Details

analyze18.0s (13.2%)

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

Compiler

Compiled 184 to 125 computations (32.1% saved)

sample2.5s (1.9%)

Algorithm

1×

intervals

Results

1.2s	116×	body	4096	valid
893.0ms	51×	body	8192	valid
303.0ms	57×	body	2048	valid
81.0ms	20×	body	1024	valid
28.0ms	9×	body	512	valid
5.0ms	1×	body	2048	invalid
4.0ms	2×	body	512	invalid
3.0ms	2×	body	256	valid
1.0ms	1×	body	128	valid

Compiler

Compiled 367 to 254 computations (30.8% saved)

simplify24.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	5065	287

prune27.0ms (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)

localize74.0ms (0.1%)

Local error

Found 4 expressions with local error:

23.4b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
23.4b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
23.4b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
40.0b	(-.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))))

rewrite1.2s (0.9%)

Algorithm

1×	rewrite-expression-head

Error

64.0b

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:

278.0ms	(-.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	(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))

Compiler

Compiled 15167 to 9281 computations (38.8% saved)

series21.2s (15.5%)

Error

63.1b

Counts

4 → 26

Calls

4 calls:

20.7s	(-.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))))
54.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
54.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
49.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 26431 to 18091 computations (31.6% saved)

simplify175.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5071	16488

prune1.2s (0.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	74	5	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	5	80

Error

63.1b

Counts

80 → 5

Compiler

Compiled 19213 to 11052 computations (42.5% saved)

localize64.0ms (0%)

Local error

Found 4 expressions with local error:

23.4b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
23.4b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
23.4b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
32.8b	(-.f64 (+.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 x-scale x-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 (.f64 (pow.f64 b 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (pow.f64 x-scale 4)) (.f64 2 (/.f64 (.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a))) (pow.f64 x-scale 4)))))))

rewrite1.0s (0.8%)

Algorithm

1×	rewrite-expression-head

Error

63.1b

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-*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:

61.0ms	(-.f64 (+.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 x-scale x-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 (.f64 (pow.f64 b 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (pow.f64 x-scale 4)) (.f64 2 (/.f64 (.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a))) (pow.f64 x-scale 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 15984 to 8826 computations (44.8% saved)

series5.8s (4.3%)

Error

60.2b

Counts

4 → 21

Calls

4 calls:

5.6s	(-.f64 (+.f64 (/.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 x-scale x-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 (.f64 (pow.f64 b 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4)) (pow.f64 x-scale 4)) (.f64 2 (/.f64 (.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 b b)) (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a))) (pow.f64 x-scale 4)))))))
50.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
48.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
46.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 7000 to 4115 computations (41.2% saved)

simplify178.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5217	14694

prune949.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	81	5	86

Error

60.2b

Counts

86 → 5

Compiler

Compiled 16654 to 9194 computations (44.8% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

16.6b	(/.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))))
16.8b	(.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))
19.0b	(.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0)
23.2b	(.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))

rewrite1.3s (0.9%)

Algorithm

1×	rewrite-expression-head

Error

56.8b

Rules

1300×	`add-exp-log_binary64`
997×	`prod-exp_binary64`
526×	`add-cbrt-cube_binary64`
400×	`cbrt-unprod_binary64`
250×	`pow1_binary64`
205×	`pow-prod-down_binary64`
145×	`div-exp_binary64`
72×	`pow-exp_binary64`
40×	`cbrt-undiv_binary64`
36×	`pow-to-exp_binary64`
14×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64` `-un-lft-identity_binary64` `associate-l_binary64` `associate-r*_binary64`
8×	`distribute-rgt-neg-out_binary64` `times-frac_binary64`
5×	`associate-*l/_binary64`
4×	`add-log-exp_binary64` `associate-/l*_binary64`
3×	`distribute-lft-neg-out_binary64` `*-commutative_binary64` `unswap-sqr_binary64` `sqrt-prod_binary64`
2×	`unpow2_binary64` `sqr-pow_binary64` `div-inv_binary64`
1×	`mul0-rgt_binary64` `unpow-prod-down_binary64` `frac-2neg_binary64` `clear-num_binary64` `sqrt-div_binary64` `associate-/l/_binary64` `associate-/r*_binary64`

Counts

4 → 386

Calls

4 calls:

38.0ms	(.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))
34.0ms	(/.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))))
32.0ms	(.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))
11.0ms	(.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0)

Compiler

Compiled 25029 to 8310 computations (66.8% saved)

series211.0ms (0.2%)

Error

42.0b

Counts

4 → 42

Calls

4 calls:

50.0ms	(.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))
50.0ms	(/.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 (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))
27.0ms	(.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) 0)

Compiler

Compiled 1764 to 1498 computations (15.1% saved)

simplify182.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

428 → 428

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4715	2635
1	4715	2635

prune575.0ms (0.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	427	1	428
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	428	5	433

Error

42.0b

Counts

433 → 5

Compiler

Compiled 10212 to 4734 computations (53.6% saved)

localize5.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

42.0b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 42.0b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune1.0ms (0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	1	1
Total	5	5

Error

42.0b

Counts

5 → 5

Compiler

Compiled 0 to 0 computations (0% saved)

regimes2.0s (1.5%)

Accuracy

Total 0.1b remaining (0.1%)

Threshold costs 0.1b (0.1%)

Compiler

Compiled 35064 to 21954 computations (37.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (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 (58.4%)

Algorithm

1×

intervals

Results

34.2s	3720×	body	4096	valid
28.5s	1545×	body	8192	valid
9.5s	1755×	body	2048	valid
2.2s	628×	body	1024	valid
501.0ms	222×	body	512	valid
149.0ms	24×	body	2048	invalid
145.0ms	40×	body	1024	invalid
121.0ms	77×	body	256	valid
56.0ms	5×	body	4096	invalid
43.0ms	53×	body	128	valid
39.0ms	19×	body	512	invalid
19.0ms	1×	body	8192	exit
11.0ms	8×	body	256	invalid
7.0ms	10×	body	128	invalid

Compiler

Compiled 4519 to 2839 computations (37.2% saved)

Details

analyze18.0s (13.2%)

sample2.5s (1.9%)

simplify24.0ms (0%)

prune27.0ms (0%)

localize74.0ms (0.1%)

rewrite1.2s (0.9%)

series21.2s (15.5%)

simplify175.0ms (0.1%)

prune1.2s (0.9%)

localize64.0ms (0%)

rewrite1.0s (0.8%)

series5.8s (4.3%)

simplify178.0ms (0.1%)

prune949.0ms (0.7%)

localize19.0ms (0%)

rewrite1.3s (0.9%)

series211.0ms (0.2%)

simplify182.0ms (0.1%)

prune575.0ms (0.4%)

localize5.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0%)

prune1.0ms (0%)

regimes2.0s (1.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.3min (58.4%)

Profiling