Details

sample130.0ms

Algorithm

intervals

Results

66.0ms	63×	body	5120	exit
25.0ms	256×	body	80	valid
22.0ms	367×	body	80	nan

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	22	5
2	44	5
3	114	5
4	321	5
5	1627	5
6	5001	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: 0.1b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (pow (sqrt (atan2 b b)) (- b a)))
0.1b	(pow (sqrt (atan2 b b)) (- b a))
1.0b	(sqrt (atan2 b b))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
11×	`unpow-prod-up`
9×	`prod-diff`
6×	`pow1` `unpow-prod-down` `sqrt-prod`
5×	`pow-unpow`
4×	`add-exp-log`
3×	`expm1-log1p-u` `pow-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

3 → 63

Calls

3 calls:

5.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
6.0ms	(pow (sqrt (atan2 b b)) (- b a))
2.0ms	(sqrt (atan2 b b))

series95.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
20.0ms	(pow (sqrt (atan2 b b)) (- b a))
11.0ms	(sqrt (atan2 b b))

simplify76.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	255	514
1	714	433
2	2702	425
3	5002	408

prune138.0ms

Filtered

72 candidates to 43 candidates (59.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	2	73

Merged error: 0.0b

Counts

73 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.0b	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
93×	`sqrt-prod`
87×	`unpow-prod-down`
59×	`unpow-prod-up`
58×	`*-un-lft-identity`
56×	`add-cube-cbrt`
45×	`prod-diff`
32×	`swap-sqr`
25×	`unswap-sqr`
24×	`associate-r` `associate-l`
17×	`add-exp-log`
15×	`sqr-pow`
9×	`pow1` `prod-exp`
7×	`pow-to-exp` `sub-neg` `pow-exp`
6×	`sqrt-pow1` `add-cbrt-cube`
5×	`pow-unpow` `pow-pow` `pow-sub`
4×	`expm1-log1p-u` `pow1/2` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 206

Calls

4 calls:

7.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
22.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
1.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series95.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
45.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
10.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))

simplify70.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	461	2468
1	2032	2166
2	5002	2132

prune431.0ms

Filtered

218 candidates to 111 candidates (50.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	216	2	218
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	217	3	220

Merged error: 0.0b

Counts

220 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- b a))
0.6b	(cbrt (- b a))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`cbrt-prod`
8×	`add-cube-cbrt`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 64

Calls

4 calls:

3.0ms	(cbrt (- b a))
3.0ms	(cbrt (- b a))
1.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series338.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(cbrt (- b a))
157.0ms	(cbrt (- b a))
10.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify113.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 4 (108.0ms)

Iter	Nodes	Cost
0	169	332
1	352	320
2	962	314
3	3198	298
4	5002	292

prune271.0ms

Filtered

76 candidates to 58 candidates (76.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	76	3	79

Merged error: 0.0b

Counts

79 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a)))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
4.6b	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-sqr-sqrt`
73×	`log-prod`
66×	`sqrt-prod`
60×	`unpow-prod-down`
49×	`exp-sum`
37×	`add-cube-cbrt` `*-un-lft-identity`
33×	`unpow-prod-up`
30×	`unswap-sqr`
27×	`associate-r` `prod-diff`
24×	`associate-l`
14×	`sqr-pow`
8×	`add-exp-log`
6×	`pow1` `add-cbrt-cube`
5×	`pow-sub`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sub-neg` `log-div` `rem-log-exp` `prod-exp`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `exp-diff` `pow-exp`
1×	`frac-times` `associate-r/` `associate-l/` `log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 166

Calls

4 calls:

26.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a)))))
1.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
6.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

series149.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a)))))
15.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))
85.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify59.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	483	2305
1	1650	1877
2	5002	1798

prune425.0ms

Filtered

178 candidates to 102 candidates (57.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	178	3	181

Merged error: 0.0b

Counts

181 → 3

regimes99.0ms

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	14	19
1	14	19

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.9s	1816×	body	5120	exit
637.0ms	7990×	body	80	valid
615.0ms	10094×	body	80	nan
3.0ms	1×	body	5120	valid
2.0ms	2×	body	2560	valid
1.0ms	3×	body	640	valid
1.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid