Details

sample62.0ms

Algorithm

intervals

Results

20.0ms	47×	body	10240	exit
15.0ms	256×	body	80	valid
13.0ms	295×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (pow (sqrt (atan2 b b)) (- b a)))
0.0b	(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:

6.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
5.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series93.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
23.0ms	(pow (sqrt (atan2 b b)) (- b a))
10.0ms	(sqrt (atan2 b b))

simplify74.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (68.0ms)

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

prune150.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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))

rewrite61.0ms

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:

6.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
44.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series90.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
37.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
15.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify70.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (44.0ms)

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

prune485.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (exp (* 2 (* (log (sqrt (sqrt (atan2 b b)))) (- b a)))))
0.0b	(exp (* 2 (* (log (sqrt (sqrt (atan2 b b)))) (- b a))))
0.2b	(* (log (sqrt (sqrt (atan2 b b)))) (- b a))
1.0b	(sqrt (atan2 b b))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

55×	`distribute-rgt-in` `distribute-lft-in`
54×	`prod-diff`
48×	`add-sqr-sqrt`
45×	`*-un-lft-identity`
44×	`exp-sum`
43×	`add-cube-cbrt`
10×	`pow1`
8×	`associate-l`
6×	`add-exp-log` `sub-neg` `add-cbrt-cube` `add-log-exp`
5×	`sqrt-pow1` `associate-r` `log-pow`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow1/2` `sqrt-prod`
2×	`associate-*r/`
1×	`rem-sqrt-square` `exp-prod` `flip3--` `exp-to-pow` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `rem-exp-log` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 131

Calls

4 calls:

24.0ms	(sin (exp (* 2 (* (log (sqrt (sqrt (atan2 b b)))) (- b a)))))
12.0ms	(exp (* 2 (* (log (sqrt (sqrt (atan2 b b)))) (- b a))))
15.0ms	(* (log (sqrt (sqrt (atan2 b b)))) (- b a))
1.0ms	(sqrt (atan2 b b))

series250.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(sin (exp (* 2 (* (log (sqrt (sqrt (atan2 b b)))) (- b a)))))
34.0ms	(exp (* 2 (* (log (sqrt (sqrt (atan2 b b)))) (- b a))))
129.0ms	(* (log (sqrt (sqrt (atan2 b b)))) (- b a))
11.0ms	(sqrt (atan2 b b))

simplify58.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	617	2085
1	1835	1489
2	5002	1419

prune265.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (pow (exp 2) (* (log (sqrt (sqrt (atan2 b b)))) (- b a))))
0.0b	(pow (exp 2) (* (log (sqrt (sqrt (atan2 b b)))) (- b a)))
0.2b	(* (log (sqrt (sqrt (atan2 b b)))) (- b a))
1.0b	(sqrt (atan2 b b))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
36×	`*-un-lft-identity` `prod-diff`
33×	`add-cube-cbrt`
22×	`unpow-prod-up` `distribute-rgt-in` `distribute-lft-in`
11×	`pow1`
8×	`associate-l`
6×	`add-exp-log` `add-cbrt-cube`
5×	`sqrt-pow1` `associate-r` `log-pow`
4×	`expm1-log1p-u` `sub-neg` `unpow-prod-down` `pow-pow` `log1p-expm1-u` `add-log-exp`
3×	`exp-prod` `pow1/2` `sqrt-prod`
2×	`associate-*r/`
1×	`pow-to-exp` `rem-sqrt-square` `pow-unpow` `flip3--` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `exp-lft-sqr` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `sqr-pow`

Counts

4 → 118

Calls

4 calls:

12.0ms	(sin (pow (exp 2) (* (log (sqrt (sqrt (atan2 b b)))) (- b a))))
6.0ms	(pow (exp 2) (* (log (sqrt (sqrt (atan2 b b)))) (- b a)))
15.0ms	(* (log (sqrt (sqrt (atan2 b b)))) (- b a))
1.0ms	(sqrt (atan2 b b))

series283.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(sin (pow (exp 2) (* (log (sqrt (sqrt (atan2 b b)))) (- b a))))
44.0ms	(pow (exp 2) (* (log (sqrt (sqrt (atan2 b b)))) (- b a)))
128.0ms	(* (log (sqrt (sqrt (atan2 b b)))) (- b a))
15.0ms	(sqrt (atan2 b b))

simplify51.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	470	1681
1	1548	1369
2	5001	1353

prune312.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

regimes32.0ms

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

sample2.0s

Algorithm

intervals

Results

747.0ms	1850×	body	10240	exit
454.0ms	9789×	body	80	nan
429.0ms	7990×	body	80	valid
5.0ms	4×	body	2560	valid
3.0ms	1×	body	5120	valid
1.0ms	2×	body	1280	valid
1.0ms	2×	body	640	valid
0.0ms	1×	body	160	valid