Details

analyze17.2s (13.8%)

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 (2%)

Algorithm

1×

intervals

Results

1.1s	130×	body	4096	valid
986.0ms	45×	body	8192	valid
240.0ms	46×	body	2048	valid
73.0ms	23×	body	1024	valid
14.0ms	7×	body	512	valid
11.0ms	3×	body	1024	invalid
3.0ms	2×	body	256	valid
2.0ms	1×	body	512	invalid
2.0ms	3×	body	128	valid

Compiler

Compiled 367 to 254 computations (30.8% saved)

simplify25.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

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

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:

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))
38.4b	(-.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

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:

313.0ms	(-.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)

series15.3s (12.3%)

Error

63.3b

Counts

4 → 24

Calls

4 calls:

15.0s	(-.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 18863 to 12686 computations (32.7% saved)

simplify183.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5038	14592

prune1.1s (0.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	4	78

Error

63.0b

Counts

78 → 4

Compiler

Compiled 17783 to 10247 computations (42.4% saved)

localize64.0ms (0.1%)

Local error

Found 4 expressions with local error:

29.0b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
29.0b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
29.0b	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
30.8b	(-.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))))))))

rewrite491.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

63.0b

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:

32.0ms	(-.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	(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 8985 to 4820 computations (46.4% saved)

series3.4s (2.7%)

Error

60.4b

Counts

4 → 18

Calls

4 calls:

3.2s	(-.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	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
37.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))
37.0ms	(sin.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 5408 to 3075 computations (43.1% saved)

simplify125.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4995	6351
1	4995	6351

prune449.0ms (0.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	66	3	69

Error

60.4b

Counts

69 → 3

Compiler

Compiled 10020 to 5206 computations (48% saved)

localize20.0ms (0%)

Local error

Found 4 expressions with local error:

17.5b	(.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))) (/.f64 0 (.f64 y-scale y-scale))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2))
17.8b	(.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (/.f64 0 (*.f64 y-scale y-scale)))
18.0b	(/.f64 0 (*.f64 y-scale y-scale))
22.7b	(.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))))

rewrite2.8s (2.3%)

Algorithm

1×	rewrite-expression-head

Error

57.6b

Rules

3774×	`add-exp-log_binary64`
2787×	`prod-exp_binary64`
1545×	`add-cbrt-cube_binary64`
1135×	`cbrt-unprod_binary64`
612×	`div-exp_binary64`
250×	`pow1_binary64`
207×	`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`
10×	`associate-l_binary64` `times-frac_binary64`
8×	`distribute-rgt-neg-out_binary64`
4×	`add-log-exp_binary64` `associate-r/_binary64` `associate-l/_binary64`
3×	`distribute-lft-neg-out_binary64` `-commutative_binary64` `div-inv_binary64` `associate-/l_binary64` `unswap-sqr_binary64`
2×	`unpow2_binary64` `sqr-pow_binary64`
1×	`frac-times_binary64` `frac-2neg_binary64` `clear-num_binary64` `div0_binary64` `associate-/r*_binary64` `sqrt-prod_binary64` `unpow-prod-down_binary64`

Counts

4 → 774

Calls

4 calls:

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))) (/.f64 0 (.f64 y-scale y-scale))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2))
43.0ms	(.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))))
15.0ms	(.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (/.f64 0 (*.f64 y-scale y-scale)))
5.0ms	(/.f64 0 (*.f64 y-scale y-scale))

Compiler

Compiled 55896 to 17487 computations (68.7% saved)

series186.0ms (0.1%)

Error

45.2b

Counts

4 → 36

Calls

4 calls:

52.0ms	(.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))))
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))) (/.f64 0 (.f64 y-scale y-scale))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2))
37.0ms	(.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (/.f64 0 (*.f64 y-scale y-scale)))
12.0ms	(/.f64 0 (*.f64 y-scale y-scale))

Compiler

Compiled 2169 to 1519 computations (30% saved)

simplify263.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

810 → 810

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4426	3243
1	4426	3243

prune1.1s (0.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	809	1	810
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	811	2	813

Error

45.2b

Counts

813 → 2

Compiler

Compiled 19074 to 8622 computations (54.8% saved)

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

45.2b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 45.2b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

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

2 alts after pruning (1 fresh and 1 done)

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

Error

45.2b

Counts

2 → 2

Compiler

Compiled 0 to 0 computations (0% saved)

regimes1.4s (1.1%)

Accuracy

Total 0.1b remaining (0.2%)

Threshold costs 0.1b (0.2%)

Compiler

Compiled 27656 to 17026 computations (38.4% 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 (61.4%)

Algorithm

1×

intervals

Results

33.8s	3760×	body	4096	valid
27.4s	1531×	body	8192	valid
9.4s	1774×	body	2048	valid
1.9s	604×	body	1024	valid
399.0ms	185×	body	512	valid
190.0ms	33×	body	2048	invalid
127.0ms	34×	body	1024	invalid
117.0ms	91×	body	256	valid
44.0ms	2×	body	8192	exit
36.0ms	55×	body	128	valid
28.0ms	14×	body	512	invalid
20.0ms	2×	body	4096	invalid
18.0ms	14×	body	256	invalid
1.0ms	2×	body	128	invalid

Compiler

Compiled 3593 to 2223 computations (38.1% saved)

Details

analyze17.2s (13.8%)

sample2.5s (2%)

simplify25.0ms (0%)

prune19.0ms (0%)

localize80.0ms (0.1%)

rewrite1.3s (1%)

series15.3s (12.3%)

simplify183.0ms (0.1%)

prune1.1s (0.9%)

localize64.0ms (0.1%)

rewrite491.0ms (0.4%)

series3.4s (2.7%)

simplify125.0ms (0.1%)

prune449.0ms (0.4%)

localize20.0ms (0%)

rewrite2.8s (2.3%)

series186.0ms (0.1%)

simplify263.0ms (0.2%)

prune1.1s (0.9%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0%)

prune1.0ms (0%)

regimes1.4s (1.1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.3min (61.4%)

Profiling