Details

Time bar (total: 6.1s)

sample52.0ms

Algorithm
intervals
Results
13.0ms479×body80nan
11.0ms205×body160nan
10.0ms256×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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.6b

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))))
28.4b
(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))

series354.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(+ x (sqrt (- (* x x) 1.0)))
44.0ms
(- (* x x) 1.0)
192.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
55.0ms
(sqrt (- (* x x) 1.0))

simplify145.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0327471
11087435
24892422
35001422

prune212.0ms

Filtered
68 candidates to 55 candidates (80.9%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New66268
Fresh000
Picked011
Done000
Total66369

Merged error: 0.0b

Counts
69 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

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:
3.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
4.0ms
(sqrt (- x (sqrt 1.0)))
2.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
13.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series727.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
76.0ms
(sqrt (- x (sqrt 1.0)))
299.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
204.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify56.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04941102
117341015
25002995

prune272.0ms

Filtered
97 candidates to 73 candidates (75.3%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New96197
Fresh101
Picked011
Done011
Total973100

Merged error: 0.0b

Counts
100 → 3

localize23.0ms

Local error

Found 3 expressions with local error:

0.2b
(- (log 2) (- 0 (- (log x) (/ (* (* 1.0 1.0) 3/32) (pow x 4)))))
0.3b
(/ (* (* 1.0 1.0) 3/32) (pow x 4))
0.6b
(/ (* 1/4 1.0) (pow x 2))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
40×add-exp-log
32×*-un-lft-identity
18×distribute-lft-out--
17×add-cbrt-cube
15×times-frac div-exp associate-/r*
14×add-sqr-sqrt
12×add-cube-cbrt unpow-prod-down prod-exp
9×pow1
8×add-log-exp
6×diff-log log-pow
5×cbrt-undiv pow-to-exp pow-exp
4×cbrt-unprod sqr-pow
3×log-prod associate--l+ associate--r+
2×sub-neg frac-2neg clear-num div-inv associate-/l* unpow2 associate--r-
1×flip3-- flip-- difference-of-squares
Counts
3 → 102
Calls
3 calls:
13.0ms
(- (log 2) (- 0 (- (log x) (/ (* (* 1.0 1.0) 3/32) (pow x 4)))))
8.0ms
(/ (* (* 1.0 1.0) 3/32) (pow x 4))
6.0ms
(/ (* 1/4 1.0) (pow x 2))

series1.5s

Counts
3 → 9
Calls
3 calls:
1.4s
(- (log 2) (- 0 (- (log x) (/ (* (* 1.0 1.0) 3/32) (pow x 4)))))
43.0ms
(/ (* (* 1.0 1.0) 3/32) (pow x 4))
26.0ms
(/ (* 1/4 1.0) (pow x 2))

simplify70.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
0526741
12624637
25001637

prune284.0ms

Filtered
111 candidates to 64 candidates (57.7%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1101111
Fresh000
Picked101
Done112
Total1122114

Merged error: 0b

Counts
114 → 2

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ (* 1/4 1.0) (pow x 2))
0.7b
(pow (- 0 (- (log x) (/ (* (* 1.0 1.0) 3/32) (pow x 4)))) 3)
1.0b
(pow (log 2) 3)
1.0b
(* (log 2) (log 2))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
36×*-un-lft-identity
26×add-sqr-sqrt
23×pow1
21×add-exp-log
20×add-cube-cbrt
17×unpow-prod-down
13×add-cbrt-cube
11×cube-prod
10×log-pow distribute-lft-out--
8×times-frac associate-/r*
6×pow-unpow log-prod swap-sqr div-exp
4×pow-to-exp associate-*r* associate-*l* pow-exp prod-exp add-log-exp sqr-pow
3×distribute-rgt-in distribute-lft-in
2×cbrt-undiv cube-div cube-mult pow-pow unpow3 cbrt-unprod unpow2 rem-cube-cbrt difference-of-squares
1×pow2 flip3-- frac-2neg pow-plus sub0-neg cube-neg pow-prod-down clear-num pow-sqr *-commutative pow-prod-up flip-- div-inv associate-/l* unswap-sqr
Counts
4 → 130
Calls
4 calls:
6.0ms
(/ (* 1/4 1.0) (pow x 2))
11.0ms
(pow (- 0 (- (log x) (/ (* (* 1.0 1.0) 3/32) (pow x 4)))) 3)
2.0ms
(pow (log 2) 3)
5.0ms
(* (log 2) (log 2))

series386.0ms

Counts
4 → 8
Calls
4 calls:
25.0ms
(/ (* 1/4 1.0) (pow x 2))
361.0ms
(pow (- 0 (- (log x) (/ (* (* 1.0 1.0) 3/32) (pow x 4)))) 3)
0.0ms
(pow (log 2) 3)
0.0ms
(* (log 2) (log 2))

simplify111.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
0636943
13321810
25001796

prune436.0ms

Filtered
138 candidates to 71 candidates (51.4%)
Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1380138
Fresh000
Picked011
Done011
Total1382140

Merged error: 0b

Counts
140 → 2

regimes15.0ms

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

sample1.3s

Algorithm
intervals
Results
354.0ms16296×body80nan
342.0ms7530×body160nan
224.0ms8000×body80valid