Details

sample396.0ms

Algorithm

intervals

Results

163.0ms	54×	body	10240	exit
59.0ms	308×	body	80	nan
28.0ms	254×	body	80	valid
3.0ms	1×	body	5120	valid
0.0ms	1×	body	160	valid

simplify537.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (sqrt (atan2 b b)) (- b a))
0.5b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite66.0ms

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:

43.0ms	(pow (sqrt (atan2 b b)) (- b a))
15.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms	(sqrt (atan2 b b))

series303.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(pow (sqrt (atan2 b b)) (- b a))
163.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
95.0ms	(sqrt (atan2 b b))

simplify670.0ms

Counts: 57 → 57

prune218.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- b a))
0.6b	(cbrt (- b a))
0.6b	(cbrt (- b a))
1.0b	(sqrt (atan2 b b))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod` `add-sqr-sqrt`
14×	`*-un-lft-identity`
8×	`add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3--` `pow1/3` `sqrt-prod` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

5.0ms	(cbrt (- b a))
4.0ms	(cbrt (- b a))
5.0ms	(cbrt (- b a))
1.0ms	(sqrt (atan2 b b))

series589.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(cbrt (- b a))
183.0ms	(cbrt (- b a))
186.0ms	(cbrt (- b a))
17.0ms	(sqrt (atan2 b b))

simplify1.5s

Counts: 70 → 70

prune450.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- b a))
0.7b	(pow (pow (sqrt (atan2 b b)) (* (cbrt (- b a)) (cbrt (- b a)))) (pow (/ 1 b) -1/3))
1.0b	(sqrt (atan2 b b))
5.1b	(pow (/ 1 b) -1/3)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

42×	`unpow-prod-down`
28×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
20×	`pow-unpow`
18×	`times-frac`
11×	`add-exp-log`
8×	`pow-exp`
7×	`pow1`
6×	`sqrt-prod`
5×	`cbrt-prod`
4×	`pow-pow` `add-cbrt-cube` `add-log-exp` `sqr-pow`
3×	`pow-to-exp`
2×	`cbrt-div` `div-exp` `div-inv`
1×	`rem-sqrt-square` `rec-exp` `flip3--` `pow-flip` `sqrt-pow1` `pow1/2` `pow1/3` `1-exp` `flip--` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 100

Calls

4 calls:

8.0ms	(cbrt (- b a))
22.0ms	(pow (pow (sqrt (atan2 b b)) (* (cbrt (- b a)) (cbrt (- b a)))) (pow (/ 1 b) -1/3))
1.0ms	(sqrt (atan2 b b))
11.0ms	(pow (/ 1 b) -1/3)

series1.5s

Counts

4 → 12

Calls

4 calls:

229.0ms	(cbrt (- b a))
976.0ms	(pow (pow (sqrt (atan2 b b)) (* (cbrt (- b a)) (cbrt (- b a)))) (pow (/ 1 b) -1/3))
12.0ms	(sqrt (atan2 b b))
235.0ms	(pow (/ 1 b) -1/3)

simplify718.0ms

Counts: 112 → 112

prune636.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize25.0ms

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)))

rewrite113.0ms

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:

74.0ms	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
2.0ms	(sqrt (atan2 b b))
29.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
4.0ms	(log (sqrt (atan2 b b)))

series603.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
11.0ms	(sqrt (atan2 b b))
265.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
87.0ms	(log (sqrt (atan2 b b)))

simplify573.0ms

Counts: 101 → 101

prune363.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.4b

regimes86.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify796.0ms

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.6s	1800×	body	10240	exit
1.2s	9851×	body	80	nan
937.0ms	7987×	body	80	valid
8.0ms	2×	body	5120	valid
2.0ms	4×	body	640	valid
1.0ms	2×	body	1280	valid
1.0ms	4×	body	160	valid
1.0ms	1×	body	320	valid