Details

sample48.0ms

Algorithm

intervals

Results

12.0ms	548×	body	80	nan
12.0ms	264×	body	160	nan
8.0ms	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

prune3.0ms

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: 31.6b

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)))
29.5b	(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))

series307.0ms

Counts

3 → 9

Calls

3 calls:

186.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
66.0ms	(+ x (sqrt (- (* x x) 1.0)))
54.0ms	(sqrt (- (* x x) 1.0))

simplify35.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (29.0ms)

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

prune139.0ms

Filtered

61 candidates to 53 candidates (86.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	3	62

Merged error: 0b

Counts

62 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x (sqrt 1.0)))
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))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
20×	`sqrt-prod`
17×	`*-un-lft-identity`
14×	`sqrt-div`
11×	`add-cube-cbrt`
10×	`pow1`
9×	`associate-r`
7×	`add-exp-log` `associate-l`
6×	`flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
3×	`log-prod` `flip3--` `fma-def` `sqrt-pow1` `pow1/2` `pow-prod-down` `flip--`
2×	`log-div` `associate-r/` `associate-l/` `hypot-def` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sqrt-unprod` `rem-log-exp` `prod-exp` `sum-log` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 96

Calls

4 calls:

4.0ms	(sqrt (+ x (sqrt 1.0)))
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))))

series679.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt (+ x (sqrt 1.0)))
278.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
147.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
194.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify57.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	524	1161
1	1829	1044
2	5002	1027

prune263.0ms

Filtered

108 candidates to 86 candidates (79.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	109	2	111

Merged error: 0b

Counts

111 → 2

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x (sqrt 1.0)))
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)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
7×	`*-un-lft-identity`
5×	`pow1` `add-cube-cbrt` `sqrt-prod`
4×	`add-exp-log`
3×	`expm1-log1p-u` `log-prod` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-div` `hypot-def`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `rem-log-exp` `log-pow` `flip-+` `fma-udef` `distribute-lft-out`

Counts

3 → 44

Calls

3 calls:

4.0ms	(sqrt (+ x (sqrt 1.0)))
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)

series729.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(sqrt (+ x (sqrt 1.0)))
415.0ms	(log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))
246.0ms	(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)

simplify45.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	423	600
1	1488	529
2	5002	511

prune150.0ms

Filtered

53 candidates to 44 candidates (83.0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	53	2	55

Merged error: 0b

Counts

55 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (expm1 (log1p (+ x (sqrt (- (* x x) 1.0))))))
0.0b	(+ x (sqrt (- (* x x) 1.0)))
5.6b	(expm1 (log1p (+ x (sqrt (- (* x x) 1.0)))))
29.5b	(sqrt (- (* x x) 1.0))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

1.0ms	(log (expm1 (log1p (+ x (sqrt (- (* x x) 1.0))))))
6.0ms	(+ x (sqrt (- (* x x) 1.0)))
1.0ms	(expm1 (log1p (+ x (sqrt (- (* x x) 1.0)))))
5.0ms	(sqrt (- (* x x) 1.0))

series900.0ms

Counts

4 → 12

Calls

4 calls:

471.0ms	(log (expm1 (log1p (+ x (sqrt (- (* x x) 1.0))))))
72.0ms	(+ x (sqrt (- (* x x) 1.0)))
299.0ms	(expm1 (log1p (+ x (sqrt (- (* x x) 1.0)))))
57.0ms	(sqrt (- (* x x) 1.0))

simplify41.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	417	574
1	1441	518
2	5002	480

prune190.0ms

Filtered

72 candidates to 65 candidates (90.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	72	2	74

Merged error: 0b

Counts

74 → 2

regimes26.0ms

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	10	8
1	10	8

end0.0ms

sample1.3s

Algorithm

intervals

Results

366.0ms	16081×	body	80	nan
343.0ms	7371×	body	160	nan
232.0ms	8000×	body	80	valid