Details

Time bar (total: 5.3s)

sample919.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 50.021364%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 0%

Results
17.0ms89×body2560nan
17.0ms105×body1280nan
10.0ms256×body80valid
5.0ms43×body640nan
1.0ms14×body320nan
1.0ms14×body160nan
1.0ms16×body80nan

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1115
2115

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.9b

Counts
2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
0.0b
(- (* x x) 1.0)
0.2b
(log (+ x (sqrt (- (* x x) 1.0))))
31.6b
(sqrt (- (* x x) 1.0))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×add-sqr-sqrt
8×add-log-exp
6×pow1 add-cube-cbrt
5×add-exp-log
4×log-prod sqrt-prod add-cbrt-cube
2×log-div flip3-- flip3-+ sqrt-div flip-- flip-+ distribute-lft-out difference-of-squares
1×+-commutative sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log rem-log-exp sum-log log-pow
Counts
4 → 56
Calls
4 calls:
6.0ms
(+ x (sqrt (- (* x x) 1.0)))
4.0ms
(- (* x x) 1.0)
8.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
4.0ms
(sqrt (- (* x x) 1.0))

series23.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(+ x (sqrt (- (* x x) 1.0)))
4.0ms
(- (* x x) 1.0)
10.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
4.0ms
(sqrt (- (* x x) 1.0))

simplify138.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0327471
11087435
24892422
35002422

prune112.0ms

Filtered
55 candidates to 68 candidates (-23.6%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New65368
Fresh000
Picked101
Done000
Total66369

Merged error: 0.0b

Counts
69 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.2b
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×sqrt-prod
12×*-un-lft-identity sqrt-div
9×associate-*r*
8×pow1 add-cube-cbrt
7×associate-*l*
6×add-exp-log
5×flip3-+ add-cbrt-cube flip-+ add-log-exp
4×frac-times unswap-sqr
3×log-prod flip3-- pow-prod-down flip--
2×log-div sqrt-pow1 pow1/2 associate-*r/ associate-*l/ difference-of-squares
1×+-commutative sqrt-unprod rem-log-exp prod-exp sum-log log-pow *-commutative cbrt-unprod distribute-lft-out distribute-lft-out--
Counts
3 → 67
Calls
3 calls:
2.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
2.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
12.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series36.0ms

Counts
3 → 9
Calls
3 calls:
9.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
15.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
12.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify44.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0426932
11622865
25001852

prune178.0ms

Filtered
58 candidates to 76 candidates (-31.0%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New76076
Fresh022
Picked011
Done000
Total76379

Merged error: 0.0b

Counts
79 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (log x) (/ (/ 0.25 x) x))
0.1b
(/ (/ 0.25 x) x)
0.2b
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
0.4b
(/ 0.09375 (pow x 4))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
99×times-frac
88×*-un-lft-identity
74×add-sqr-sqrt
65×add-cube-cbrt
16×associate-/l*
14×add-exp-log
12×unpow-prod-down distribute-lft-out--
11×pow1 associate--l+ add-cbrt-cube
10×associate-/r* add-log-exp
9×log-prod
8×distribute-lft-out
7×associate-+r+ log-pow
6×div-exp div-inv
4×cbrt-undiv diff-log sqr-pow
3×sub-neg associate-+l+ sum-log difference-of-squares
2×frac-2neg clear-num
1×+-commutative pow-to-exp associate-+r- flip3-- flip3-+ pow-exp flip-- flip-+ associate-/l/
Counts
4 → 167
Calls
4 calls:
14.0ms
(- (log x) (/ (/ 0.25 x) x))
6.0ms
(/ (/ 0.25 x) x)
32.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
4.0ms
(/ 0.09375 (pow x 4))

series43.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(- (log x) (/ (/ 0.25 x) x))
3.0ms
(/ (/ 0.25 x) x)
10.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
4.0ms
(/ 0.09375 (pow x 4))

simplify61.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
06941225
125461106
250011095

prune263.0ms

Filtered
119 candidates to 179 candidates (-50.4%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1781179
Fresh011
Picked101
Done011
Total1793182

Merged error: 0b

Counts
182 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (log 2) (log (sqrt x)))
0.1b
(/ (/ 0.25 x) x)
0.2b
(+ (+ (log 2) (log (sqrt x))) (- (- (log (sqrt x)) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
0.4b
(/ 0.09375 (pow x 4))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
131×*-un-lft-identity
96×times-frac
67×add-sqr-sqrt add-cube-cbrt
40×distribute-lft-out
29×pow1
25×log-pow distribute-lft-out--
17×add-log-exp
16×associate-+r+ associate-/l*
15×log-prod
14×add-exp-log associate--l+
12×unpow-prod-down
11×add-cbrt-cube
10×associate-/r* sum-log
8×frac-add
6×flip3-+ diff-log div-exp sqrt-prod flip-+ div-inv
4×cbrt-undiv associate-+l+ flip3-- frac-sub flip-- sqr-pow
2×+-commutative sub-neg frac-2neg clear-num
1×pow-to-exp associate-+r- pow-exp associate-/l/
Counts
4 → 195
Calls
4 calls:
5.0ms
(+ (log 2) (log (sqrt x)))
8.0ms
(/ (/ 0.25 x) x)
39.0ms
(+ (+ (log 2) (log (sqrt x))) (- (- (log (sqrt x)) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
4.0ms
(/ 0.09375 (pow x 4))

series22.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(+ (log 2) (log (sqrt x)))
3.0ms
(/ (/ 0.25 x) x)
9.0ms
(+ (+ (log 2) (log (sqrt x))) (- (- (log (sqrt x)) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
4.0ms
(/ 0.09375 (pow x 4))

simplify91.0ms

Algorithm
egg-herbie
Counts
207 → 207
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
09892167
140201966
250011951

prune323.0ms

Filtered
129 candidates to 207 candidates (-60.5%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New2070207
Fresh011
Picked011
Done011
Total2073210

Merged error: 0b

Counts
210 → 3

regimes98.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0139
1139

end0.0ms

sample2.7s

Algorithm
intervals
sampling

Space saved by range analysis: 50.021364%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 0%

Results
561.0ms2941×body2560nan
384.0ms2491×body1280nan
312.0ms8000×body80valid
161.0ms1252×body640nan
56.0ms592×body320nan
20.0ms319×body160nan
10.0ms312×body80nan

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