Details

analyze18.4s (12.9%)

Algorithm

1×

Search

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

Compiler

Compiled 184 to 125 computations (32.1% saved)

sample2.6s (1.8%)

Algorithm

1×

intervals

Results

1.3s	113×	body	4096	valid
806.0ms	44×	body	8192	valid
401.0ms	69×	body	2048	valid
76.0ms	23×	body	1024	valid
14.0ms	2×	body	2048	invalid
11.0ms	5×	body	512	valid
2.0ms	1×	body	512	invalid
1.0ms	2×	body	128	valid

Compiler

Compiled 367 to 254 computations (30.8% saved)

simplify121.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5065	287

prune19.0ms (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

63.9b

Counts

2 → 1

Compiler

Compiled 360 to 236 computations (34.4% saved)

localize81.0ms (0.1%)

Local error

Found 4 expressions with local error:

29.0b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
29.0b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
29.0b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
35.5b	(-.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))))

rewrite351.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

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` `frac-sub_binary64` `sqrt-div_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`pow1_binary64` `distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64`
3×	`distribute-lft-out--_binary64`
2×	`diff-log_binary64` `frac-add_binary64` `difference-of-squares_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `flip--_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

4 → 53

Calls

4 calls:

312.0ms	(-.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))

series30.4s (21.3%)

Counts

4 → 29

Calls

4 calls:

30.3s	(-.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))))
49.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
49.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
49.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 27091 to 19090 computations (29.5% saved)

simplify186.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5285	18656

prune1.2s (0.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	76	6	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	6	83

Error

62.7b

Counts

83 → 6

Compiler

Compiled 20893 to 12216 computations (41.5% saved)

localize68.0ms (0%)

Local error

Found 4 expressions with local error:

29.1b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
29.1b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
29.1b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
31.8b	(-.f64 (+.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 y-scale y-scale)) (/.f64 (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.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 y-scale) (.f64 x-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))))))

rewrite112.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`frac-add_binary64`
15×	`frac-sub_binary64` `sqrt-div_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-r/_binary64` `associate-l/_binary64`
2×	`diff-log_binary64` `distribute-lft-out_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `flip--_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

4 → 60

Calls

4 calls:

70.0ms	(-.f64 (+.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 y-scale y-scale)) (/.f64 (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.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 y-scale) (.f64 x-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)))

series7.4s (5.2%)

Counts

4 → 21

Calls

4 calls:

7.3s	(-.f64 (+.f64 (/.f64 (.f64 (.f64 a a) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 y-scale y-scale)) (/.f64 (.f64 (.f64 a a) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.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 y-scale) (.f64 x-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))))))
44.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
42.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
39.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 4590 to 2862 computations (37.6% saved)

simplify148.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4988	15249
1	4988	15249

prune982.0ms (0.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	80	7	87

Error

60.5b

Counts

87 → 7

Compiler

Compiled 17683 to 9538 computations (46.1% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

15.4b	(.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (*.f64 b (neg.f64 a))))
18.0b	(.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0))
18.5b	(.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))
20.3b	(/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0))) (.f64 (.f64 b a) (*.f64 b (neg.f64 a))))

rewrite248.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

1392×	`add-exp-log_binary64`
1054×	`prod-exp_binary64`
549×	`add-cbrt-cube_binary64`
413×	`cbrt-unprod_binary64`
250×	`pow1_binary64`
205×	`pow-prod-down_binary64`
165×	`div-exp_binary64`
82×	`pow-exp_binary64`
45×	`cbrt-undiv_binary64`
41×	`pow-to-exp_binary64`
31×	`associate-l_binary64`
26×	`times-frac_binary64`
23×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`distribute-rgt-neg-out_binary64`
8×	`associate-r_binary64`
6×	`associate-*l/_binary64`
5×	`unpow2_binary64` `sqr-pow_binary64`
4×	`add-log-exp_binary64` `unpow-prod-down_binary64` `associate-/l*_binary64`
3×	`unswap-sqr_binary64` `div-inv_binary64` `sqrt-prod_binary64` `*-commutative_binary64`
2×	`distribute-lft-neg-out_binary64`
1×	`associate-/l/_binary64` `associate-/r*_binary64` `clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`

Counts

4 → 430

Calls

4 calls:

41.0ms	(.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))
36.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0))) (.f64 (.f64 b a) (*.f64 b (neg.f64 a))))
33.0ms	(.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0))
17.0ms	(.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (*.f64 b (neg.f64 a))))

series618.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

476.0ms	(.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (*.f64 b (neg.f64 a))))
50.0ms	(.f64 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (*.f64 x-scale y-scale) 2))
47.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0))) (.f64 (.f64 b a) (*.f64 b (neg.f64 a))))
45.0ms	(.f64 (.f64 (/.f64 8 (pow.f64 (.f64 x-scale y-scale) 2)) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0))

Compiler

Compiled 1848 to 1704 computations (7.8% saved)

simplify177.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

478 → 478

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4724	4526
1	4724	4526

prune661.0ms (0.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	477	1	478
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	478	7	485

Error

43.5b

Counts

485 → 7

Compiler

Compiled 13637 to 6144 computations (54.9% saved)

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune1.0ms (0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	0	0
Total	7	7

Error

43.5b

Counts

7 → 7

Compiler

Compiled 0 to 0 computations (0% saved)

regimes975.0ms (0.7%)

Accuracy

Total 0.1b remaining (0.2%)

Threshold costs 0.1b (0.2%)

Compiler

Compiled 18968 to 12042 computations (36.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	3	1
1	3	1

end0.0ms (0%)

sample1.3min (54.5%)

Algorithm

1×

intervals

Results

33.8s	3713×	body	4096	valid
28.7s	1529×	body	8192	valid
9.9s	1803×	body	2048	valid
2.0s	594×	body	1024	valid
526.0ms	224×	body	512	valid
266.0ms	42×	body	2048	invalid
158.0ms	98×	body	256	valid
110.0ms	35×	body	1024	invalid
40.0ms	2×	body	8192	exit
35.0ms	39×	body	128	valid
33.0ms	12×	body	512	invalid
20.0ms	2×	body	4096	invalid
14.0ms	10×	body	256	invalid
4.0ms	5×	body	128	invalid

Compiler

Compiled 2507 to 1600 computations (36.2% saved)

Details

analyze18.4s (12.9%)

sample2.6s (1.8%)

simplify121.0ms (0.1%)

prune19.0ms (0%)

localize81.0ms (0.1%)

rewrite351.0ms (0.2%)

series30.4s (21.3%)

simplify186.0ms (0.1%)

prune1.2s (0.9%)

localize68.0ms (0%)

rewrite112.0ms (0.1%)

series7.4s (5.2%)

simplify148.0ms (0.1%)

prune982.0ms (0.7%)

localize19.0ms (0%)

rewrite248.0ms (0.2%)

series618.0ms (0.4%)

simplify177.0ms (0.1%)

prune661.0ms (0.5%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0%)

prune1.0ms (0%)

regimes975.0ms (0.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.3min (54.5%)

Profiling