Details

Time bar (total: 4.1s)

sample304.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
10.0ms275×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

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b
(/ (- 1.0 x) (+ 1.0 x))
0.0b
(atan (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:
7.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
9.0ms
(/ (- 1.0 x) (+ 1.0 x))
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

series156.0ms

Counts
3 → 9
Calls
3 calls:
92.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
55.0ms
(/ (- 1.0 x) (+ 1.0 x))
9.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify43.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0354753
11071709
25001688

prune194.0ms

Filtered
100 candidates to 70 candidates (70.0%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New973100
Fresh000
Picked101
Done000
Total983101

Merged error: 0b

Counts
101 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

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
(sqrt (+ 1.0 x))
3.0ms
(sqrt (- 1.0 x))
3.0ms
(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
9.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

series205.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(sqrt (+ 1.0 x))
54.0ms
(sqrt (- 1.0 x))
2.0ms
(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
94.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

simplify48.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
03871280
112211220
250011157

prune232.0ms

Filtered
140 candidates to 82 candidates (58.6%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1400140
Fresh022
Picked011
Done000
Total1403143

Merged error: 0b

Counts
143 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
148×add-sqr-sqrt
144×*-un-lft-identity
134×times-frac
83×sqrt-prod
72×add-cube-cbrt
41×associate-*r*
32×add-exp-log
27×associate-*l*
20×add-cbrt-cube
18×distribute-lft-out
15×distribute-lft-out-- difference-of-squares unswap-sqr
14×associate-/r*
11×div-exp
8×pow1 sqrt-div prod-exp associate-/r/ associate-/l*
6×cbrt-undiv
4×flip3-+ cbrt-unprod flip-+ div-inv add-log-exp
3×rec-exp pow-flip 1-exp
2×frac-2neg clear-num associate-/l/
1×frac-times flip3-- sqrt-pow1 pow1/2 div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative flip-- inv-pow
Counts
4 → 229
Calls
4 calls:
1.0ms
(atan (sqrt (* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))))
7.0ms
(/ 1 (sqrt (+ 1.0 x)))
9.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))
33.0ms
(* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))

series247.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan (sqrt (* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))))
80.0ms
(/ 1 (sqrt (+ 1.0 x)))
128.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))
38.0ms
(* (/ 1 (sqrt (+ 1.0 x))) (/ (- 1.0 x) (sqrt (+ 1.0 x))))

simplify103.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
08202309
138672013
250011893

prune368.0ms

Filtered
241 candidates to 125 candidates (51.9%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New2410241
Fresh011
Picked011
Done011
Total2413244

Merged error: 0b

Counts
244 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (- 1.0 x))
0.0b
(cbrt (- 1.0 x))
0.0b
(* (cbrt (- 1.0 x)) (cbrt (- 1.0 x)))
0.0b
(/ (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (sqrt (+ 1.0 x)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
38×cbrt-prod add-sqr-sqrt
28×cbrt-div
18×add-cube-cbrt
14×flip3-- flip--
11×pow1 add-exp-log
10×swap-sqr
8×frac-times pow1/3 associate-*r* associate-*l* sqrt-prod associate-/l/ distribute-lft-out--
7×times-frac associate-/r* add-cbrt-cube
6×difference-of-squares
4×associate-*r/ associate-*l/ add-log-exp unswap-sqr
2×cbrt-undiv sqrt-div div-exp pow-prod-down prod-exp associate-/r/ pow-sqr pow-prod-up cbrt-unprod distribute-lft-out
1×pow2 frac-2neg flip3-+ pow-plus clear-num *-commutative flip-+ div-inv associate-/l*
Counts
4 → 125
Calls
4 calls:
3.0ms
(cbrt (- 1.0 x))
3.0ms
(cbrt (- 1.0 x))
11.0ms
(* (cbrt (- 1.0 x)) (cbrt (- 1.0 x)))
18.0ms
(/ (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (sqrt (+ 1.0 x)))

series574.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(cbrt (- 1.0 x))
90.0ms
(cbrt (- 1.0 x))
109.0ms
(* (cbrt (- 1.0 x)) (cbrt (- 1.0 x)))
282.0ms
(/ (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (sqrt (+ 1.0 x)))

simplify75.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06131232
123471151
250011093

prune394.0ms

Filtered
137 candidates to 98 candidates (71.5%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1370137
Fresh000
Picked011
Done022
Total1373140

Merged error: 0b

Counts
140 → 3

regimes18.0ms

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

sample893.0ms

Algorithm
intervals
Results
413.0ms8000×body80valid
299.0ms8051×body80nan

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