Details

sample75.0ms

Algorithm

intervals

Results

23.0ms	57×	body	10240	exit
18.0ms	255×	body	80	valid
15.0ms	334×	body	80	nan
3.0ms	1×	body	5120	valid

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	315	5
5	1609	5
6	5001	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
2×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

2 → 20

Calls

2 calls:

4.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms	(sqrt (atan2 b b))

series71.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
10.0ms	(sqrt (atan2 b b))

simplify64.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 6 (61.0ms)

Iter	Nodes	Cost
0	60	132
1	102	120
2	172	114
3	291	114
4	566	114
5	2095	114
6	5002	113

prune65.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
1.0b	(sqrt (atan2 b b))
1.0b	(* (cos 1) (log (sqrt (atan2 b b))))
2.0b	(log (sqrt (atan2 b b)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`log-prod`
16×	`pow1` `*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`add-exp-log` `sqrt-prod`
11×	`associate-r` `add-cbrt-cube`
8×	`distribute-rgt-in` `distribute-lft-in`
6×	`log-pow`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`sqrt-pow1` `pow1/2`
2×	`sub-neg` `associate-r/` `-commutative`
1×	`rem-sqrt-square` `flip3--` `rem-log-exp` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

13.0ms	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
1.0ms	(sqrt (atan2 b b))
6.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
1.0ms	(log (sqrt (atan2 b b)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
10.0ms	(sqrt (atan2 b b))
164.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
70.0ms	(log (sqrt (atan2 b b)))

simplify106.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	240	758
1	1120	651
2	4795	634
3	5001	634

prune222.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (cos 1) (log (log (exp (sqrt (atan2 b b)))))) (- b a))
1.0b	(* (cos 1) (log (log (exp (sqrt (atan2 b b))))))
1.0b	(sqrt (atan2 b b))
2.0b	(log (log (exp (sqrt (atan2 b b)))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

30×	`log-prod`
23×	`log-pow`
22×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
18×	`exp-prod`
17×	`pow1` `add-cube-cbrt`
12×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
11×	`add-cbrt-cube`
9×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`sub-neg` `associate-r/` `-commutative`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `rem-log-exp` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 97

Calls

4 calls:

13.0ms	(* (* (cos 1) (log (log (exp (sqrt (atan2 b b)))))) (- b a))
7.0ms	(* (cos 1) (log (log (exp (sqrt (atan2 b b))))))
1.0ms	(sqrt (atan2 b b))
2.0ms	(log (log (exp (sqrt (atan2 b b)))))

series428.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(* (* (cos 1) (log (log (exp (sqrt (atan2 b b)))))) (- b a))
167.0ms	(* (cos 1) (log (log (exp (sqrt (atan2 b b))))))
10.0ms	(sqrt (atan2 b b))
71.0ms	(log (log (exp (sqrt (atan2 b b)))))

simplify112.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	272	1002
1	1189	805
2	4618	768
3	5001	768

prune267.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (atan2 b b))
2.0b	(log (log (exp (sqrt (atan2 b b)))))
2.0b	(log (log (exp (sqrt (atan2 b b)))))
2.0b	(log (log (exp (sqrt (atan2 b b)))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

30×	`log-prod`
24×	`log-pow`
18×	`exp-prod`
15×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`sqrt-prod`
11×	`pow1`
7×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`rem-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 70

Calls

4 calls:

1.0ms	(sqrt (atan2 b b))
2.0ms	(log (log (exp (sqrt (atan2 b b)))))
2.0ms	(log (log (exp (sqrt (atan2 b b)))))
2.0ms	(log (log (exp (sqrt (atan2 b b)))))

series224.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt (atan2 b b))
65.0ms	(log (log (exp (sqrt (atan2 b b)))))
71.0ms	(log (log (exp (sqrt (atan2 b b)))))
73.0ms	(log (log (exp (sqrt (atan2 b b)))))

simplify90.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 7 (84.0ms)

Iter	Nodes	Cost
0	61	503
1	85	424
2	114	424
3	151	424
4	278	424
5	748	424
6	3455	423
7	5001	404

prune314.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

regimes90.0ms

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	7	5

end0.0ms

sample2.2s

Algorithm

intervals

Results

740.0ms	1762×	body	10240	exit
590.0ms	7990×	body	80	valid
458.0ms	9778×	body	80	nan
6.0ms	2×	body	5120	valid
1.0ms	3×	body	640	valid
1.0ms	1×	body	1280	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	320	valid