Details

analyze17.3s (3.4%)

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
2.3%	97.4%	0.2%	9
3.5%	96.2%	0.2%	10
5.3%	94.5%	0.2%	11
6.1%	93.6%	0.2%	12
9.2%	90.6%	0.2%	13
13.8%	85.9%	0.2%	14

Compiler

Compiled 170 to 127 computations (25.3% saved)

sample1.6s (0.3%)

Algorithm

1×

intervals

Results

470.0ms	48×	body	4096	valid
415.0ms	6×	body	8192	exit
286.0ms	44×	body	2048	valid
247.0ms	52×	body	1024	valid
110.0ms	34×	body	512	valid
53.0ms	72×	body	128	valid
13.0ms	6×	body	256	valid

Compiler

Compiled 342 to 266 computations (22.2% saved)

simplify137.0ms (0%)

Algorithm

1×	egg-herbie

Counts

4 → 4

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5229	276

prune13.0ms (0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Kept	Total
New	4	4
Fresh	4	4
Picked	0	0
Done	0	0
Total	8	8

Error

40.1b

Counts

8 → 5

Compiler

Compiled 172 to 122 computations (29.1% saved)

localize267.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 (/.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) (/.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)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.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)) 2) (pow.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) 2)))) (/.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))) PI.f64)
0.0b	(+.f64 (pow.f64 (-.f64 (/.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)) 2) (pow.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) 2))
0.0b	(+.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))
0.0b	(+.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))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite23.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`

Counts

4 → 28

Calls

8 calls:

4.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 (/.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) (/.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)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.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)) 2) (pow.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) 2)))) (/.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))) PI.f64)

series261.0ms (0.1%)

Counts

4 → 16

Calls

4 calls:

74.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
64.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
62.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
61.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 4840 to 3612 computations (25.4% saved)

simplify82.0ms (0%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4796	604
1	4796	604

localize82.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) x-scale) y-scale) 2))
0.0b	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 (/.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 2)) x-scale) x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2)))) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale))) PI.f64)
0.0b	(+.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))
0.0b	(+.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))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite20.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`

Counts

4 → 28

Calls

8 calls:

2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 (/.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 2)) x-scale) x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2)))) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale))) PI.f64)

series238.0ms (0%)

Counts

4 → 16

Calls

4 calls:

62.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
60.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
58.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
58.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 4840 to 3416 computations (29.4% saved)

simplify84.0ms (0%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4796	604
1	4796	604

prune1.6s (0.3%)

Pruning

39 alts after pruning (37 fresh and 2 done)

	Pruned	Kept	Total
New	54	34	88
Fresh	0	3	3
Picked	0	0	0
Done	0	2	2
Total	54	39	93

Error

38.1b

Counts

93 → 39

Compiler

Compiled 19750 to 13751 computations (30.4% saved)

localize96.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (-.f64 (.f64 1/180 (.f64 angle PI.f64)) (.f64 1/34992000 (.f64 (pow.f64 angle 3) (pow.f64 PI.f64 3))))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2))
0.0b	(+.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))
0.0b	(+.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))
0.0b	(.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 (/.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 2)) x-scale) x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (-.f64 (.f64 1/180 (.f64 angle PI.f64)) (.f64 1/34992000 (.f64 (pow.f64 angle 3) (pow.f64 PI.f64 3))))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2)))) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale))) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite20.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`

Counts

4 → 28

Calls

8 calls:

2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 (/.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 2)) x-scale) x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (-.f64 (.f64 1/180 (.f64 angle PI.f64)) (.f64 1/34992000 (.f64 (pow.f64 angle 3) (pow.f64 PI.f64 3))))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2)))) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale))) PI.f64))

series213.0ms (0%)

Counts

4 → 13

Calls

4 calls:

64.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
50.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
50.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
49.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 4501 to 3164 computations (29.7% saved)

simplify80.0ms (0%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4796	532
1	4796	532

localize84.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 (/.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 2)) x-scale) x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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 (.f64 1/180 (.f64 angle PI.f64))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2)))) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) x-scale) y-scale))) PI.f64)
0.0b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (.f64 1/180 (*.f64 angle PI.f64))) 2))
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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 (.f64 1/180 (.f64 angle PI.f64))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2))
0.0b	(+.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))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite20.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`

Counts

4 → 28

Calls

8 calls:

2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 (/.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 2)) x-scale) x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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 (.f64 1/180 (.f64 angle PI.f64))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2)))) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) x-scale) y-scale))) PI.f64)

series235.0ms (0%)

Counts

4 → 16

Calls

4 calls:

59.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
59.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
59.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
58.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 4812 to 3360 computations (30.2% saved)

simplify82.0ms (0%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4796	604
1	4796	604

localize86.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (log.f64 (exp.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64))))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) x-scale) y-scale) 2))
0.0b	(+.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))
0.0b	(+.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))
0.0b	(+.f64 (pow.f64 (.f64 a (log.f64 (exp.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64))))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 2))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite20.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`

Counts

4 → 28

Calls

8 calls:

2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (log.f64 (exp.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64))))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) x-scale) y-scale) 2))

series229.0ms (0%)

Counts

4 → 15

Calls

4 calls:

62.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
60.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
59.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
48.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 4706 to 3336 computations (29.1% saved)

simplify82.0ms (0%)

Algorithm

1×	egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4796	580
1	4796	580

localize85.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.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))
0.0b	(+.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))
0.0b	(+.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))
0.0b	(+.f64 (pow.f64 (-.f64 (/.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 (.f64 1/180 (.f64 angle PI.f64))) 2)) y-scale) y-scale)) 2) (pow.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) 2))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite20.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`

Counts

4 → 28

Calls

8 calls:

2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(+.f64 (pow.f64 (-.f64 (/.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 (.f64 1/180 (.f64 angle PI.f64))) 2)) y-scale) y-scale)) 2) (pow.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) 2))

series243.0ms (0%)

Counts

4 → 16

Calls

4 calls:

62.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
61.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
60.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
60.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 4812 to 3556 computations (26.1% saved)

simplify83.0ms (0%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4796	604
1	4796	604

localize90.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (pow.f64 (-.f64 (/.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)) 2) (pow.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) 2))
0.0b	(+.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))
0.0b	(+.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))
0.0b	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 (/.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) (/.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)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.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)) 2) (pow.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) 2)))) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (log.f64 (exp.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64))))) (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale))) PI.f64)
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite20.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`

Counts

4 → 28

Calls

8 calls:

2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 (/.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) (/.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)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.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)) 2) (pow.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) 2)))) (/.f64 (/.f64 (.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (log.f64 (exp.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64))))) (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) x-scale) y-scale))) PI.f64)

series238.0ms (0%)

Counts

4 → 15

Calls

4 calls:

63.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
62.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
61.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
52.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 4706 to 3525 computations (25.1% saved)

simplify82.0ms (0%)

Algorithm

1×	egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4796	580
1	4796	580

prune6.0s (1.2%)

Pruning

101 alts after pruning (98 fresh and 3 done)

	Pruned	Kept	Total
New	149	66	215
Fresh	0	32	32
Picked	0	0	0
Done	4	3	7
Total	153	101	254

Error

37.2b

Counts

254 → 101

Compiler

Compiled 50277 to 34778 computations (30.8% saved)

localize97.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (-.f64 (.f64 1/180 (.f64 angle PI.f64)) (.f64 1/34992000 (.f64 (pow.f64 angle 3) (pow.f64 PI.f64 3))))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2))
0.0b	(+.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))
0.0b	(+.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))
0.0b	(.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 (/.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 2)) x-scale) x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (-.f64 (.f64 1/180 (.f64 angle PI.f64)) (.f64 1/34992000 (.f64 (pow.f64 angle 3) (pow.f64 PI.f64 3))))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2)))) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) x-scale) y-scale))) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.2b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

rewrite21.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`

Counts

4 → 28

Calls

8 calls:

3.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
3.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 (/.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 2)) x-scale) x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (-.f64 (.f64 1/180 (.f64 angle PI.f64)) (.f64 1/34992000 (.f64 (pow.f64 angle 3) (pow.f64 PI.f64 3))))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2)))) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) x-scale) y-scale))) PI.f64))

series209.0ms (0%)

Counts

4 → 13

Calls

4 calls:

61.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
50.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
49.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
48.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 4501 to 3146 computations (30.1% saved)

simplify81.0ms (0%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4807	532
1	4807	532

localize93.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 2))
0.0b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (.f64 1/180 (*.f64 angle PI.f64))) 2))
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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 (.f64 1/180 (.f64 angle PI.f64))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2))
0.0b	(+.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))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.0b	(/.f64 (-.f64 (-.f64 (/.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 2)) x-scale) x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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 (.f64 1/180 (.f64 angle PI.f64))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2)))) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (.f64 1/180 (.f64 angle PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale))

rewrite547.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

415×	`times-frac_binary64`
272×	`*-un-lft-identity_binary64`
246×	`add-sqr-sqrt_binary64`
142×	`add-cube-cbrt_binary64`
78×	`distribute-lft-out--_binary64`
63×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
52×	`difference-of-squares_binary64`
33×	`div-inv_binary64`
27×	`cbrt-undiv_binary64` `div-exp_binary64`
26×	`sqrt-prod_binary64`
25×	`associate-/r*_binary64`
22×	`cbrt-unprod_binary64` `prod-exp_binary64`
8×	`associate-/l/_binary64` `frac-sub_binary64`
7×	`associate-/l*_binary64`
6×	`sqrt-div_binary64`
4×	`add-log-exp_binary64` `pow1_binary64`
3×	`flip3-+_binary64` `flip3--_binary64` `flip--_binary64` `flip-+_binary64`
1×	`associate-/r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 268

Calls

8 calls:

353.0ms	(/.f64 (-.f64 (-.f64 (/.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 2)) x-scale) x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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 (.f64 1/180 (.f64 angle PI.f64))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2)))) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (.f64 1/180 (.f64 angle PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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 (.f64 1/180 (.f64 angle PI.f64))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2))

series1.5min (17.2%)

Counts

4 → 34

Calls

4 calls:

1.5min	(/.f64 (-.f64 (-.f64 (/.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 2)) x-scale) x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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 (.f64 1/180 (.f64 angle PI.f64))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2)))) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (.f64 1/180 (.f64 angle PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale))
57.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
57.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
56.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 46615 to 33303 computations (28.6% saved)

simplify854.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

302 → 302

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	5069	110791

localize93.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 2))
0.0b	(+.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))
0.0b	(+.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))
0.0b	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 (/.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 2)) x-scale) x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (log.f64 (exp.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2)))) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale))) PI.f64)
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite20.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`

Counts

4 → 28

Calls

8 calls:

2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 (/.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 2)) x-scale) x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (log.f64 (exp.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2)))) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale))) PI.f64)

series234.0ms (0%)

Counts

4 → 15

Calls

4 calls:

64.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
63.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
59.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
48.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 4706 to 3336 computations (29.1% saved)

simplify81.0ms (0%)

Algorithm

1×	egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4796	580
1	4796	580

localize109.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 (/.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 2)) x-scale) x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (-.f64 (.f64 1/180 (.f64 angle PI.f64)) (.f64 1/34992000 (.f64 (pow.f64 angle 3) (pow.f64 PI.f64 3))))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (cbrt.f64 (pow.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) 3)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2)))) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale))) PI.f64))
0.0b	(+.f64 (pow.f64 (.f64 a (-.f64 (.f64 1/180 (.f64 angle PI.f64)) (.f64 1/34992000 (.f64 (pow.f64 angle 3) (pow.f64 PI.f64 3))))) 2) (pow.f64 (.f64 (cos.f64 (*.f64 (/.f64 angle 180) PI.f64)) b) 2))
0.0b	(+.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))
0.0b	(+.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))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite20.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`

Counts

4 → 28

Calls

8 calls:

2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(.f64 180 (/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 (/.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 2)) x-scale) x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (-.f64 (.f64 1/180 (.f64 angle PI.f64)) (.f64 1/34992000 (.f64 (pow.f64 angle 3) (pow.f64 PI.f64 3))))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (cbrt.f64 (pow.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) 3)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2)))) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale))) PI.f64))

series214.0ms (0%)

Counts

4 → 13

Calls

4 calls:

63.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
51.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
50.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
50.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 4576 to 3239 computations (29.2% saved)

simplify80.0ms (0%)

Algorithm

1×	egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4796	532
1	4796	532

localize98.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.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))
0.0b	(+.f64 (pow.f64 (-.f64 (/.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)) 2) (pow.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) 2))
0.0b	(+.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))
0.0b	(+.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))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite21.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`

Counts

4 → 28

Calls

8 calls:

2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(+.f64 (pow.f64 (-.f64 (/.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)) 2) (pow.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) 2))

series258.0ms (0.1%)

Counts

4 → 16

Calls

4 calls:

66.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
64.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
64.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
64.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 5092 to 3780 computations (25.8% saved)

simplify80.0ms (0%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4796	604
1	4796	604

prune25.3s (4.9%)

Pruning

255 alts after pruning (248 fresh and 7 done)

	Pruned	Kept	Total
New	301	170	471
Fresh	15	78	93
Picked	0	0	0
Done	1	7	8
Total	317	255	572

Error

28.9b

Counts

572 → 255

Compiler

Compiled 145099 to 95417 computations (34.2% saved)

localize70.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2))
0.1b	(.f64 (-.f64 (.f64 b b) (.f64 a a)) (cos.f64 (.f64 1/180 (*.f64 angle PI.f64))))
0.0b	(.f64 (pow.f64 b 4) (pow.f64 (cos.f64 (.f64 1/180 (*.f64 angle PI.f64))) 4))
0.0b	(+.f64 (.f64 y-scale (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2))) (+.f64 (.f64 y-scale (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2))) (.f64 y-scale (sqrt.f64 (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 a 4)) (+.f64 (.f64 (pow.f64 b 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (.f64 2 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (*.f64 angle PI.f64))) 2)))))))))))
27.2b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
27.2b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
27.2b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
28.6b	(/.f64 (+.f64 (.f64 y-scale (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2))) (+.f64 (.f64 y-scale (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2))) (.f64 y-scale (sqrt.f64 (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 a 4)) (+.f64 (.f64 (pow.f64 b 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (.f64 2 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2))))))))))) (.f64 angle (.f64 x-scale (.f64 PI.f64 (.f64 (-.f64 (.f64 b b) (.f64 a a)) (cos.f64 (.f64 1/180 (*.f64 angle PI.f64))))))))

rewrite70.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`-un-lft-identity_binary64` `associate-r/_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
5×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `distribute-lft-out_binary64` `associate-/l*_binary64` `times-frac_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64` `associate-*l/_binary64`
1×	`flip3-+_binary64` `associate-/r*_binary64` `flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 54

Calls

8 calls:

36.0ms	(/.f64 (+.f64 (.f64 y-scale (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2))) (+.f64 (.f64 y-scale (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2))) (.f64 y-scale (sqrt.f64 (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 a 4)) (+.f64 (.f64 (pow.f64 b 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (.f64 2 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2))))))))))) (.f64 angle (.f64 x-scale (.f64 PI.f64 (.f64 (-.f64 (.f64 b b) (.f64 a a)) (cos.f64 (.f64 1/180 (*.f64 angle PI.f64))))))))
3.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
3.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
3.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
0.0ms	(+.f64 (.f64 y-scale (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2))) (+.f64 (.f64 y-scale (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2))) (.f64 y-scale (sqrt.f64 (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 a 4)) (+.f64 (.f64 (pow.f64 b 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (.f64 2 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (*.f64 angle PI.f64))) 2)))))))))))

series7.2s (1.4%)

Counts

4 → 34

Calls

4 calls:

7.1s	(/.f64 (+.f64 (.f64 y-scale (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2))) (+.f64 (.f64 y-scale (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2))) (.f64 y-scale (sqrt.f64 (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 a 4)) (+.f64 (.f64 (pow.f64 b 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (.f64 2 (.f64 (.f64 a a) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 (.f64 b b) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2))))))))))) (.f64 angle (.f64 x-scale (.f64 PI.f64 (.f64 (-.f64 (.f64 b b) (.f64 a a)) (cos.f64 (.f64 1/180 (*.f64 angle PI.f64))))))))
58.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
49.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
35.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 6798 to 4778 computations (29.7% saved)

simplify162.0ms (0%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5046	9016

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 180 (/.f64 (atan.f64 (.f64 -1/360 (/.f64 (.f64 angle (.f64 x-scale (.f64 PI.f64 (.f64 b b)))) (.f64 (-.f64 (.f64 b b) (.f64 a a)) (.f64 y-scale (cos.f64 (.f64 1/180 (.f64 angle PI.f64)))))))) PI.f64))
0.1b	(/.f64 (atan.f64 (.f64 -1/360 (/.f64 (.f64 angle (.f64 x-scale (.f64 PI.f64 (.f64 b b)))) (.f64 (-.f64 (.f64 b b) (.f64 a a)) (.f64 y-scale (cos.f64 (.f64 1/180 (*.f64 angle PI.f64)))))))) PI.f64)
0.1b	(.f64 y-scale (cos.f64 (.f64 1/180 (*.f64 angle PI.f64))))
0.0b	(atan.f64 (.f64 -1/360 (/.f64 (.f64 angle (.f64 x-scale (.f64 PI.f64 (.f64 b b)))) (.f64 (-.f64 (.f64 b b) (.f64 a a)) (.f64 y-scale (cos.f64 (.f64 1/180 (*.f64 angle PI.f64))))))))
7.0b	(.f64 (-.f64 (.f64 b b) (.f64 a a)) (.f64 y-scale (cos.f64 (.f64 1/180 (.f64 angle PI.f64)))))
8.7b	(.f64 x-scale (.f64 PI.f64 (*.f64 b b)))
21.4b	(/.f64 (.f64 angle (.f64 x-scale (.f64 PI.f64 (.f64 b b)))) (.f64 (-.f64 (.f64 b b) (.f64 a a)) (.f64 y-scale (cos.f64 (.f64 1/180 (.f64 angle PI.f64))))))
26.8b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

rewrite65.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
54×	`cbrt-unprod_binary64` `prod-exp_binary64`
18×	`pow1_binary64`
15×	`cbrt-undiv_binary64` `div-exp_binary64`
9×	`pow-prod-down_binary64`
7×	`associate-l_binary64`
6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `associate-*l/_binary64`
2×	`flip3--_binary64` `associate-r_binary64` `associate-/r/_binary64` `flip--_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64`

Counts

4 → 94

Calls

8 calls:

27.0ms	(/.f64 (.f64 angle (.f64 x-scale (.f64 PI.f64 (.f64 b b)))) (.f64 (-.f64 (.f64 b b) (.f64 a a)) (.f64 y-scale (cos.f64 (.f64 1/180 (.f64 angle PI.f64))))))
11.0ms	(.f64 (-.f64 (.f64 b b) (.f64 a a)) (.f64 y-scale (cos.f64 (.f64 1/180 (.f64 angle PI.f64)))))
8.0ms	(.f64 x-scale (.f64 PI.f64 (*.f64 b b)))
3.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
0.0ms	(atan.f64 (.f64 -1/360 (/.f64 (.f64 angle (.f64 x-scale (.f64 PI.f64 (.f64 b b)))) (.f64 (-.f64 (.f64 b b) (.f64 a a)) (.f64 y-scale (cos.f64 (.f64 1/180 (*.f64 angle PI.f64))))))))

series1.9s (0.4%)

Counts

4 → 48

Calls

4 calls:

1.2s	(/.f64 (.f64 angle (.f64 x-scale (.f64 PI.f64 (.f64 b b)))) (.f64 (-.f64 (.f64 b b) (.f64 a a)) (.f64 y-scale (cos.f64 (.f64 1/180 (.f64 angle PI.f64))))))
604.0ms	(.f64 (-.f64 (.f64 b b) (.f64 a a)) (.f64 y-scale (cos.f64 (.f64 1/180 (.f64 angle PI.f64)))))
90.0ms	(.f64 x-scale (.f64 PI.f64 (*.f64 b b)))
22.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 3460 to 2798 computations (19.1% saved)

simplify115.0ms (0%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5121	4264

localize94.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 (/.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 2)) x-scale) x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2)))) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (cbrt.f64 (pow.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) 3)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale))) PI.f64)
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) x-scale) y-scale) 2))
0.0b	(+.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))
0.0b	(+.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))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite22.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`

Counts

4 → 28

Calls

8 calls:

3.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
3.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(/.f64 (atan.f64 (/.f64 (-.f64 (-.f64 (/.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) (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 2)) x-scale) x-scale)) (sqrt.f64 (+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2)))) (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (cbrt.f64 (pow.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) 3)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale))) PI.f64)

series250.0ms (0%)

Counts

4 → 16

Calls

4 calls:

63.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
63.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
63.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
60.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 4924 to 3500 computations (28.9% saved)

simplify85.0ms (0%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4796	604
1	4796	604

localize103.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (pow.f64 (.f64 a (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (.f64 1/180 (*.f64 angle PI.f64))) 2))
0.0b	(+.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))
0.0b	(+.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))
0.0b	(+.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))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite23.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`

Counts

4 → 28

Calls

8 calls:

2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(+.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))

series239.0ms (0%)

Counts

4 → 15

Calls

4 calls:

64.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
63.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
61.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
50.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 4679 to 3471 computations (25.8% saved)

simplify85.0ms (0%)

Algorithm

1×	egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4796	580
1	4796	580

localize132.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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 (.f64 1/180 (.f64 angle PI.f64))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2))
0.0b	(+.f64 (pow.f64 (-.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) b) 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 (.f64 1/180 (.f64 angle PI.f64))) 2)) y-scale) y-scale)) 2) (pow.f64 (/.f64 (/.f64 (.f64 (cos.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (.f64 a a))))) x-scale) y-scale) 2))
0.0b	(+.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))
0.0b	(+.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))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.1b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite30.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`

Counts

4 → 28

Calls

8 calls:

3.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
3.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(+.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))

series329.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

87.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
82.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
80.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
80.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 8000 to 5328 computations (33.4% saved)

simplify166.0ms (0%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (154.0ms)

Iter	Nodes	Cost
0	4741	508
1	4741	508

prune20.5s (4%)

Pruning

359 alts after pruning (350 fresh and 9 done)

	Pruned	Kept	Total
New	246	111	357
Fresh	4	239	243
Picked	0	0	0
Done	3	9	12
Total	253	359	612

Error

15.6b

Counts

612 → 359

Compiler

Compiled 35778 to 22417 computations (37.3% saved)

simplify4.2s (0.8%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	6521	262896

regimes2.6min (30%)

Compiler: Compiled 1849966 to 1290640 computations (30.2% saved)

bsearch1.7s (0.3%)

Steps

Iters	Range		Point
6	1.5531103678881556e-28	2.040132256684584e-27	2.0857365397169568e-28
8	-3.720978506492585e+36	-1.1005765273721677e+34	-2.449232896210209e+35

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes749.0ms (0.1%)

Compiler: Compiled 5735 to 4540 computations (20.8% saved)

bsearch3.5s (0.7%)

Steps

Iters	Range		Point
8	1.2191629843249697e+150	3.4777240570980565e+152	1.6635112831079266e+150
9	1.5867575223033557e-113	1.6742765163298943e-108	1.608006355534297e-113
8	-1.95083753592412e-222	-1.2008961781653361e-225	-1.4278917460056073e-223
10	-9.559048152815373e+63	-1.2310108245050895e+52	-7.054005081354844e+52

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes147.0ms (0%)

Compiler: Compiled 540 to 560 computations (-3.7% saved)

bsearch2.7s (0.5%)

Steps

Iters

Range

Point

4.294155529664601e-115

1.5867575223033557e-113

4.376061765703892e-115

-8.756424209212937e-146

-1.071854377519911e-151

-1.2040234655516484e-151

-2.943583939195158e+158

-4.519845453948353e+147

-1.3517085611470228e+154

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes76.0ms (0%)

Compiler: Compiled 155 to 240 computations (-54.8% saved)

bsearch1.2s (0.2%)

Steps

Iters	Range		Point
6	1.3459036505315227e-126	1.9551416502736504e-125	8.077542025564833e-126
8	-4.0588430813457363e-16	-6.841170771861991e-21	-2.669032133350017e-19

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes51.0ms (0%)

Accuracy

Total 17.9b remaining (50%)

Threshold costs 0b (0%)

Compiler

Compiled 20 to 110 computations (-450% saved)

bsearch18.0ms (0%)

Compiler: Compiled 319 to 218 computations (31.7% saved)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	155	297
1	155	297

end0.0ms (0%)

sample2.8min (32.5%)

Algorithm

1×

intervals

Results

16.6s	1615×	body	4096	valid
9.2s	1410×	body	2048	valid
8.6s	1628×	body	1024	valid
6.3s	90×	body	8192	exit
2.5s	718×	body	512	valid
1.8s	2289×	body	128	valid
747.0ms	340×	body	256	valid

Compiler

Compiled 163250 to 113798 computations (30.3% saved)

Pareto

0.4542445533778097