Details

sample147.0ms

Algorithm

intervals

Results

47.0ms	62×	body	10240	exit
33.0ms	306×	body	80	nan
30.0ms	255×	body	80	valid
5.0ms	1×	body	5120	valid

simplify3.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	13	9
2	22	9
3	45	9
4	115	9
5	274	9
6	837	9
7	3217	9
done	5001	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 2 expressions with local error:

0.3b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite23.0ms

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:

20.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
2.0ms	(sqrt (atan2 b b))

series112.0ms

Counts

2 → 6

Calls

2 calls:

94.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
18.0ms	(sqrt (atan2 b b))

simplify4.6s

Counts

30 → 30

Iterations

Useful iterations: 4 (128.0ms)

Iter	Nodes	Cost
0	41	268
1	66	253
2	112	233
3	201	225
4	355	224
5	607	224
6	1288	224
7	4100	224
done	5000	224

prune120.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(sin (pow (sqrt (atan2 b b)) (- b a)))
0.3b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 48

Calls

4 calls:

13.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
22.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series199.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
102.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
11.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))

simplify4.6s

Counts

60 → 60

Iterations

Useful iterations: 4 (147.0ms)

Iter	Nodes	Cost
0	41	536
1	66	506
2	112	466
3	201	450
4	355	448
5	607	448
6	1288	448
7	4100	448
done	5000	448

prune358.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize29.0ms

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)))

rewrite25.0ms

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))
14.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
2.0ms	(sqrt (atan2 b b))
7.0ms	(log (sqrt (atan2 b b)))

series503.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(fma (* (cos 1) (log (sqrt (atan2 b b)))) (- b a) (sin 1))
233.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
12.0ms	(sqrt (atan2 b b))
94.0ms	(log (sqrt (atan2 b b)))

simplify3.0s

Counts

91 → 91

Iterations

Useful iterations: 3 (350.0ms)

Iter	Nodes	Cost
0	98	1029
1	152	979
2	383	858
3	865	854
4	3283	854
done	5000	854

prune367.0ms

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	(* (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)))))

rewrite155.0ms

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:

112.0ms	(* (cos 1) (log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b))))))
3.0ms	(sqrt (atan2 b b))
3.0ms	(sqrt (atan2 b b))
29.0ms	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))

series390.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(* (cos 1) (log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b))))))
20.0ms	(sqrt (atan2 b b))
19.0ms	(sqrt (atan2 b b))
108.0ms	(log (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))))

simplify3.3s

Counts

120 → 120

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	99	1161
1	179	749
2	495	697
3	2615	697
done	5001	697

prune492.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.2b

regimes137.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
done	9	21

end0.0ms

sample5.3s

Algorithm

intervals

Results

1.7s	1890×	body	10240	exit
1.6s	7992×	body	80	valid
1.1s	9694×	body	80	nan
8.0ms	2×	body	5120	valid
3.0ms	2×	body	2560	valid
1.0ms	2×	body	320	valid
1.0ms	2×	body	160	valid