Details

sample99.0ms

Algorithm

intervals

Results

23.0ms	122×	body	2560	nan
23.0ms	612×	body	80	nan
15.0ms	96×	body	1280	nan
10.0ms	256×	body	80	valid
6.0ms	49×	body	640	nan
3.0ms	29×	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: 31.4b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (+ x (sqrt (- (* x x) 1.0))))
0.0b	(+ x (sqrt (- (* x x) 1.0)))
0.0b	(- (* x x) 1.0)
29.2b	(sqrt (- (* x x) 1.0))

rewrite24.0ms

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:

6.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
6.0ms	(+ x (sqrt (- (* x x) 1.0)))
4.0ms	(- (* x x) 1.0)
5.0ms	(sqrt (- (* x x) 1.0))

series375.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
74.0ms	(+ x (sqrt (- (* x x) 1.0)))
40.0ms	(- (* x x) 1.0)
56.0ms	(sqrt (- (* x x) 1.0))

simplify41.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	384	532
1	1355	471
2	5001	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)))))
0.0b	(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))))))
12.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series671.0ms

Counts

3 → 9

Calls

3 calls:

152.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
288.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
230.0ms	(* (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

prune213.0ms

Filtered

85 candidates to 69 candidates (81.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	85	2	87

Merged error: 0b

Counts

87 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))
0.1b	(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
0.5b	(cbrt (pow (log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)) 3))
0.7b	(pow (log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)) 3)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
8×	`unpow-prod-down` `cube-prod`
6×	`add-exp-log`
5×	`log-pow` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `log-prod`
2×	`cube-mult` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `rem-log-exp` `pow-exp` `rem-cbrt-cube` `fma-udef` `rem-cube-cbrt`

Counts

4 → 76

Calls

4 calls:

1.0ms	(log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))
1.0ms	(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
2.0ms	(cbrt (pow (log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)) 3))
2.0ms	(pow (log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)) 3)

series2.2s

Counts

4 → 12

Calls

4 calls:

429.0ms	(log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))
263.0ms	(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
436.0ms	(cbrt (pow (log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)) 3))
1.1s	(pow (log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)) 3)

simplify89.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	872	1575
1	3911	1461
2	5001	1458

prune257.0ms

Filtered

88 candidates to 60 candidates (68.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	88	2	90

Merged error: 0b

Counts

90 → 2

regimes12.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

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

555.0ms	2940×	body	2560	nan
540.0ms	16061×	body	80	nan
395.0ms	2511×	body	1280	nan
318.0ms	8000×	body	80	valid
164.0ms	1251×	body	640	nan
63.0ms	661×	body	320	nan
20.0ms	301×	body	160	nan