Details

sample184.0ms

Algorithm

intervals

Results

67.0ms	46×	body	10240	exit
50.0ms	312×	body	80	nan
43.0ms	256×	body	80	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
7	2494
6	745
5	254
4	110
3	45
2	22
1	13
0	7

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
11×	`unpow-prod-up`
9×	`prod-diff`
6×	`pow1` `unpow-prod-down` `sqrt-prod`
5×	`pow-unpow`
4×	`add-exp-log`
3×	`expm1-log1p-u` `pow-pow` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `rem-sqrt-square` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

3 → 66

Calls

3 calls:

10.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
6.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series139.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
37.0ms	(pow (sqrt (atan2 b b)) (- b a))
20.0ms	(sqrt (atan2 b b))

simplify2.0s

Counts

75 → 75

Iterations

Iter	Nodes
4	3500
3	1486
2	616
1	299
0	120

prune786.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
26×	`add-cube-cbrt`
24×	`sqrt-prod`
22×	`unpow-prod-up`
18×	`unpow-prod-down` `prod-diff`
12×	`pow1`
10×	`pow-unpow` `pow-pow` `sqrt-pow1`
6×	`pow1/2` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 122

Calls

4 calls:

10.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
12.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series125.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
49.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
13.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))

simplify2.5s

Counts

134 → 134

Iterations

Iter	Nodes
4	4382
3	1816
2	698
1	326
0	124

prune1.8s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (/ (log (atan2 b b)) (/ 4 (- b a))))
0.3b	(/ (log (atan2 b b)) (/ 4 (- b a)))
1.0b	(sqrt (atan2 b b))
1.6b	(log (atan2 b b))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

303×	`times-frac`
186×	`add-sqr-sqrt`
185×	`*-un-lft-identity`
131×	`add-cube-cbrt`
89×	`exp-prod`
49×	`pow1`
44×	`log-pow`
27×	`distribute-lft-out--` `difference-of-squares`
21×	`associate-/r*`
20×	`associate-/r/`
12×	`div-inv`
10×	`add-exp-log`
9×	`flip3--` `add-cbrt-cube` `flip--`
5×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`cbrt-undiv` `log-prod` `div-exp` `sqrt-prod`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `exp-to-pow` `pow1/2` `rem-log-exp` `rem-exp-log`

Counts

4 → 259

Calls

4 calls:

18.0ms	(exp (/ (log (atan2 b b)) (/ 4 (- b a))))
13.0ms	(/ (log (atan2 b b)) (/ 4 (- b a)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(log (atan2 b b))

series254.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(exp (/ (log (atan2 b b)) (/ 4 (- b a))))
95.0ms	(/ (log (atan2 b b)) (/ 4 (- b a)))
20.0ms	(sqrt (atan2 b b))
110.0ms	(log (atan2 b b))

simplify853.0ms

Counts

271 → 271

Iterations

Iter	Nodes
2	2009
1	666
0	316

prune4.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

1.6b	(log (atan2 b b))
1.6b	(cbrt (log (atan2 b b)))
1.6b	(cbrt (log (atan2 b b)))
1.6b	(cbrt (log (atan2 b b)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cube-cbrt`
5×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log-pow` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `pow1/3`
1×	`rem-log-exp`

Counts

4 → 60

Calls

4 calls:

1.0ms	(log (atan2 b b))
1.0ms	(cbrt (log (atan2 b b)))
1.0ms	(cbrt (log (atan2 b b)))
1.0ms	(cbrt (log (atan2 b b)))

series851.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(log (atan2 b b))
281.0ms	(cbrt (log (atan2 b b)))
284.0ms	(cbrt (log (atan2 b b)))
219.0ms	(cbrt (log (atan2 b b)))

simplify1.0s

Counts

72 → 72

Iterations

Iter	Nodes
5	2469
4	466
3	146
2	78
1	47
0	35

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes86.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	19
1	19
0	17

end0.0ms

sample7.0s

Algorithm

intervals

Results

3.3s	1808×	body	10240	exit
1.8s	9757×	body	80	nan
1.5s	7990×	body	80	valid
14.0ms	3×	body	5120	valid
4.0ms	4×	body	640	valid
2.0ms	1×	body	2560	valid
1.0ms	2×	body	320	valid