Details

sample42.0ms

Algorithm

intervals

Results

10.0ms	213×	body	160	nan
10.0ms	438×	body	80	nan
7.0ms	256×	body	80	valid

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: 28.1b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (+ x (sqrt (- (* x x) 1.0))))
0.0b	(+ x (sqrt (- (* x x) 1.0)))
26.2b	(sqrt (- (* x x) 1.0))

rewrite18.0ms

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:

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

series308.0ms

Counts

3 → 9

Calls

3 calls:

188.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
66.0ms	(+ x (sqrt (- (* x x) 1.0)))
53.0ms	(sqrt (- (* x x) 1.0))

simplify33.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	339	436
1	1140	401
2	5001	389

prune152.0ms

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: 0b

Counts

62 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (+ x (- x (fma 0.5 (/ 1 x) (/ 0.125 (pow x 3))))))
0.0b	(+ x (- x (fma 0.5 (/ 1 x) (/ 0.125 (pow x 3)))))
0.0b	(fma 0.5 (/ 1 x) (/ 0.125 (pow x 3)))
0.5b	(/ 0.125 (pow x 3))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

47×	`*-un-lft-identity`
37×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`times-frac`
12×	`unpow-prod-down` `cube-prod` `associate-/r*`
11×	`associate-+r+`
10×	`add-exp-log`
9×	`prod-diff` `add-log-exp`
6×	`add-cbrt-cube`
5×	`pow1` `log-prod`
4×	`expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u` `distribute-lft-out` `sqr-pow`
3×	`fma-def` `div-exp` `associate-/l*`
2×	`log-div` `flip3-+` `sum-log` `flip-+` `distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `associate-+r-` `sub-neg` `frac-2neg` `diff-log` `rem-log-exp` `pow-exp` `clear-num` `log-pow` `fma-udef` `div-inv`

Counts

4 → 126

Calls

4 calls:

9.0ms	(log (+ x (- x (fma 0.5 (/ 1 x) (/ 0.125 (pow x 3))))))
7.0ms	(+ x (- x (fma 0.5 (/ 1 x) (/ 0.125 (pow x 3)))))
1.0ms	(fma 0.5 (/ 1 x) (/ 0.125 (pow x 3)))
6.0ms	(/ 0.125 (pow x 3))

series332.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(log (+ x (- x (fma 0.5 (/ 1 x) (/ 0.125 (pow x 3))))))
51.0ms	(+ x (- x (fma 0.5 (/ 1 x) (/ 0.125 (pow x 3)))))
83.0ms	(fma 0.5 (/ 1 x) (/ 0.125 (pow x 3)))
36.0ms	(/ 0.125 (pow x 3))

simplify59.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	447	911
1	2048	786
2	5002	785

prune279.0ms

Filtered

138 candidates to 84 candidates (60.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	138	2	140

Merged error: 0b

Counts

140 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
0.0b	(+ x (sqrt (- (* x x) 1.0)))
26.2b	(sqrt (- (* x x) 1.0))
26.2b	(sqrt (- (* x x) 1.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt` `sqrt-prod` `add-log-exp`
6×	`pow1` `fma-def`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
2×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `sum-log` `flip--` `flip-+` `distribute-lft-out` `difference-of-squares`

Counts

4 → 70

Calls

4 calls:

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

series236.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(+ x (sqrt (- (* x x) 1.0)))
67.0ms	(+ x (sqrt (- (* x x) 1.0)))
48.0ms	(sqrt (- (* x x) 1.0))
53.0ms	(sqrt (- (* x x) 1.0))

simplify80.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	235	478
1	739	446
2	2858	436
3	5001	432

prune276.0ms

Filtered

82 candidates to 72 candidates (87.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Merged error: 0b

Counts

84 → 2

regimes29.0ms

Accuracy

0% (0.1b 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	15	7
1	15	7

end0.0ms

sample1.4s

Algorithm

intervals

Results

382.0ms	17075×	body	80	nan
362.0ms	7816×	body	160	nan
237.0ms	8000×	body	80	valid