Details

sample306.0ms

Algorithm

intervals

Results

79.0ms	62×	body	10240	exit
79.0ms	255×	body	80	valid
40.0ms	337×	body	80	nan
0.0ms	1×	body	160	valid

simplify715.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (sqrt (atan2 b b)) (- b a))
0.1b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`pow1` `unpow-prod-down` `sqrt-prod`
5×	`pow-unpow`
4×	`add-exp-log`
3×	`pow-pow` `add-cbrt-cube` `add-log-exp`
2×	`unpow-prod-up` `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 → 48

Calls

3 calls:

19.0ms	(pow (sqrt (atan2 b b)) (- b a))
14.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms	(sqrt (atan2 b b))

series215.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(pow (sqrt (atan2 b b)) (- b a))
117.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
60.0ms	(sqrt (atan2 b b))

simplify638.0ms

Counts: 57 → 57

prune251.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
0.1b	(sin (* (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))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

84×	`sqrt-prod`
78×	`unpow-prod-down`
76×	`add-sqr-sqrt`
25×	`unswap-sqr`
23×	`swap-sqr`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log`
15×	`associate-r` `associate-l`
14×	`sqr-pow`
12×	`unpow-prod-up`
9×	`prod-exp`
6×	`pow1` `pow-to-exp` `sub-neg` `pow-exp` `add-cbrt-cube`
4×	`pow-sub` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow2` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 136

Calls

4 calls:

55.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
39.0ms	(sin (* (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))

series219.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
133.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
11.0ms	(sqrt (atan2 b b))
16.0ms	(sqrt (atan2 b b))

simplify768.0ms

Counts: 148 → 148

prune521.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
0.1b	(sin (* (pow 1 (* 2 (- b a))) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
1.0b	(sqrt (atan2 b b))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

12×	`sqrt-prod`
9×	`unpow-prod-down`
8×	`add-sqr-sqrt`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow-pow` `sqrt-pow1`
4×	`unpow-prod-up` `add-exp-log`
3×	`pow1/2` `add-cbrt-cube` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`pow-to-exp` `rem-sqrt-square` `pow-unpow` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

3 → 50

Calls

3 calls:

20.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
28.0ms	(sin (* (pow 1 (* 2 (- b a))) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
1.0ms	(sqrt (atan2 b b))

series8.6m

Counts

3 → 9

Calls

3 calls:

35.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
8.6m	(sin (* (pow 1 (* 2 (- b a))) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
21.0ms	(sqrt (atan2 b b))

simplify1.0s

Counts: 59 → 59

prune186.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (* 2 (* (- b a) (log (pow (atan2 b b) 1/4)))))
0.1b	(sin (exp (* 2 (* (- b a) (log (pow (atan2 b b) 1/4))))))
0.2b	(* (- b a) (log (pow (atan2 b b) 1/4)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

42×	`log-prod`
35×	`distribute-rgt-in` `distribute-lft-in`
28×	`exp-sum`
21×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
18×	`unpow-prod-down`
17×	`add-cube-cbrt`
6×	`sqr-pow`
5×	`pow1` `add-exp-log` `associate-l` `add-cbrt-cube` `add-log-exp`
4×	`associate-r`
2×	`associate-*l/`
1×	`exp-prod` `flip3--` `exp-to-pow` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `flip--` `cbrt-unprod` `rem-exp-log` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 82

Calls

3 calls:

26.0ms	(exp (* 2 (* (- b a) (log (pow (atan2 b b) 1/4)))))
35.0ms	(sin (exp (* 2 (* (- b a) (log (pow (atan2 b b) 1/4))))))
26.0ms	(* (- b a) (log (pow (atan2 b b) 1/4)))

series255.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(exp (* 2 (* (- b a) (log (pow (atan2 b b) 1/4)))))
81.0ms	(sin (exp (* 2 (* (- b a) (log (pow (atan2 b b) 1/4))))))
135.0ms	(* (- b a) (log (pow (atan2 b b) 1/4)))

simplify501.0ms

Counts: 91 → 91

prune177.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

regimes42.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.5s

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.3s	1833×	body	10240	exit
669.0ms	9736×	body	80	nan
614.0ms	7995×	body	80	valid
2.0ms	1×	body	2560	valid
1.0ms	3×	body	160	valid
0.0ms	1×	body	320	valid

Details

sample306.0ms

simplify715.0ms

prune5.0ms

localize14.0ms

rewrite42.0ms

series215.0ms

simplify638.0ms

prune251.0ms

localize14.0ms

rewrite103.0ms

series219.0ms

simplify768.0ms

prune521.0ms

localize15.0ms

rewrite52.0ms

series8.6m

simplify1.0s

prune186.0ms

localize15.0ms

rewrite90.0ms

series255.0ms

simplify501.0ms

prune177.0ms

regimes42.0ms

bsearch0.0ms

simplify1.5s

end0.0ms

sample3.1s

end1.2m