Details

sample338.0ms

Algorithm

intervals

Results

26.0ms	57×	body	10240	exit
16.0ms	255×	body	80	valid
15.0ms	334×	body	80	nan
3.0ms	1×	body	5120	valid

simplify56.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
2×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

2 → 24

Calls

2 calls:

6.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
3.0ms	(sqrt (atan2 b b))

series89.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
26.0ms	(sqrt (atan2 b b))

simplify68.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 6 (64.0ms)

Iter	Nodes	Cost
0	65	150
1	112	137
2	200	132
3	372	131
4	681	131
5	2254	131
6	5001	130

prune80.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma (* (cos 1) (log (sqrt (atan2 b b)))) (- b a) (sin 1))
1.0b	(* (cos 1) (log (sqrt (atan2 b b))))
1.0b	(sqrt (atan2 b b))
2.0b	(log (sqrt (atan2 b b)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

18×	`log-prod`
16×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`sqrt-prod`
11×	`pow1`
7×	`add-exp-log`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `log-pow` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `pow1/2` `associate-l`
1×	`rem-sqrt-square` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 79

Calls

4 calls:

0.0ms	(fma (* (cos 1) (log (sqrt (atan2 b b)))) (- b a) (sin 1))
6.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(log (sqrt (atan2 b b)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(fma (* (cos 1) (log (sqrt (atan2 b b)))) (- b a) (sin 1))
159.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
10.0ms	(sqrt (atan2 b b))
72.0ms	(log (sqrt (atan2 b b)))

simplify141.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	152	637
1	495	555
2	1583	539
3	4758	539
4	5001	539

prune228.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize15.0ms

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)))))

rewrite46.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 108

Calls

4 calls:

33.0ms	(* (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))
8.0ms	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))

series252.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(* (cos 1) (log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b))))))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))
70.0ms	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))

simplify38.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	192	627
1	690	542
2	5001	510

prune308.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize21.0ms

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)))))

rewrite28.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow2` `log-prod` `pow-plus` `prod-exp` `sqrt-prod`
1×	`rem-sqrt-square`

Counts

4 → 117

Calls

4 calls:

1.0ms	(sqrt (atan2 b b))
7.0ms	(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)))))

series217.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (atan2 b b))
67.0ms	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))
68.0ms	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))
72.0ms	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 5 (46.0ms)

Iter	Nodes	Cost
0	44	599
1	93	526
2	287	520
3	782	520
4	1964	520
5	5001	513

prune561.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

regimes87.0ms

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

sample2.1s

Algorithm

intervals

Results

754.0ms	1762×	body	10240	exit
463.0ms	7990×	body	80	valid
452.0ms	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