Details

sample86.0ms

Algorithm

intervals

Results

19.0ms	105×	body	2560	nan
17.0ms	516×	body	80	nan
15.0ms	80×	body	1280	nan
10.0ms	256×	body	80	valid
5.0ms	41×	body	640	nan
1.0ms	15×	body	320	nan
1.0ms	9×	body	160	nan

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 34.4b

Counts

2 → 1

localize7.0ms

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))))
32.0b	(sqrt (- (* x x) 1.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `log-prod` `sqrt-prod`
3×	`expm1-log1p-u` `fma-def` `add-cbrt-cube` `log1p-expm1-u`
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 → 52

Calls

3 calls:

7.0ms	(+ x (sqrt (- (* x x) 1.0)))
6.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
5.0ms	(sqrt (- (* x x) 1.0))

series330.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(+ x (sqrt (- (* x x) 1.0)))
202.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
55.0ms	(sqrt (- (* x x) 1.0))

simplify36.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	339	437
1	1134	401
2	5001	389

prune136.0ms

Filtered

61 candidates to 53 candidates (86.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	2	62

Merged error: 0.0b

Counts

62 → 2

localize11.0ms

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))))

rewrite24.0ms

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))))))
16.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series658.0ms

Counts

3 → 9

Calls

3 calls:

148.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
306.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
204.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify48.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (39.0ms)

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

prune402.0ms

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: 0.0b

Counts

87 → 2

localize14.0ms

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))))
0.4b	(/ 0.09375 (pow x 4))

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

1176×	`add-sqr-sqrt`
1116×	`times-frac`
887×	`*-un-lft-identity`
744×	`prod-diff`
707×	`add-cube-cbrt`
379×	`associate-+r+`
360×	`associate--l+`
157×	`unpow-prod-down` `difference-of-squares`
149×	`pow1`
145×	`log-pow`
117×	`distribute-lft-out--`
54×	`div-inv`
53×	`sqr-pow`
16×	`associate-/l*`
14×	`add-exp-log`
13×	`add-log-exp`
11×	`add-cbrt-cube`
10×	`associate-/r*`
9×	`log-prod`
8×	`fma-neg` `distribute-lft-out`
6×	`diff-log` `div-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `sub-neg` `fma-def` `log1p-expm1-u`
3×	`associate-+l+` `sum-log`
2×	`flip3--` `frac-2neg` `clear-num` `frac-sub` `flip--`
1×	`+-commutative` `associate--l-` `pow-to-exp` `associate-+r-` `flip3-+` `pow-exp` `flip-+` `associate-/l/`

Counts

4 → 939

Calls

4 calls:

54.0ms	(- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))
6.0ms	(/ (/ 0.25 x) x)
74.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
5.0ms	(/ 0.09375 (pow x 4))

series233.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4)))
25.0ms	(/ (/ 0.25 x) x)
97.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
45.0ms	(/ 0.09375 (pow x 4))

simplify211.0ms

Algorithm

egg-herbie

Counts

951 → 951

Iterations

Useful iterations: 1 (50.0ms)

Iter	Nodes	Cost
0	2884	20064
1	5001	16939

prune2.4s

Filtered

951 candidates to 543 candidates (57.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	950	1	951
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	951	2	953

Merged error: 0b

Counts

953 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 0.25 x) x)
0.2b	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
0.4b	(/ 0.09375 (pow x 4))
1.1b	(expm1 (log1p (+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

610×	`add-sqr-sqrt`
603×	`times-frac`
480×	`*-un-lft-identity`
385×	`add-cube-cbrt`
379×	`associate-+r+`
372×	`prod-diff`
180×	`associate--l+`
84×	`unpow-prod-down`
79×	`pow1`
75×	`log-pow` `difference-of-squares`
60×	`distribute-lft-out--`
30×	`div-inv`
28×	`sqr-pow`
16×	`associate-/l*`
14×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`associate-/r*`
9×	`add-log-exp`
8×	`distribute-lft-out`
6×	`log-prod` `div-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `fma-def` `log1p-expm1-u`
3×	`associate-+l+` `diff-log` `sum-log`
2×	`sub-neg` `frac-2neg` `clear-num`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `expm1-log1p` `flip3-+` `pow-exp` `flip-+` `associate-/l/` `expm1-udef`

Counts

4 → 540

Calls

4 calls:

6.0ms	(/ (/ 0.25 x) x)
74.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
5.0ms	(/ 0.09375 (pow x 4))
1.0ms	(expm1 (log1p (+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))))

series439.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (/ 0.25 x) x)
101.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
44.0ms	(/ 0.09375 (pow x 4))
269.0ms	(expm1 (log1p (+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))))

simplify121.0ms

Algorithm

egg-herbie

Counts

552 → 552

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	2546	8616
1	5001	7571

prune1.7s

Filtered

552 candidates to 347 candidates (62.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	552	0	552
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	552	2	554

Merged error: 0b

Counts

554 → 2

regimes16.0ms

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)

Iter	Nodes	Cost
0	13	9
1	13	9

end0.0ms

sample2.5s

Algorithm

intervals

Results

556.0ms	2971×	body	2560	nan
550.0ms	16447×	body	80	nan
390.0ms	2541×	body	1280	nan
319.0ms	8000×	body	80	valid
165.0ms	1329×	body	640	nan
60.0ms	644×	body	320	nan
19.0ms	296×	body	160	nan