Details

analyze12.9s (18.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
6.2%	93.5%	0.2%	11
6.2%	93.5%	0.2%	12
7.8%	92%	0.2%	13
8.6%	91.2%	0.2%	14

Compiler

Compiled 115 to 84 computations (27% saved)

sample47.6s (68%)

Results

12.3s	1442×	body	4096	valid
9.3s	1808×	body	2048	valid
7.3s	854×	body	4096	invalid
6.1s	1149×	body	2048	invalid
3.0s	835×	body	1024	valid
2.9s	3546×	body	128	valid
2.5s	692×	body	1024	invalid
1.1s	59×	body	8192	valid
869.0ms	384×	body	512	valid
772.0ms	1075×	body	128	invalid
601.0ms	269×	body	512	invalid
482.0ms	25×	body	8192	invalid
260.0ms	182×	body	256	valid
205.0ms	134×	body	256	invalid

Compiler

Compiled 344 to 251 computations (27% saved)

simplify22.0ms (0%)

Algorithm

1×	egg-herbie

Rules

545×	`associate-/l/_binary64`
526×	`associate-/r/_binary64`
263×	`distribute-rgt-in_binary64`
260×	`distribute-lft-in_binary64`
157×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	175
1	104	173
2	339	173
3	1688	170

Stop Event

1×	node limit

Counts

1 → 2

prune11.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

39.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	39.4b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
	45.4b	(fma.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) (.f64 y-scale y-scale)) (.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) (.f64 x-scale x-scale)) -4) (.f64 (/.f64 (/.f64 (.f64 4 (.f64 (.f64 (-.f64 (.f64 b b) (.f64 a a)) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (.f64 (-.f64 (.f64 b b) (.f64 a a)) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))))) (.f64 y-scale (/.f64 x-scale (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))))) x-scale) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) y-scale)))

Status

Error

Program

▶

39.4b

(-.f64 (*.f64 (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (*.f64 (*.f64 (*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (*.f64 (*.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))

45.4b

(fma.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 y-scale y-scale)) (*.f64 (/.f64 (+.f64 (pow.f64 (*.f64 a (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (*.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) (*.f64 x-scale x-scale)) -4) (*.f64 (/.f64 (/.f64 (*.f64 4 (*.f64 (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) (*.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) (*.f64 y-scale (/.f64 x-scale (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))))) x-scale) (/.f64 (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64))) y-scale)))

Compiler

Compiled 670 to 462 computations (31% saved)

localize42.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	10.6b	(/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale)
✓	26.6b	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	26.8b	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
✓	28.8b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))

series2.1s (3%)

Counts

4 → 132

Calls

4 calls:

2.0s	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
133.0ms	(/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale)
4.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
3.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))

rewrite81.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

429×	`log1p-expm1-u_binary64`
429×	`expm1-log1p-u_binary64`
413×	`add-log-exp_binary64`
398×	`pow1_binary64`
152×	`log-prod_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	190
1	918	181

Stop Event

1×	node limit

Counts

4 → 91

Calls

4 calls:

72.0ms	(/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale)
72.0ms	(sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
72.0ms	(cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))
72.0ms	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))

simplify184.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

509×	`unswap-sqr_binary64`
356×	`fma-neg_binary64`
278×	`times-frac_binary64`
265×	`associate-/l*_binary64`
264×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	256	12980
1	1026	12263
2	4207	12135

Stop Event

1×	node limit

Counts

223 → 150

prune998.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	278	10	288
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	280	10	290

Error

21.0b

Counts

290 → 10

Alt Table

Status	Error	Program
	39.4b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (+.f64 (.f64 (/.f64 (.f64 b b) y-scale) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2)) (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) y-scale) (*.f64 a a))) y-scale)))
	38.7b	(.f64 -1 (.f64 (pow.f64 a 2) (+.f64 (.f64 4 (/.f64 (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)) (.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2)))) (+.f64 (.f64 8 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 b 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2))) (.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2)))) (.f64 4 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (pow.f64 b 2)) (.f64 (pow.f64 x-scale 2) (pow.f64 y-scale 2))))))))
	40.1b	(.f64 (fma.f64 4 (.f64 (.f64 (/.f64 b x-scale) (/.f64 b x-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 y-scale y-scale))) (fma.f64 4 (/.f64 (.f64 b b) (/.f64 (.f64 y-scale (.f64 y-scale (.f64 x-scale x-scale))) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4))) (.f64 (/.f64 8 (.f64 y-scale y-scale)) (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b))) (.f64 x-scale x-scale))))) (neg.f64 (*.f64 a a)))
	42.4b	(-.f64 (.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 y-scale y-scale)) (.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (/.f64 (.f64 x-scale x-scale) (pow.f64 b 4))) 4)) (fma.f64 8 (.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 a a)) (.f64 x-scale x-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (/.f64 (.f64 y-scale y-scale) (.f64 b b)))) (.f64 4 (+.f64 (.f64 (.f64 (/.f64 (.f64 b b) x-scale) (/.f64 (.f64 a a) x-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 y-scale y-scale))) (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 y-scale y-scale)) (/.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (/.f64 (.f64 x-scale x-scale) (pow.f64 b 4))) (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (/.f64 (.f64 y-scale y-scale) (.f64 b b)) (/.f64 (.f64 x-scale x-scale) (*.f64 a a)))))))))
	32.1b	0
	51.8b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (exp.f64 (log.f64 (sin.f64 (.f64 (.f64 angle 1/180) (PI.f64)))))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2)) y-scale) y-scale)))
	39.4b	(/.f64 (neg.f64 (fma.f64 4 (.f64 (/.f64 (/.f64 (.f64 a a) x-scale) x-scale) (.f64 b (.f64 b (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)))) (fma.f64 8 (.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 a a)) x-scale) (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)) x-scale)) (.f64 4 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (/.f64 (/.f64 (.f64 x-scale x-scale) (.f64 a a)) (.f64 b b))))))) (.f64 y-scale y-scale))
	36.3b	(/.f64 (neg.f64 (fma.f64 4 (/.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4) (.f64 (/.f64 y-scale (.f64 a a)) (/.f64 y-scale (.f64 b b)))) (fma.f64 4 (.f64 (.f64 (/.f64 a y-scale) (/.f64 a y-scale)) (.f64 b (.f64 b (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 4)))) (.f64 (/.f64 8 y-scale) (/.f64 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle (PI.f64)))) 2) (.f64 b b)))) y-scale))))) (.f64 x-scale x-scale))
	39.3b	(-.f64 (.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) (cos.f64 (.f64 (/.f64 angle 180) (PI.f64)))) x-scale) y-scale)) (.f64 (.f64 4 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) (PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (*.f64 (/.f64 angle 180) (PI.f64)))) 2)) x-scale) x-scale)) (/.f64 (/.f64 a (/.f64 y-scale a)) y-scale)))
▶	26.6b	(.f64 -4 (.f64 (/.f64 (/.f64 (.f64 a a) x-scale) x-scale) (.f64 (/.f64 b y-scale) (/.f64 b y-scale))))

Compiler

Compiled 36733 to 25165 computations (31.5% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 b y-scale) (/.f64 b y-scale))
✓	3.9b	(/.f64 (/.f64 (*.f64 a a) x-scale) x-scale)
✓	9.5b	(/.f64 (*.f64 a a) x-scale)
✓	15.9b	(.f64 (/.f64 (/.f64 (.f64 a a) x-scale) x-scale) (*.f64 (/.f64 b y-scale) (/.f64 b y-scale)))

series203.0ms (0.3%)

Counts

4 → 120

Calls

4 calls:

145.0ms	(.f64 (/.f64 (/.f64 (.f64 a a) x-scale) x-scale) (*.f64 (/.f64 b y-scale) (/.f64 b y-scale)))
25.0ms	(*.f64 (/.f64 b y-scale) (/.f64 b y-scale))
25.0ms	(/.f64 (/.f64 (*.f64 a a) x-scale) x-scale)
9.0ms	(/.f64 (*.f64 a a) x-scale)

rewrite65.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

216×	`expm1-udef_binary64`
216×	`log1p-udef_binary64`
200×	`log-pow_binary64`
161×	`egg-rr`
122×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	43
1	243	34
2	3742	34

Stop Event

1×	node limit

Counts

4 → 161

Calls

4 calls:

62.0ms	(*.f64 (/.f64 b y-scale) (/.f64 b y-scale))
62.0ms	(/.f64 (/.f64 (*.f64 a a) x-scale) x-scale)
62.0ms	(/.f64 (*.f64 a a) x-scale)
62.0ms	(.f64 (/.f64 (/.f64 (.f64 a a) x-scale) x-scale) (*.f64 (/.f64 b y-scale) (/.f64 b y-scale)))

simplify40.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

749×	`associate-/r*_binary64`
435×	`associate-/l/_binary64`
401×	`associate-*l/_binary64`
394×	`associate-l_binary64`
369×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	1704
1	45	1704
2	149	1704
3	1053	1704

Stop Event

1×	node limit

Counts

281 → 169

prune232.0ms (0.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	154	15	169
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	163	16	179

Error

4.2b

Counts

179 → 16

Alt Table

Status	Error	Program
	16.8b	(.f64 -4 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 a x-scale) 2)) 3) (*.f64 (/.f64 b y-scale) (/.f64 b y-scale))))
	32.0b	(.f64 -4 (/.f64 (.f64 (/.f64 a (/.f64 x-scale a)) (.f64 b b)) (.f64 x-scale (*.f64 y-scale y-scale))))
	31.0b	(.f64 -4 (.f64 b (.f64 b (/.f64 (.f64 a a) (.f64 y-scale (.f64 x-scale (*.f64 y-scale x-scale)))))))
	18.3b	(.f64 -4 (.f64 (/.f64 (.f64 (/.f64 a (pow.f64 (cbrt.f64 x-scale) 2)) (/.f64 a (cbrt.f64 x-scale))) x-scale) (.f64 (/.f64 b y-scale) (/.f64 b y-scale))))
	39.3b	(.f64 -4 (/.f64 (.f64 (.f64 a a) (.f64 b b)) (.f64 (.f64 x-scale x-scale) (*.f64 y-scale y-scale))))
	32.1b	0
▶	5.3b	(.f64 -4 (pow.f64 (.f64 (/.f64 b y-scale) (/.f64 a x-scale)) 2))
	14.0b	(.f64 -4 (/.f64 (.f64 (pow.f64 (/.f64 a x-scale) 2) (/.f64 b y-scale)) (/.f64 y-scale b)))
	17.2b	(.f64 -4 (/.f64 (.f64 (*.f64 (pow.f64 (/.f64 a x-scale) 2) (/.f64 b y-scale)) b) y-scale))
	18.1b	(.f64 -4 (/.f64 1 (/.f64 x-scale (.f64 (/.f64 a (/.f64 x-scale a)) (pow.f64 (/.f64 b y-scale) 2)))))
	21.4b	(.f64 -4 (/.f64 (.f64 (/.f64 a (/.f64 x-scale a)) (.f64 b (/.f64 b y-scale))) (.f64 x-scale y-scale)))
	32.4b	(.f64 -4 (/.f64 (.f64 (.f64 a a) (.f64 b (/.f64 b y-scale))) (.f64 (.f64 x-scale x-scale) y-scale)))
	24.1b	(.f64 -4 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (/.f64 b y-scale) (/.f64 a x-scale)) 2) 3)))
	5.6b	(.f64 -4 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 b y-scale) (/.f64 a x-scale)) 2)) 3))
	17.9b	(.f64 -4 (/.f64 (.f64 (/.f64 a (/.f64 x-scale a)) (pow.f64 (/.f64 b y-scale) 2)) x-scale))
	19.0b	(.f64 -4 (/.f64 (.f64 (*.f64 b (/.f64 b y-scale)) (pow.f64 (/.f64 a x-scale) 2)) y-scale))

Compiler

Compiled 3829 to 1657 computations (56.7% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 -4 (pow.f64 (.f64 (/.f64 b y-scale) (/.f64 a x-scale)) 2))
✓	0.3b	(pow.f64 (*.f64 (/.f64 b y-scale) (/.f64 a x-scale)) 2)
✓	7.0b	(*.f64 (/.f64 b y-scale) (/.f64 a x-scale))

series246.0ms (0.4%)

Counts

3 → 144

Calls

3 calls:

170.0ms	(.f64 -4 (pow.f64 (.f64 (/.f64 b y-scale) (/.f64 a x-scale)) 2))
47.0ms	(pow.f64 (*.f64 (/.f64 b y-scale) (/.f64 a x-scale)) 2)
29.0ms	(*.f64 (/.f64 b y-scale) (/.f64 a x-scale))

rewrite59.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

670×	`log-prod_binary64`
229×	`expm1-udef_binary64`
229×	`log1p-udef_binary64`
201×	`log-pow_binary64`
165×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	39
1	262	39
2	3470	39

Stop Event

1×	node limit

Counts

3 → 117

Calls

3 calls:

56.0ms	(.f64 -4 (pow.f64 (.f64 (/.f64 b y-scale) (/.f64 a x-scale)) 2))
56.0ms	(pow.f64 (*.f64 (/.f64 b y-scale) (/.f64 a x-scale)) 2)
56.0ms	(*.f64 (/.f64 b y-scale) (/.f64 a x-scale))

simplify56.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

827×	`associate-r_binary64`
799×	`associate-l_binary64`
589×	`associate-/l/_binary64`
436×	`associate-/r/_binary64`
256×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	2736
1	72	2736
2	224	2736
3	1517	2736

Stop Event

1×	node limit

Counts

261 → 126

prune200.0ms (0.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	118	8	126
Fresh	6	9	15
Picked	1	0	1
Done	0	0	0
Total	125	17	142

Error

0.0b

Counts

142 → 17

Alt Table

Status	Error	Program
	21.1b	(.f64 -4 (/.f64 (.f64 (.f64 b a) (.f64 b a)) (.f64 (.f64 y-scale x-scale) (*.f64 y-scale x-scale))))
	21.4b	(.f64 -4 (/.f64 (.f64 (/.f64 a (/.f64 x-scale a)) (.f64 b (/.f64 b y-scale))) (.f64 x-scale y-scale)))
	22.1b	(.f64 -4 (/.f64 (.f64 (.f64 b (/.f64 a x-scale)) (.f64 b (/.f64 a x-scale))) (*.f64 y-scale y-scale)))
	32.4b	(.f64 -4 (/.f64 (.f64 (.f64 a a) (.f64 b (/.f64 b y-scale))) (.f64 (.f64 x-scale x-scale) y-scale)))
	24.9b	(.f64 -4 (.f64 (sqrt.f64 (.f64 (/.f64 b y-scale) (/.f64 a x-scale))) (.f64 (sqrt.f64 (.f64 (/.f64 b y-scale) (/.f64 a x-scale))) (.f64 (/.f64 b y-scale) (/.f64 a x-scale)))))
	16.8b	(.f64 -4 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 a x-scale) 2)) 3) (*.f64 (/.f64 b y-scale) (/.f64 b y-scale))))
	27.8b	(.f64 (.f64 (/.f64 a y-scale) (/.f64 a y-scale)) (/.f64 (.f64 b -4) (/.f64 (.f64 x-scale x-scale) b)))
	24.1b	(.f64 -4 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (/.f64 b y-scale) (/.f64 a x-scale)) 2) 3)))
	6.3b	(.f64 -4 (.f64 (/.f64 a x-scale) (.f64 (/.f64 b y-scale) (.f64 (/.f64 b y-scale) (/.f64 a x-scale)))))
	6.2b	(.f64 -4 (pow.f64 (/.f64 (.f64 a b) (*.f64 x-scale y-scale)) 2))
	17.9b	(.f64 -4 (/.f64 (.f64 (/.f64 a (/.f64 x-scale a)) (pow.f64 (/.f64 b y-scale) 2)) x-scale))
	18.3b	(.f64 -4 (.f64 (/.f64 (.f64 (/.f64 a (pow.f64 (cbrt.f64 x-scale) 2)) (/.f64 a (cbrt.f64 x-scale))) x-scale) (.f64 (/.f64 b y-scale) (/.f64 b y-scale))))
	14.0b	(.f64 -4 (/.f64 (.f64 (pow.f64 (/.f64 a x-scale) 2) (/.f64 b y-scale)) (/.f64 y-scale b)))
▶	5.6b	(.f64 -4 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 b y-scale) (/.f64 a x-scale)) 2)) 3))
	8.7b	(.f64 -4 (.f64 (/.f64 b y-scale) (.f64 (/.f64 a x-scale) (.f64 (/.f64 b y-scale) (/.f64 a x-scale)))))
	17.2b	(.f64 -4 (/.f64 (.f64 (*.f64 (pow.f64 (/.f64 a x-scale) 2) (/.f64 b y-scale)) b) y-scale))
	6.3b	(.f64 -4 (pow.f64 (/.f64 1 (/.f64 (.f64 y-scale x-scale) (*.f64 b a))) 2))

Compiler

Compiled 2710 to 1336 computations (50.7% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (*.f64 (/.f64 b y-scale) (/.f64 a x-scale)) 2)
✓	0.3b	(pow.f64 (cbrt.f64 (pow.f64 (*.f64 (/.f64 b y-scale) (/.f64 a x-scale)) 2)) 3)
	7.0b	(*.f64 (/.f64 b y-scale) (/.f64 a x-scale))
✓	20.3b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 b y-scale) (/.f64 a x-scale)) 2))

series101.0ms (0.1%)

Counts

2 → 0

Calls

2 calls:

61.0ms	(pow.f64 (cbrt.f64 (pow.f64 (*.f64 (/.f64 b y-scale) (/.f64 a x-scale)) 2)) 3)
40.0ms	(cbrt.f64 (pow.f64 (*.f64 (/.f64 b y-scale) (/.f64 a x-scale)) 2))

rewrite51.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

221×	`expm1-udef_binary64`
221×	`log1p-udef_binary64`
200×	`log-pow_binary64`
165×	`log-div_binary64`
126×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	28
1	281	28
2	3522	28

Stop Event

1×	node limit

Counts

2 → 68

Calls

2 calls:

50.0ms	(pow.f64 (cbrt.f64 (pow.f64 (*.f64 (/.f64 b y-scale) (/.f64 a x-scale)) 2)) 3)
50.0ms	(cbrt.f64 (pow.f64 (*.f64 (/.f64 b y-scale) (/.f64 a x-scale)) 2))

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

68 → 68

prune276.0ms (0.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	173	2	175
Fresh	2	14	16
Picked	1	0	1
Done	0	0	0
Total	176	16	192

Error

0.0b

Counts

192 → 16

Alt Table

Status	Error	Program
	21.1b	(.f64 -4 (/.f64 (.f64 (.f64 b a) (.f64 b a)) (.f64 (.f64 y-scale x-scale) (*.f64 y-scale x-scale))))
	21.4b	(.f64 -4 (/.f64 (.f64 (/.f64 a (/.f64 x-scale a)) (.f64 b (/.f64 b y-scale))) (.f64 x-scale y-scale)))
	22.1b	(.f64 -4 (/.f64 (.f64 (.f64 b (/.f64 a x-scale)) (.f64 b (/.f64 a x-scale))) (*.f64 y-scale y-scale)))
	32.4b	(.f64 -4 (/.f64 (.f64 (.f64 a a) (.f64 b (/.f64 b y-scale))) (.f64 (.f64 x-scale x-scale) y-scale)))
	27.8b	(.f64 (.f64 (/.f64 a y-scale) (/.f64 a y-scale)) (/.f64 (.f64 b -4) (/.f64 (.f64 x-scale x-scale) b)))
	5.5b	(*.f64 -4 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (/.f64 b y-scale) (/.f64 x-scale a)) 2)) 3))
	24.1b	(.f64 -4 (cbrt.f64 (pow.f64 (pow.f64 (.f64 (/.f64 b y-scale) (/.f64 a x-scale)) 2) 3)))
	6.3b	(.f64 -4 (.f64 (/.f64 a x-scale) (.f64 (/.f64 b y-scale) (.f64 (/.f64 b y-scale) (/.f64 a x-scale)))))
	6.2b	(.f64 -4 (pow.f64 (/.f64 (.f64 a b) (*.f64 x-scale y-scale)) 2))
	17.9b	(.f64 -4 (/.f64 (.f64 (/.f64 a (/.f64 x-scale a)) (pow.f64 (/.f64 b y-scale) 2)) x-scale))
	8.7b	(.f64 -4 (.f64 (/.f64 b y-scale) (.f64 (/.f64 a x-scale) (.f64 (/.f64 b y-scale) (/.f64 a x-scale)))))
	5.5b	(.f64 -4 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 1 (.f64 (/.f64 x-scale a) (/.f64 y-scale b))) 2)) 3))
	24.9b	(.f64 -4 (.f64 (sqrt.f64 (.f64 (/.f64 b y-scale) (/.f64 a x-scale))) (.f64 (sqrt.f64 (.f64 (/.f64 b y-scale) (/.f64 a x-scale))) (.f64 (/.f64 b y-scale) (/.f64 a x-scale)))))
	14.0b	(.f64 -4 (/.f64 (.f64 (pow.f64 (/.f64 a x-scale) 2) (/.f64 b y-scale)) (/.f64 y-scale b)))
	17.2b	(.f64 -4 (/.f64 (.f64 (*.f64 (pow.f64 (/.f64 a x-scale) 2) (/.f64 b y-scale)) b) y-scale))
	6.3b	(.f64 -4 (pow.f64 (/.f64 1 (/.f64 (.f64 y-scale x-scale) (*.f64 b a))) 2))

Compiler

Compiled 3586 to 1701 computations (52.6% saved)

regimes2.1s (2.9%)

Accuracy

Total 5.6b remaining (98%)

Threshold costs 0b (0%)

Counts

157 → 3

Compiler

Compiled 46728 to 33551 computations (28.2% saved)

bsearch2.3s (3.3%)

Steps

Iters	Range		Point
9	4.940068468857467e-129	7.502660156178328e-120	7.375080175177962e-129
10	-136773668221383.03	-2.2268282407577833	-251570.8691730476

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	64
1	49	64
2	61	64
3	72	64
4	79	64
5	83	64
6	84	64

Stop Event

1×

saturated

end208.0ms (0.3%)

Compiler: Compiled 435 to 283 computations (34.9% saved)

Details

analyze12.9s (18.3%)

sample47.6s (68%)

simplify22.0ms (0%)

prune11.0ms (0%)

localize42.0ms (0.1%)

series2.1s (3%)

rewrite81.0ms (0.1%)

simplify184.0ms (0.3%)

prune998.0ms (1.4%)

localize10.0ms (0%)

series203.0ms (0.3%)

rewrite65.0ms (0.1%)

simplify40.0ms (0.1%)

prune232.0ms (0.3%)

localize8.0ms (0%)

series246.0ms (0.4%)

rewrite59.0ms (0.1%)

simplify56.0ms (0.1%)

prune200.0ms (0.3%)

localize11.0ms (0%)

series101.0ms (0.1%)

rewrite51.0ms (0.1%)

simplify7.0ms (0%)

prune276.0ms (0.4%)

regimes2.1s (2.9%)

bsearch2.3s (3.3%)

simplify6.0ms (0%)

end208.0ms (0.3%)

Profiling