Details

Time bar (total: 5.6s)

sample47.0ms

Algorithm
intervals
Results
12.0ms508×body80nan
11.0ms229×body160nan
7.0ms256×body80valid

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
0.2b
(log (+ x (sqrt (- (* x x) 1.0))))
28.5b
(sqrt (- (* x x) 1.0))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
7×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×add-exp-log log-prod sqrt-prod
3×add-cbrt-cube
2×log-div flip3-+ sqrt-div flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square flip3-- sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow flip-- difference-of-squares
Counts
3 → 43
Calls
3 calls:
6.0ms
(+ x (sqrt (- (* x x) 1.0)))
7.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
4.0ms
(sqrt (- (* x x) 1.0))

series319.0ms

Counts
3 → 9
Calls
3 calls:
70.0ms
(+ x (sqrt (- (* x x) 1.0)))
198.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
51.0ms
(sqrt (- (* x x) 1.0))

simplify133.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 3 (128.0ms)

IterNodesCost
0316408
11042379
24663366
35003365

prune143.0ms

Filtered
52 candidates to 43 candidates (82.7%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

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:
17.0ms
(- (log x) (/ (/ 0.25 x) x))
5.0ms
(/ 0.09375 (pow x 4))
7.0ms
(/ (/ 0.25 x) x)
38.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))

series660.0ms

Counts
4 → 12
Calls
4 calls:
497.0ms
(- (log x) (/ (/ 0.25 x) x))
35.0ms
(/ 0.09375 (pow x 4))
29.0ms
(/ (/ 0.25 x) x)
97.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))

simplify65.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
06831218
124921094
250011089

prune482.0ms

Filtered
179 candidates to 117 candidates (65.4%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

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))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
22×sqrt-prod
16×*-un-lft-identity
14×sqrt-div
10×pow1 add-cube-cbrt
9×associate-*r*
7×add-exp-log associate-*l*
6×add-cbrt-cube add-log-exp
5×flip3-+ flip-+
4×frac-times flip3-- flip-- difference-of-squares unswap-sqr
3×log-prod sqrt-pow1 pow1/2 pow-prod-down
2×log-div associate-*r/ associate-*l/ distribute-lft-out--
1×+-commutative rem-sqrt-square sqrt-unprod rem-log-exp prod-exp sum-log log-pow *-commutative cbrt-unprod distribute-lft-out
Counts
4 → 85
Calls
4 calls:
4.0ms
(sqrt (- x (sqrt 1.0)))
3.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
3.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
13.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series716.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(sqrt (- x (sqrt 1.0)))
151.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
286.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
205.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify48.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04941102
117341015
25002995

prune292.0ms

Filtered
97 candidates to 73 candidates (75.3%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt x) (cbrt x))
0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 73
Calls
4 calls:
6.0ms
(* (cbrt x) (cbrt x))
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series741.0ms

Counts
4 → 12
Calls
4 calls:
203.0ms
(* (cbrt x) (cbrt x))
176.0ms
(cbrt x)
178.0ms
(cbrt x)
183.0ms
(cbrt x)

simplify87.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 3 (82.0ms)

IterNodesCost
0115288
1472261
22959238
35003235

prune326.0ms

Filtered
85 candidates to 64 candidates (75.3%)
Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes14.0ms

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

sample1.4s

Algorithm
intervals
Results
378.0ms15888×body80nan
369.0ms7614×body160nan
238.0ms8000×body80valid