Details

analyze17.0s (22.1%)

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)

sample1.5s (2%)

Algorithm

1×

intervals

Results

558.0ms	56×	body	4096	valid
324.0ms	53×	body	2048	valid
222.0ms	46×	body	1024	valid
203.0ms	3×	body	8192	exit
84.0ms	25×	body	512	valid
45.0ms	63×	body	128	valid
25.0ms	13×	body	256	valid

Compiler

Compiled 339 to 258 computations (23.9% saved)

simplify132.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5229	273

prune39.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

57.9b

Counts

2 → 1

Compiler

Compiled 338 to 238 computations (29.6% saved)

localize85.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 2 (-.f64 (.f64 b b) (*.f64 a a)))
0.0b	(.f64 2 (-.f64 (.f64 b b) (*.f64 a a)))
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 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 (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))
30.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.1b	(cos.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:

4.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(cos.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 (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))

series462.0ms (0.6%)

Counts

4 → 22

Calls

4 calls:

256.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
69.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
68.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
68.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 5568 to 3952 computations (29% saved)

simplify133.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	4926	724
1	4926	724

prune802.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	42	8	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	8	51

Error

55.7b

Counts

51 → 8

Compiler

Compiled 10083 to 6671 computations (33.8% saved)

localize84.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 2 (-.f64 (.f64 b b) (*.f64 a a)))
0.0b	(.f64 2 (-.f64 (.f64 b b) (*.f64 a a)))
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 (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 1 (.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 (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 1 (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) x-scale) y-scale))) PI.f64)
30.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite19.0ms (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	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(cos.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 1 (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) x-scale) y-scale))) PI.f64)

series259.0ms (0.3%)

Counts

4 → 22

Calls

4 calls:

69.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
68.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
66.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
56.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 5219 to 3719 computations (28.7% saved)

simplify137.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	4926	737
1	4926	737

prune702.0ms (0.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	49	9	58

Error

55.2b

Counts

58 → 9

Compiler

Compiled 10022 to 6655 computations (33.6% saved)

localize86.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 2 (-.f64 (.f64 b b) (*.f64 a a)))
0.0b	(.f64 2 (-.f64 (.f64 b b) (*.f64 a a)))
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 (-.f64 1 (.f64 1/64800 (pow.f64 (.f64 angle PI.f64) 2))) (.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 1 (.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 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 (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 (-.f64 1 (.f64 1/64800 (pow.f64 (.f64 angle PI.f64) 2))) (.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 1 (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) x-scale) y-scale))) PI.f64))
30.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite19.0ms (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	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(cos.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 (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 (-.f64 1 (.f64 1/64800 (pow.f64 (.f64 angle PI.f64) 2))) (.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 1 (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))) x-scale) y-scale))) PI.f64))

series269.0ms (0.4%)

Counts

4 → 24

Calls

4 calls:

69.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
67.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
67.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
66.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 5504 to 3936 computations (28.5% saved)

simplify128.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (113.0ms)

Iter	Nodes	Cost
0	4926	804
1	4926	804

prune616.0ms (0.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	51	10	61

Error

54.7b

Counts

61 → 10

Compiler

Compiled 10545 to 6998 computations (33.6% saved)

localize90.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 2 (-.f64 (.f64 b b) (*.f64 a a)))
0.0b	(.f64 2 (-.f64 (.f64 b b) (*.f64 a a)))
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 (-.f64 1 (.f64 1/64800 (pow.f64 (.f64 angle PI.f64) 2)))) 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 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 (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 (-.f64 1 (.f64 1/64800 (pow.f64 (.f64 angle PI.f64) 2)))) 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))
30.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite19.0ms (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	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(cos.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 (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 (-.f64 1 (.f64 1/64800 (pow.f64 (.f64 angle PI.f64) 2)))) 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))

series207.0ms (0.3%)

Counts

4 → 14

Calls

4 calls:

69.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
46.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
46.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
45.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 4512 to 3198 computations (29.1% saved)

simplify92.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4782	521
1	4782	521

prune383.0ms (0.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	42	10	52

Error

54.7b

Counts

52 → 10

Compiler

Compiled 7366 to 4827 computations (34.5% saved)

simplify109.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	991	8261
1	991	8261

regimes2.0s (2.5%)

Compiler: Compiled 35971 to 25611 computations (28.8% saved)

bsearch987.0ms (1.3%)

Steps

Iters	Range		Point
8	2.5560831862969764e-66	1.5137134506813564e-62	1.4900124830572083e-62
4	-6.07562879176322e+73	-3.833643042059855e+73	-3.8971157501057044e+73

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes164.0ms (0.2%)

Compiler: Compiled 1132 to 971 computations (14.2% saved)

bsearch972.0ms (1.3%)

Steps

Iters	Range		Point
8	2.5560831862969764e-66	1.5137134506813564e-62	1.5981539602088595e-63
4	-6.07562879176322e+73	-3.833643042059855e+73	-4.9126790788392896e+73

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes63.0ms (0.1%)

Compiler: Compiled 25 to 140 computations (-460% saved)

bsearch1.1s (1.4%)

Steps

Iters	Range		Point
8	1.0170414225065345e-49	5.5369631232211274e-45	1.0605051678061434e-48
7	-1.365138191187364e+18	-20237591132538404.0	-59888888921953816.0

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes56.0ms (0.1%)

Accuracy

Total 9.3b remaining (19.5%)

Threshold costs 0b (0%)

Compiler

Compiled 20 to 110 computations (-450% saved)

bsearch923.0ms (1.2%)

Steps

Iters	Range		Point
3	1.5137134506813564e-62	1.9990394582847513e-62	1.9432313403315025e-62
10	-300226983.15335494	-0.0008795880509297812	-467244.6681672348

Compiler

Compiled 354 to 273 computations (22.9% saved)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	257	557
1	257	557

end0.0ms (0%)

sample47.1s (61.4%)

Algorithm

1×

intervals

Results

15.4s	1596×	body	4096	valid
8.6s	1416×	body	2048	valid
7.6s	1579×	body	1024	valid
6.7s	95×	body	8192	exit
2.4s	746×	body	512	valid
1.7s	2344×	body	128	valid
616.0ms	319×	body	256	valid

Compiler

Compiled 5658 to 4047 computations (28.5% saved)

Pareto

0.6841637224169477

Details

analyze17.0s (22.1%)

sample1.5s (2%)

simplify132.0ms (0.2%)

prune39.0ms (0.1%)

localize85.0ms (0.1%)

rewrite22.0ms (0%)

series462.0ms (0.6%)

simplify133.0ms (0.2%)

prune802.0ms (1%)

localize84.0ms (0.1%)

rewrite19.0ms (0%)

series259.0ms (0.3%)

simplify137.0ms (0.2%)

prune702.0ms (0.9%)

localize86.0ms (0.1%)

rewrite19.0ms (0%)

series269.0ms (0.4%)

simplify128.0ms (0.2%)

prune616.0ms (0.8%)

localize90.0ms (0.1%)

rewrite19.0ms (0%)

series207.0ms (0.3%)

simplify92.0ms (0.1%)

prune383.0ms (0.5%)

simplify109.0ms (0.1%)

regimes2.0s (2.5%)

bsearch987.0ms (1.3%)

regimes164.0ms (0.2%)

bsearch972.0ms (1.3%)

regimes63.0ms (0.1%)

bsearch1.1s (1.4%)

regimes56.0ms (0.1%)

bsearch923.0ms (1.2%)

simplify10.0ms (0%)

end0.0ms (0%)

sample47.1s (61.4%)

Profiling