Details

Time bar (total: 6.4s)

sample84.0ms

Algorithm
intervals
Results
21.0ms94×body2560nan
18.0ms524×body80nan
13.0ms82×body1280nan
10.0ms256×body80valid
4.0ms32×body640nan
2.0ms23×body320nan
1.0ms9×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: 32.6b

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))))
30.3b
(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:
6.0ms
(+ x (sqrt (- (* x x) 1.0)))
4.0ms
(- (* x x) 1.0)
6.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
4.0ms
(sqrt (- (* x x) 1.0))

series368.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(+ x (sqrt (- (* x x) 1.0)))
44.0ms
(- (* x x) 1.0)
201.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
57.0ms
(sqrt (- (* x x) 1.0))

simplify158.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0327471
11087435
24892422
35002422

prune219.0ms

Filtered
68 candidates to 55 candidates (80.9%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New65368
Fresh000
Picked101
Done000
Total66369

Merged error: 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))))

series757.0ms

Counts
3 → 9
Calls
3 calls:
159.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
305.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
293.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify44.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0424932
11608865
25002852

prune189.0ms

Filtered
76 candidates to 58 candidates (76.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New76076
Fresh022
Picked011
Done000
Total76379

Merged error: 0b

Counts
79 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (log x) (/ (/ 0.25 x) x))
0.1b
(/ (/ 0.25 x) x)
0.3b
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
0.3b
(/ 0.09375 (pow x 4))

rewrite66.0ms

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)
35.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
5.0ms
(/ 0.09375 (pow x 4))

series481.0ms

Counts
4 → 12
Calls
4 calls:
317.0ms
(- (log x) (/ (/ 0.25 x) x))
25.0ms
(/ (/ 0.25 x) x)
97.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
41.0ms
(/ 0.09375 (pow x 4))

simplify70.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
06831218
124921094
250011089

prune375.0ms

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

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(log (+ x (sqrt (- (* x x) 1.0))))
0.5b
(* (sqrt (log (+ x (sqrt (- (* x x) 1.0))))) (sqrt (log (+ x (sqrt (- (* x x) 1.0))))))
30.3b
(sqrt (- (* x x) 1.0))
30.3b
(sqrt (- (* x x) 1.0))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
34×sqrt-prod
31×add-sqr-sqrt
28×pow1
19×*-un-lft-identity
15×add-cube-cbrt
11×swap-sqr
10×sqrt-pow1 pow1/2
7×add-exp-log associate-*r* associate-*l* log-pow
6×add-cbrt-cube
5×pow-prod-up
4×log-prod sqrt-div add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square log-div flip3-- flip-- difference-of-squares
1×pow2 flip3-+ pow-plus sqrt-unprod rem-log-exp prod-exp rem-square-sqrt *-commutative cbrt-unprod flip-+ distribute-lft-out
Counts
4 → 101
Calls
4 calls:
6.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
6.0ms
(* (sqrt (log (+ x (sqrt (- (* x x) 1.0))))) (sqrt (log (+ x (sqrt (- (* x x) 1.0))))))
4.0ms
(sqrt (- (* x x) 1.0))
4.0ms
(sqrt (- (* x x) 1.0))

series700.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
392.0ms
(* (sqrt (log (+ x (sqrt (- (* x x) 1.0))))) (sqrt (log (+ x (sqrt (- (* x x) 1.0))))))
58.0ms
(sqrt (- (* x x) 1.0))
58.0ms
(sqrt (- (* x x) 1.0))

simplify49.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0341922
11476829
25001787

prune230.0ms

Filtered
113 candidates to 68 candidates (60.2%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1130113
Fresh000
Picked011
Done022
Total1133116

Merged error: 0b

Counts
116 → 3

regimes53.0ms

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
587.0ms2968×body2560nan
549.0ms15920×body80nan
407.0ms2532×body1280nan
331.0ms8000×body80valid
162.0ms1249×body640nan
62.0ms630×body320nan
21.0ms314×body160nan

Profiling

Loading profile data...