Details

Time bar (total: 13.9s)

sample87.0ms

Algorithm
intervals
Results
21.0ms115×body2560nan
17.0ms519×body80nan
14.0ms90×body1280nan
10.0ms256×body80valid
5.0ms37×body640nan
2.0ms17×body320nan
1.0ms10×body160nan

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1115
2115

prune2.0ms

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: 32.9b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* x x) 1.0)
0.0b
(+ x (sqrt (- (* x x) 1.0)))
0.2b
(log (+ x (sqrt (- (* x x) 1.0))))
30.6b
(sqrt (- (* x x) 1.0))

rewrite21.0ms

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:
4.0ms
(- (* x x) 1.0)
6.0ms
(+ x (sqrt (- (* x x) 1.0)))
6.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
4.0ms
(sqrt (- (* x x) 1.0))

series338.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(- (* x x) 1.0)
66.0ms
(+ x (sqrt (- (* x x) 1.0)))
186.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
49.0ms
(sqrt (- (* x x) 1.0))

simplify134.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0327471
11087435
24892422
35001422

prune137.0ms

Filtered
68 candidates to 55 candidates (80.9%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New66268
Fresh000
Picked101
Done000
Total67269

Merged error: 0.0b

Counts
69 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x (sqrt 1.0)))
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))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×sqrt-prod
16×*-un-lft-identity
14×sqrt-div
10×pow1 add-cube-cbrt
9×associate-*r*
7×add-exp-log associate-*l*
6×flip3-+ add-cbrt-cube flip-+ add-log-exp
4×frac-times unswap-sqr
3×log-prod flip3-- sqrt-pow1 pow1/2 pow-prod-down flip--
2×log-div associate-*r/ associate-*l/ distribute-lft-out difference-of-squares
1×+-commutative rem-sqrt-square sqrt-unprod rem-log-exp prod-exp sum-log log-pow *-commutative cbrt-unprod distribute-lft-out--
Counts
4 → 83
Calls
4 calls:
4.0ms
(sqrt (+ x (sqrt 1.0)))
3.0ms
(+ 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))))))
16.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series672.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(sqrt (+ x (sqrt 1.0)))
138.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
279.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
192.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify48.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04911081
11717994
25002974

prune237.0ms

Filtered
95 candidates to 72 candidates (75.8%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New94195
Fresh011
Picked011
Done000
Total94397

Merged error: 0b

Counts
97 → 3

localize15.0ms

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))))
0.3b
(/ 0.09375 (pow x 4))

rewrite71.0ms

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:
19.0ms
(- (log x) (/ (/ 0.25 x) x))
7.0ms
(/ (/ 0.25 x) x)
34.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
5.0ms
(/ 0.09375 (pow x 4))

series461.0ms

Counts
4 → 12
Calls
4 calls:
300.0ms
(- (log x) (/ (/ 0.25 x) x))
29.0ms
(/ (/ 0.25 x) x)
95.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
37.0ms
(/ 0.09375 (pow x 4))

simplify60.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
06831218
124921094
250011089

prune356.0ms

Filtered
179 candidates to 117 candidates (65.4%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1790179
Fresh011
Picked011
Done011
Total1793182

Merged error: 0b

Counts
182 → 3

localize25.0ms

Local error

Found 4 expressions with local error:

5.4b
(+ (* x x) (- (* (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))) (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))) (* x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))
31.8b
(log (+ (* x x) (- (* (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))) (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))) (* x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))))
42.3b
(log (+ (pow x 3) (pow (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))) 3)))
44.2b
(- (* (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))) (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))) (* x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))

rewrite283.0ms

Algorithm
rewrite-expression-head
Rules
2752×sqrt-div
1432×frac-times
1192×associate-*r/
691×flip3-+ flip-+
689×flip3-- flip--
640×frac-sub
532×associate-*l/
20×sub-div
11×add-log-exp
8×log-prod *-un-lft-identity
6×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt
4×log-div add-cbrt-cube
2×sub-neg associate-+r+ diff-log rem-log-exp sum-log log-pow
1×+-commutative associate-+r- distribute-rgt-out-- sum-cubes distribute-lft-out
Counts
4 → 718
Calls
4 calls:
27.0ms
(+ (* x x) (- (* (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))) (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))) (* x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))
21.0ms
(log (+ (* x x) (- (* (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))) (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))) (* x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))))
8.0ms
(log (+ (pow x 3) (pow (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))) 3)))
64.0ms
(- (* (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))) (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))) (* x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))

series1.6s

Counts
4 → 12
Calls
4 calls:
244.0ms
(+ (* x x) (- (* (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))) (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))) (* x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))
498.0ms
(log (+ (* x x) (- (* (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))) (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))) (* x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))))
490.0ms
(log (+ (pow x 3) (pow (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))) 3)))
395.0ms
(- (* (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))) (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))) (* x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))

simplify490.0ms

Algorithm
egg-herbie
Counts
730 → 730
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
0500160857

prune6.2s

Filtered
730 candidates to 709 candidates (97.1%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New7300730
Fresh000
Picked011
Done022
Total7303733

Merged error: 0b

Counts
733 → 3

regimes18.0ms

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

sample2.5s

Algorithm
intervals
Results
596.0ms3062×body2560nan
559.0ms16376×body80nan
401.0ms2500×body1280nan
328.0ms8000×body80valid
162.0ms1265×body640nan
60.0ms612×body320nan
21.0ms313×body160nan

Profiling

Loading profile data...