Details

sample80.0ms

Algorithm

intervals

Results

17.0ms	89×	body	2560	nan
15.0ms	468×	body	80	nan
14.0ms	76×	body	1280	nan
10.0ms	256×	body	80	valid
5.0ms	42×	body	640	nan
2.0ms	25×	body	320	nan
1.0ms	13×	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: 33.1b

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 x) 1.0)
0.0b	(+ x (sqrt (- (* x x) 1.0)))
30.8b	(sqrt (- (* x x) 1.0))

rewrite27.0ms

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:

10.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
4.0ms	(- (* x x) 1.0)
6.0ms	(+ x (sqrt (- (* x x) 1.0)))
5.0ms	(sqrt (- (* x x) 1.0))

series362.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
43.0ms	(- (* x x) 1.0)
71.0ms	(+ x (sqrt (- (* x x) 1.0)))
52.0ms	(sqrt (- (* x x) 1.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (36.0ms)

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

prune176.0ms

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	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite21.0ms

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:

2.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
3.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
13.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series850.0ms

Counts

3 → 9

Calls

3 calls:

493.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
154.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
202.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify53.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (42.0ms)

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

prune209.0ms

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

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
0.5b	(cbrt (pow (log (+ x (sqrt (- (* x x) 1.0)))) 3))
0.7b	(pow (log (+ x (sqrt (- (* x x) 1.0)))) 3)
30.8b	(sqrt (- (* x x) 1.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity`
12×	`add-cube-cbrt`
10×	`pow1`
8×	`unpow-prod-down` `cube-prod`
6×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-prod` `log-pow` `log1p-expm1-u`
3×	`pow-unpow` `fma-def`
2×	`cube-mult` `sqrt-div` `unpow3` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `rem-sqrt-square` `flip3--` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `pow-exp` `sum-log` `flip--` `rem-cbrt-cube` `flip-+` `distribute-lft-out` `rem-cube-cbrt` `difference-of-squares`

Counts

4 → 87

Calls

4 calls:

7.0ms	(+ x (sqrt (- (* x x) 1.0)))
2.0ms	(cbrt (pow (log (+ x (sqrt (- (* x x) 1.0)))) 3))
3.0ms	(pow (log (+ x (sqrt (- (* x x) 1.0)))) 3)
5.0ms	(sqrt (- (* x x) 1.0))

series630.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(+ x (sqrt (- (* x x) 1.0)))
194.0ms	(cbrt (pow (log (+ x (sqrt (- (* x x) 1.0)))) 3))
309.0ms	(pow (log (+ x (sqrt (- (* x x) 1.0)))) 3)
58.0ms	(sqrt (- (* x x) 1.0))

simplify93.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	744	936
1	3357	877
2	5001	869

prune211.0ms

Filtered

99 candidates to 68 candidates (68.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	99	2	101

Merged error: 0b

Counts

101 → 2

regimes45.0ms

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

573.0ms	3046×	body	2560	nan
542.0ms	16231×	body	80	nan
396.0ms	2547×	body	1280	nan
321.0ms	8000×	body	80	valid
160.0ms	1256×	body	640	nan
61.0ms	648×	body	320	nan
22.0ms	335×	body	160	nan