Details

analyze17.3s (12.5%)

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 (1.8%)

Algorithm

1×

intervals

Results

1.0s	116×	body	4096	valid
795.0ms	45×	body	8192	valid
496.0ms	58×	body	2048	valid
68.0ms	19×	body	1024	valid
20.0ms	10×	body	512	valid
11.0ms	2×	body	2048	invalid
9.0ms	7×	body	256	valid
3.0ms	1×	body	1024	invalid
1.0ms	1×	body	256	invalid
1.0ms	1×	body	128	valid

Compiler

Compiled 367 to 254 computations (30.8% saved)

simplify27.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5065	287

prune20.0ms (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)

localize75.0ms (0.1%)

Local error

Found 4 expressions with local error:

28.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
28.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
28.1b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
37.0b	(-.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))))

rewrite1.1s (0.8%)

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:

293.0ms	(-.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)

series25.1s (18.2%)

Error

62.8b

Counts

4 → 27

Calls

4 calls:

24.7s	(-.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))))
51.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
49.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
48.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 27235 to 18843 computations (30.8% saved)

simplify177.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5072	17047

prune1.1s (0.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	74	6	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	6	81

Error

62.8b

Counts

81 → 6

Compiler

Compiled 19800 to 11350 computations (42.7% saved)

localize68.0ms (0%)

Local error

Found 4 expressions with local error:

27.9b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
27.9b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
27.9b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
33.1b	(-.f64 (+.f64 (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a))) (sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 a 4)) (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 b 4)) (.f64 2 (.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))))))))

rewrite527.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

62.8b

Rules

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

Counts

4 → 47

Calls

4 calls:

33.0ms	(-.f64 (+.f64 (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a))) (sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 a 4)) (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 b 4)) (.f64 2 (.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))))))))
3.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
3.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
3.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 8985 to 4820 computations (46.4% saved)

series3.3s (2.4%)

Error

60.5b

Counts

4 → 18

Calls

4 calls:

3.1s	(-.f64 (+.f64 (.f64 (.f64 b b) (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 2)) (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 2) (.f64 a a))) (sqrt.f64 (+.f64 (.f64 (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 a 4)) (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 b 4)) (.f64 2 (.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))))))))
38.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
35.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
35.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 5372 to 3066 computations (42.9% saved)

simplify122.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4993	6330
1	4993	6330

prune460.0ms (0.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	62	3	65
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	64	7	71

Error

60.5b

Counts

71 → 7

Compiler

Compiled 10578 to 5561 computations (47.4% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

17.8b	(.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (/.f64 0 (*.f64 y-scale y-scale)))
18.5b	(/.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))) (/.f64 0 (.f64 y-scale y-scale))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a))))
19.0b	(.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))) (/.f64 0 (.f64 y-scale y-scale))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2))
19.5b	(.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))) (/.f64 0 (*.f64 y-scale y-scale))))

rewrite3.0s (2.1%)

Algorithm

1×	rewrite-expression-head

Error

57.3b

Rules

3787×	`add-exp-log_binary64`
2794×	`prod-exp_binary64`
1558×	`add-cbrt-cube_binary64`
1142×	`cbrt-unprod_binary64`
615×	`div-exp_binary64`
250×	`pow1_binary64`
210×	`cbrt-undiv_binary64`
205×	`pow-prod-down_binary64`
172×	`pow-exp_binary64`
86×	`pow-to-exp_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`associate-r_binary64`
11×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64` `times-frac_binary64`
10×	`associate-l_binary64`
8×	`distribute-rgt-neg-out_binary64`
7×	`associate-r/_binary64` `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` `div-inv_binary64` `sqrt-div_binary64` `associate-/l/_binary64`
2×	`frac-times_binary64` `unpow2_binary64` `sqr-pow_binary64`
1×	`unpow-prod-down_binary64` `frac-2neg_binary64` `clear-num_binary64` `associate-/r*_binary64`

Counts

4 → 784

Calls

4 calls:

45.0ms	(/.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))) (/.f64 0 (.f64 y-scale y-scale))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a))))
44.0ms	(.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))) (/.f64 0 (*.f64 y-scale y-scale))))
40.0ms	(.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))) (/.f64 0 (.f64 y-scale y-scale))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2))
14.0ms	(.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (/.f64 0 (*.f64 y-scale y-scale)))

Compiler

Compiled 57176 to 17864 computations (68.8% saved)

series240.0ms (0.2%)

Error

42.3b

Counts

4 → 45

Calls

4 calls:

54.0ms	(.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))) (/.f64 0 (*.f64 y-scale y-scale))))
53.0ms	(/.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))) (/.f64 0 (.f64 y-scale y-scale))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a))))
49.0ms	(.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))) (/.f64 0 (.f64 y-scale y-scale))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2))
40.0ms	(.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (/.f64 0 (*.f64 y-scale y-scale)))

Compiler

Compiled 2088 to 1684 computations (19.3% saved)

simplify262.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

829 → 829

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4747	3685
1	4747	3685

prune1.1s (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	828	1	829
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	829	7	836

Error

42.3b

Counts

836 → 7

Compiler

Compiled 19608 to 9100 computations (53.6% saved)

localize2.0ms (0%)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

42.3b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 42.3b
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

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

42.3b

Counts

7 → 7

Compiler

Compiled 0 to 0 computations (0% saved)

regimes2.8s (2%)

Accuracy

Total 0.1b remaining (0.2%)

Threshold costs 0.1b (0.2%)

Compiler

Compiled 56000 to 35322 computations (36.9% 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 (57%)

Algorithm

1×

intervals

Results

32.5s	3697×	body	4096	valid
28.6s	1538×	body	8192	valid
9.7s	1824×	body	2048	valid
1.8s	560×	body	1024	valid
482.0ms	224×	body	512	valid
150.0ms	25×	body	2048	invalid
136.0ms	39×	body	1024	invalid
126.0ms	95×	body	256	valid
42.0ms	62×	body	128	valid
38.0ms	4×	body	4096	invalid
11.0ms	8×	body	256	invalid
10.0ms	5×	body	512	invalid
6.0ms	10×	body	128	invalid

Compiler

Compiled 7136 to 4510 computations (36.8% saved)

Details

analyze17.3s (12.5%)

sample2.5s (1.8%)

simplify27.0ms (0%)

prune20.0ms (0%)

localize75.0ms (0.1%)

rewrite1.1s (0.8%)

series25.1s (18.2%)

simplify177.0ms (0.1%)

prune1.1s (0.8%)

localize68.0ms (0%)

rewrite527.0ms (0.4%)

series3.3s (2.4%)

simplify122.0ms (0.1%)

prune460.0ms (0.3%)

localize20.0ms (0%)

rewrite3.0s (2.1%)

series240.0ms (0.2%)

simplify262.0ms (0.2%)

prune1.1s (0.8%)

localize2.0ms (0%)

rewrite1.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0%)

prune1.0ms (0%)

regimes2.8s (2%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.3min (57%)

Profiling