Details

sample98.0ms

Algorithm

intervals

Results

33.0ms	57×	body	10240	exit
23.0ms	334×	body	80	nan
21.0ms	255×	body	80	valid
3.0ms	1×	body	5120	valid

simplify53.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

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))

series30.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms	(sqrt (atan2 b b))

simplify68.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 6 (65.0ms)

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

prune126.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

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)))

rewrite24.0ms

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:

14.0ms	(* (* (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)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
3.0ms	(sqrt (atan2 b b))
25.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
17.0ms	(log (sqrt (atan2 b b)))

simplify112.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (31.0ms)

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

prune498.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cos 1) (log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b))))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
2.0b	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

66×	`sqrt-pow1`
56×	`pow1`
44×	`log-pow`
34×	`pow1/2`
25×	`associate-r`
18×	`pow-prod-up`
12×	`add-sqr-sqrt`
11×	`pow-prod-down`
10×	`pow-sqr`
9×	`add-exp-log`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-prod` `add-cbrt-cube`
4×	`add-log-exp`
3×	`log-prod` `associate-l`
2×	`pow2` `rem-sqrt-square` `pow-plus` `rem-log-exp` `prod-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

31.0ms	(* (cos 1) (log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b))))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
7.0ms	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))

series46.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (cos 1) (log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b))))))
6.0ms	(sqrt (atan2 b b))
3.0ms	(sqrt (atan2 b b))
16.0ms	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))

simplify282.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	186	575
1	672	490
2	4815	458
3	5001	458

prune689.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

97×	`sqrt-pow1`
77×	`pow1`
66×	`log-pow`
49×	`pow1/2`
27×	`pow-prod-up`
15×	`pow-prod-down` `pow-sqr`
13×	`add-exp-log`
6×	`add-sqr-sqrt` `rem-log-exp`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow2` `log-prod` `pow-plus` `prod-exp` `sqrt-prod`
1×	`rem-sqrt-square`

Counts

4 → 109

Calls

4 calls:

1.0ms	(sqrt (atan2 b b))
9.0ms	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))
7.0ms	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))
8.0ms	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))

series50.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (atan2 b b))
15.0ms	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))
16.0ms	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))
16.0ms	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 5 (45.0ms)

Iter	Nodes	Cost
0	40	539
1	89	466
2	273	460
3	728	460
4	1750	460
5	5001	453

prune1.7s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

regimes248.0ms

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

sample2.8s

Algorithm

intervals

Results

1.0s	1762×	body	10240	exit
681.0ms	9778×	body	80	nan
645.0ms	7990×	body	80	valid
6.0ms	2×	body	5120	valid
2.0ms	3×	body	640	valid
1.0ms	1×	body	1280	valid
1.0ms	3×	body	160	valid
0.0ms	1×	body	320	valid