Details

Time bar (total: 5.0s)

sample41.0ms

Algorithm
intervals
Results
11.0ms479×body80nan
9.0ms205×body160nan
7.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0115
1125
2125

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))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
2×log-div flip3-- flip3-+ fma-neg sqrt-div flip-- flip-+
1×+-commutative sub-neg pow1/2 *-commutative
Counts
4 → 14
Calls
4 calls:
3.0ms
(+ x (sqrt (- (* x x) 1.0)))
4.0ms
(- (* x x) 1.0)
4.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
4.0ms
(sqrt (- (* x x) 1.0))

series356.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(+ x (sqrt (- (* x x) 1.0)))
44.0ms
(- (* x x) 1.0)
189.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
54.0ms
(sqrt (- (* x x) 1.0))

simplify116.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 3 (111.0ms)

IterNodesCost
0272208
1945197
24309184
35001183

prune69.0ms

Filtered
26 candidates to 21 candidates (80.8%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New24226
Fresh000
Picked011
Done000
Total24327

Merged error: 0.0b

Counts
27 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))
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))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
8×frac-sub
5×flip3-- frac-2neg clear-num flip--
4×sub-neg associate-+r+ associate--l+
3×associate-/r* div-inv associate-/l/ sqr-pow
2×associate--l- associate-+r-
1×+-commutative flip3-+ flip-+ associate-/l*
Counts
4 → 35
Calls
4 calls:
5.0ms
(- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))
3.0ms
(/ (/ 0.25 x) x)
5.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
2.0ms
(/ 0.09375 (pow x 4))

series237.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))
24.0ms
(/ (/ 0.25 x) x)
106.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
39.0ms
(/ 0.09375 (pow x 4))

simplify40.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0339513
11347480
25003476

prune112.0ms

Filtered
47 candidates to 31 candidates (66.0%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New46147
Fresh011
Picked101
Done011
Total47350

Merged error: 0b

Counts
50 → 3

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma 0.5 (/ 1 x) (* 0.125 (/ 1 (pow x 3))))
0.2b
(log (fma 2 x (- (fma 0.5 (/ 1 x) (* 0.125 (/ 1 (pow x 3)))))))
0.3b
(/ 1 (pow x 3))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
2×associate-/r*
1×pow-to-exp rec-exp pow-flip frac-2neg unpow3 clear-num fma-udef div-inv inv-pow sqr-pow
Counts
3 → 9
Calls
3 calls:
1.0ms
(fma 0.5 (/ 1 x) (* 0.125 (/ 1 (pow x 3))))
1.0ms
(log (fma 2 x (- (fma 0.5 (/ 1 x) (* 0.125 (/ 1 (pow x 3)))))))
3.0ms
(/ 1 (pow x 3))

series268.0ms

Counts
3 → 9
Calls
3 calls:
82.0ms
(fma 0.5 (/ 1 x) (* 0.125 (/ 1 (pow x 3))))
155.0ms
(log (fma 2 x (- (fma 0.5 (/ 1 x) (* 0.125 (/ 1 (pow x 3)))))))
31.0ms
(/ 1 (pow x 3))

simplify66.0ms

Algorithm
egg-herbie
Counts
18 → 18
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
013773
144972
2205065
3500265

prune65.0ms

Filtered
18 candidates to 12 candidates (66.7%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New18018
Fresh011
Picked011
Done011
Total18321

Merged error: 0b

Counts
21 → 3

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (+ (pow (log 2) 3) (pow (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))) 3)) (fma (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))) (- (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))) (log 2)) (* (log 2) (log 2))))
0.7b
(pow (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))) 3)
1.0b
(pow (log 2) 3)
1.0b
(* (log 2) (log 2))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
2×pow-to-exp unpow3 associate-/l/ sqr-pow
1×pow2 frac-2neg flip3-+ clear-num sum-cubes *-commutative flip-+ div-inv associate-/l*
Counts
4 → 14
Calls
4 calls:
7.0ms
(/ (+ (pow (log 2) 3) (pow (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))) 3)) (fma (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))) (- (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))) (log 2)) (* (log 2) (log 2))))
2.0ms
(pow (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))) 3)
2.0ms
(pow (log 2) 3)
3.0ms
(* (log 2) (log 2))

series1.7s

Counts
4 → 8
Calls
4 calls:
1.6s
(/ (+ (pow (log 2) 3) (pow (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))) 3)) (fma (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))) (- (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))) (log 2)) (* (log 2) (log 2))))
115.0ms
(pow (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))) 3)
0.0ms
(pow (log 2) 3)
0.0ms
(* (log 2) (log 2))

simplify83.0ms

Algorithm
egg-herbie
Counts
22 → 22
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
017383058
150013053

prune293.0ms

Filtered
22 candidates to 19 candidates (86.4%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New22022
Fresh000
Picked011
Done022
Total22325

Merged error: 0b

Counts
25 → 3

regimes56.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0178
1178

end0.0ms

sample1.3s

Algorithm
intervals
Results
370.0ms16296×body80nan
350.0ms7530×body160nan
233.0ms8000×body80valid