (+ x 1.0))) 3)

simplify65.0ms

Algorithm
egg-herbie
Counts
210 → 210
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
06112023
118941878
250021838

prune289.0ms

Filtered
210 candidates to 95 candidates (45.2%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New2100210
Fresh022
Picked011
Done011
Total2104214

Merged error: 0b

Counts
214 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
121×*-un-lft-identity
106×sqrt-prod
95×add-sqr-sqrt
93×times-frac
59×add-cube-cbrt
16×distribute-lft-out
15×distribute-lft-out-- difference-of-squares
14×associate-/r*
10×add-exp-log
9×sqrt-div
8×pow1 add-cbrt-cube associate-/l*
6×associate-/r/
4×rem-sqrt-square flip3-+ flip-+ add-log-exp
3×pow-flip sqrt-pow1 pow1/2 div-exp div-inv
2×cbrt-undiv frac-2neg clear-num associate-/l/
1×rec-exp flip3-- 1-exp div-sub flip-- inv-pow
Counts
4 → 185
Calls
4 calls:
3.0ms
(sqrt (+ 1.0 x))
10.0ms
(sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))
7.0ms
(/ 1 (sqrt (+ 1.0 x)))
10.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

series448.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(sqrt (+ 1.0 x))
268.0ms
(sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))
58.0ms
(/ 1 (sqrt (+ 1.0 x)))
92.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

simplify67.0ms

Algorithm
egg-herbie
Counts
197 → 197
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
06521705
122421537
250011492

prune372.0ms

Filtered
197 candidates to 108 candidates (54.8%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1970197
Fresh011
Picked011
Done022
Total1974201

Merged error: 0b

Counts
201 → 4

regimes55.0ms

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
0127
1127

end0.0ms

sample672.0ms

Algorithm
intervals
Results
298.0ms8000×body80valid
199.0ms8036×body80nan

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