Details

sample80.0ms

Algorithm

intervals

Results

16.0ms	486×	body	80	nan
16.0ms	84×	body	2560	nan
15.0ms	75×	body	1280	nan
10.0ms	256×	body	80	valid
4.0ms	32×	body	640	nan
2.0ms	18×	body	320	nan
1.0ms	9×	body	160	nan

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	5
1	12	5
2	12	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 32.1b

Counts

2 → 1

localize7.0ms

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))))
29.9b	(sqrt (- (* x x) 1.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1`
5×	`add-exp-log`
4×	`expm1-log1p-u` `log-prod` `sqrt-prod` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `prod-diff`
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` `fma-neg` `diff-log` `rem-log-exp` `sum-log` `log-pow`

Counts

4 → 71

Calls

4 calls:

5.0ms	(- (* x x) 1.0)
6.0ms	(+ x (sqrt (- (* x x) 1.0)))
6.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
5.0ms	(sqrt (- (* x x) 1.0))

series363.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* x x) 1.0)
69.0ms	(+ x (sqrt (- (* x x) 1.0)))
194.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
56.0ms	(sqrt (- (* x x) 1.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	384	531
1	1360	471
2	5002	457

prune164.0ms

Filtered

83 candidates to 67 candidates (80.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	2	84

Merged error: 0b

Counts

84 → 2

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))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
15×	`sqrt-prod`
13×	`*-un-lft-identity`
12×	`sqrt-div`
9×	`add-cube-cbrt` `associate-r`
8×	`pow1`
7×	`associate-l`
6×	`add-exp-log`
5×	`flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
4×	`frac-times` `unswap-sqr`
3×	`expm1-log1p-u` `log-prod` `flip3--` `fma-def` `pow-prod-down` `flip--` `log1p-expm1-u`
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 → 76

Calls

3 calls:

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))))))
13.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series630.0ms

Counts

3 → 9

Calls

3 calls:

148.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
282.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
200.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify47.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	467	1012
1	1665	907
2	5001	894

prune208.0ms

Filtered

85 candidates to 69 candidates (81.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	85	2	87

Merged error: 0b

Counts

87 → 2

localize201.0ms

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))))
0.8b	(/ 0.09375 (pow x 4))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

870×	`times-frac`
804×	`add-sqr-sqrt`
668×	`*-un-lft-identity`
570×	`add-cube-cbrt`
544×	`prod-diff`
379×	`associate-+r+`
183×	`associate--l+`
124×	`pow1`
120×	`log-pow`
84×	`unpow-prod-down`
78×	`difference-of-squares`
62×	`distribute-lft-out--`
46×	`div-inv`
28×	`sqr-pow`
16×	`associate-/l*`
14×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`associate-/r*` `add-log-exp`
9×	`log-prod`
8×	`distribute-lft-out`
6×	`div-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `fma-def` `fma-neg` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `associate-+l+` `sum-log`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `flip3--` `flip3-+` `pow-exp` `flip--` `flip-+` `associate-/l/`

Counts

4 → 727

Calls

4 calls:

20.0ms	(- (log x) (/ (/ 0.25 x) x))
6.0ms	(/ (/ 0.25 x) x)
75.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
5.0ms	(/ 0.09375 (pow x 4))

series457.0ms

Counts

4 → 12

Calls

4 calls:

294.0ms	(- (log x) (/ (/ 0.25 x) x))
24.0ms	(/ (/ 0.25 x) x)
93.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
45.0ms	(/ 0.09375 (pow x 4))

simplify154.0ms

Algorithm

egg-herbie

Counts

739 → 739

Iterations

Useful iterations: 1 (46.0ms)

Iter	Nodes	Cost
0	2647	14534
1	5002	11801

prune1.6s

Filtered

739 candidates to 412 candidates (55.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	739	0	739
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	739	2	741

Merged error: 0b

Counts

741 → 2

regimes11.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

end0.0ms

sample2.5s

Algorithm

intervals

Results

580.0ms	3053×	body	2560	nan
539.0ms	16249×	body	80	nan
390.0ms	2488×	body	1280	nan
326.0ms	8000×	body	80	valid
165.0ms	1317×	body	640	nan
62.0ms	640×	body	320	nan
23.0ms	324×	body	160	nan