Details

analyze17.9s (13.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5001	3121
0	5	5
1	5	5

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0%	99.8%	0.2%	13
0%	99.8%	0.2%	14

Symmetry

Compiler

Compiled 184 to 125 computations (32.1% saved)

sample2.5s (1.9%)

Algorithm

1×

intervals

Results

1.1s	126×	body	4096	valid
961.0ms	44×	body	8192	valid
273.0ms	53×	body	2048	valid
75.0ms	21×	body	1024	valid
25.0ms	9×	body	512	valid
6.0ms	1×	body	2048	invalid
4.0ms	2×	body	512	invalid
3.0ms	2×	body	256	valid
1.0ms	1×	body	256	invalid
1.0ms	1×	body	128	valid

Compiler

Compiled 367 to 254 computations (30.8% saved)

simplify23.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5065	287

prune18.0ms (0%)

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

64.0b

Counts

2 → 1

Compiler

Compiled 360 to 236 computations (34.4% saved)

localize80.0ms (0.1%)

Local error

Found 4 expressions with local error:

26.7b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
26.7b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
26.7b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
36.5b	(-.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)) (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 (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))))) (.f64 x-scale y-scale)) 2))))

rewrite1.3s (1%)

Algorithm

1×	rewrite-expression-head

Error

63.9b

Rules

18×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`add-log-exp_binary64` `cancel-sign-sub-inv_binary64`
7×	`sqrt-prod_binary64`
6×	`add-cube-cbrt_binary64` `sqrt-div_binary64` `frac-sub_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64` `distribute-lft-out_binary64`
3×	`distribute-lft-out--_binary64`
2×	`diff-log_binary64` `frac-add_binary64` `difference-of-squares_binary64`
1×	`sum-log_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `associate--l+_binary64`

Counts

4 → 53

Calls

4 calls:

282.0ms	(-.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)) (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 (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))))) (.f64 x-scale y-scale)) 2))))
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))

Compiler

Compiled 15167 to 9281 computations (38.8% saved)

series22.2s (16.6%)

Error

62.9b

Counts

4 → 26

Calls

4 calls:

21.8s	(-.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)) (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 (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))))) (.f64 x-scale y-scale)) 2))))
48.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
48.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
46.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 24091 to 16402 computations (31.9% saved)

simplify154.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5049	16317

prune1.0s (0.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	73	6	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	6	80

Error

62.8b

Counts

80 → 6

Compiler

Compiled 19317 to 11142 computations (42.3% saved)

localize59.0ms (0%)

Local error

Found 4 expressions with local error:

26.9b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
26.9b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
26.9b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
26.9b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

rewrite166.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Error

62.8b

Rules

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

Counts

4 → 28

Calls

4 calls:

3.0ms	(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)))

Compiler

Compiled 3780 to 1915 computations (49.3% saved)

series211.0ms (0.2%)

Error

62.8b

Counts

4 → 12

Calls

4 calls:

40.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
39.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
37.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
36.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 4624 to 2660 computations (42.5% saved)

simplify162.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (151.0ms)

Iter	Nodes	Cost
0	5187	501

prune233.0ms (0.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	40	6	46

Error

62.8b

Counts

46 → 6

Compiler

Compiled 6024 to 3126 computations (48.1% saved)

localize62.0ms (0%)

Local error

Found 4 expressions with local error:

26.9b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
26.9b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
26.9b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
26.9b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

rewrite161.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Error

62.8b

Rules

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

Counts

4 → 28

Calls

4 calls:

3.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
3.0ms	(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)))

Compiler

Compiled 3780 to 1915 computations (49.3% saved)

series207.0ms (0.2%)

Error

62.8b

Counts

4 → 12

Calls

4 calls:

38.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
37.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
36.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
36.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 4624 to 2660 computations (42.5% saved)

simplify166.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (155.0ms)

Iter	Nodes	Cost
0	5187	501

prune229.0ms (0.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	40	6	46

Error

62.8b

Counts

46 → 6

Compiler

Compiled 5896 to 3048 computations (48.3% saved)

localize70.0ms (0.1%)

Local error

Found 4 expressions with local error:

26.9b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
26.9b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
26.9b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
30.3b	(-.f64 (+.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a)) (.f64 y-scale y-scale)) (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a)) (.f64 x-scale x-scale))) (sqrt.f64 (+.f64 (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 a 4)) (pow.f64 x-scale 4)) (+.f64 (.f64 2 (/.f64 (.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (pow.f64 a 4)) (.f64 (.f64 x-scale x-scale) (.f64 y-scale y-scale)))) (.f64 (/.f64 (pow.f64 a 4) (pow.f64 y-scale 4)) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4))))))

rewrite1.1s (0.8%)

Algorithm

1×	rewrite-expression-head

Error

62.8b

Rules

17×	`frac-add_binary64`
15×	`sqrt-div_binary64` `frac-sub_binary64`
13×	`*-un-lft-identity_binary64`
11×	`flip3-+_binary64` `flip-+_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`add-log-exp_binary64`
7×	`cancel-sign-sub-inv_binary64`
6×	`add-cube-cbrt_binary64`
5×	`sqrt-prod_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-l/_binary64` `associate-r/_binary64`
2×	`diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out_binary64` `distribute-lft-out--_binary64`
1×	`sum-log_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `associate--l+_binary64`

Counts

4 → 60

Calls

4 calls:

68.0ms	(-.f64 (+.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a)) (.f64 y-scale y-scale)) (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a)) (.f64 x-scale x-scale))) (sqrt.f64 (+.f64 (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 a 4)) (pow.f64 x-scale 4)) (+.f64 (.f64 2 (/.f64 (.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (pow.f64 a 4)) (.f64 (.f64 x-scale x-scale) (.f64 y-scale y-scale)))) (.f64 (/.f64 (pow.f64 a 4) (pow.f64 y-scale 4)) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4))))))
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)))

Compiler

Compiled 16020 to 8665 computations (45.9% saved)

series6.0s (4.5%)

Error

61.0b

Counts

4 → 21

Calls

4 calls:

5.8s	(-.f64 (+.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a)) (.f64 y-scale y-scale)) (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a)) (.f64 x-scale x-scale))) (sqrt.f64 (+.f64 (/.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 a 4)) (pow.f64 x-scale 4)) (+.f64 (.f64 2 (/.f64 (.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (pow.f64 a 4)) (.f64 (.f64 x-scale x-scale) (.f64 y-scale y-scale)))) (.f64 (/.f64 (pow.f64 a 4) (pow.f64 y-scale 4)) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4))))))
42.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
42.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
40.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 6870 to 4005 computations (41.7% saved)

simplify147.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5313	15126

prune909.0ms (0.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	3	0	3
Picked	0	1	1
Done	2	0	2
Total	85	2	87

Error

61.0b

Counts

87 → 2

Compiler

Compiled 16467 to 8857 computations (46.2% saved)

regimes2.0s (1.5%)

Accuracy

Total 0.1b remaining (0.1%)

Threshold costs 0.1b (0.1%)

Compiler

Compiled 42448 to 27298 computations (35.7% saved)

bsearch0.0ms (0%)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	179	65
1	179	65

Removed

()

end0.0ms (0%)

sample1.3min (57.3%)

Algorithm

1×

intervals

Results

33.7s	3779×	body	4096	valid
26.4s	1433×	body	8192	valid
9.5s	1803×	body	2048	valid
2.0s	605×	body	1024	valid
533.0ms	248×	body	512	valid
187.0ms	31×	body	2048	invalid
126.0ms	35×	body	1024	invalid
118.0ms	88×	body	256	valid
41.0ms	20×	body	512	invalid
38.0ms	4×	body	4096	invalid
29.0ms	44×	body	128	valid
19.0ms	1×	body	8192	exit
7.0ms	5×	body	256	invalid
5.0ms	8×	body	128	invalid

Compiler

Compiled 5484 to 3527 computations (35.7% saved)

Details

analyze17.9s (13.3%)

sample2.5s (1.9%)

simplify23.0ms (0%)

prune18.0ms (0%)

localize80.0ms (0.1%)

rewrite1.3s (1%)

series22.2s (16.6%)

simplify154.0ms (0.1%)

prune1.0s (0.8%)

localize59.0ms (0%)

rewrite166.0ms (0.1%)

series211.0ms (0.2%)

simplify162.0ms (0.1%)

prune233.0ms (0.2%)

localize62.0ms (0%)

rewrite161.0ms (0.1%)

series207.0ms (0.2%)

simplify166.0ms (0.1%)

prune229.0ms (0.2%)

localize70.0ms (0.1%)

rewrite1.1s (0.8%)

series6.0s (4.5%)

simplify147.0ms (0.1%)

prune909.0ms (0.7%)

regimes2.0s (1.5%)

bsearch0.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample1.3min (57.3%)

Profiling