Details

analyze17.6s (13.7%)

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)

sample2.7s (2.1%)

Algorithm

1×

intervals

Results

1.1s	59×	body	8192	valid
979.0ms	115×	body	4096	valid
498.0ms	60×	body	2048	valid
32.0ms	11×	body	1024	valid
12.0ms	6×	body	512	valid
3.0ms	2×	body	256	valid
2.0ms	3×	body	128	valid

Compiler

Compiled 367 to 254 computations (30.8% saved)

simplify28.0ms (0%)

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

64.0b

Counts

2 → 1

Compiler

Compiled 360 to 236 computations (34.4% saved)

localize79.0ms (0.1%)

Local error

Found 4 expressions with local error:

27.9b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.9b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
27.9b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
38.7b	(-.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 (0.9%)

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:

277.0ms	(-.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))))
3.0ms	(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)

series18.4s (14.3%)

Error

62.7b

Counts

4 → 25

Calls

4 calls:

18.0s	(-.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))))
47.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
45.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
44.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 21445 to 14533 computations (32.2% saved)

simplify148.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5000	15710

prune1.2s (0.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	72	6	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	6	79

Error

62.7b

Counts

79 → 6

Compiler

Compiled 19333 to 11180 computations (42.2% saved)

localize62.0ms (0%)

Local error

Found 4 expressions with local error:

28.3b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
28.3b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
28.3b	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
30.5b	(-.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))) (sqrt.f64 (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 a 4)) (+.f64 (.f64 (pow.f64 b 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 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))))))))

rewrite507.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

62.7b

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:

30.0ms	(-.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))) (sqrt.f64 (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 a 4)) (+.f64 (.f64 (pow.f64 b 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 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 (2.6%)

Error

61.5b

Counts

4 → 18

Calls

4 calls:

3.2s	(-.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))) (sqrt.f64 (+.f64 (.f64 (pow.f64 (sin.f64 (.f64 1/180 (.f64 angle PI.f64))) 4) (pow.f64 a 4)) (+.f64 (.f64 (pow.f64 b 4) (pow.f64 (cos.f64 (.f64 1/180 (.f64 angle PI.f64))) 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))))))))
36.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
36.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))
35.0ms	(cos.f64 (.f64 1/180 (.f64 angle PI.f64)))

Compiler

Compiled 5336 to 3038 computations (43.1% saved)

simplify120.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4964	6330
1	4964	6330

prune462.0ms (0.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	66	5	71

Error

61.5b

Counts

71 → 5

Compiler

Compiled 10814 to 5714 computations (47.2% saved)

localize21.0ms (0%)

Local error

Found 4 expressions with local error:

16.3b	(/.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))) (/.f64 0 (.f64 x-scale x-scale))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a))))
18.0b	(.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (/.f64 0 (*.f64 x-scale x-scale)))
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))) (/.f64 0 (.f64 x-scale x-scale))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2))
21.7b	(.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 x-scale x-scale))))

rewrite2.8s (2.2%)

Algorithm

1×	rewrite-expression-head

Error

58.1b

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:

43.0ms	(/.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 x-scale x-scale))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a))))
41.0ms	(.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 x-scale x-scale))))
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))) (/.f64 0 (.f64 x-scale x-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 x-scale x-scale)))

Compiler

Compiled 57176 to 17864 computations (68.8% saved)

series227.0ms (0.2%)

Error

43.2b

Counts

4 → 45

Calls

4 calls:

52.0ms	(/.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 x-scale x-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 x-scale x-scale))))) (.f64 (.f64 b a) (.f64 b (neg.f64 a)))) (pow.f64 (.f64 x-scale y-scale) 2))
48.0ms	(.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 x-scale x-scale))))
35.0ms	(.f64 (.f64 (.f64 b a) (.f64 b (neg.f64 a))) (/.f64 0 (*.f64 x-scale x-scale)))

Compiler

Compiled 2088 to 1684 computations (19.3% saved)

simplify264.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

829 → 829

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4764	3685
1	4764	3685

prune1.2s (0.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	828	1	829
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	830	4	834

Error

43.2b

Counts

834 → 4

Compiler

Compiled 19716 to 9174 computations (53.5% saved)

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

43.2b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 43.2b
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

4 alts after pruning (3 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	0	0
Total	4	4

Error

43.2b

Counts

4 → 4

Compiler

Compiled 0 to 0 computations (0% saved)

regimes1.9s (1.5%)

Accuracy

Total 0.1b remaining (0.2%)

Threshold costs 0.1b (0.2%)

Compiler

Compiled 39696 to 24690 computations (37.8% 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 (59.4%)

Algorithm

1×

intervals

Results

32.8s	3716×	body	4096	valid
26.8s	1477×	body	8192	valid
9.9s	1873×	body	2048	valid
1.8s	565×	body	1024	valid
721.0ms	215×	body	512	valid
203.0ms	34×	body	2048	invalid
141.0ms	41×	body	1024	invalid
140.0ms	97×	body	256	valid
38.0ms	57×	body	128	valid
31.0ms	15×	body	512	invalid
19.0ms	2×	body	4096	invalid
19.0ms	1×	body	8192	exit
15.0ms	11×	body	256	invalid
5.0ms	7×	body	128	invalid

Compiler

Compiled 5098 to 3181 computations (37.6% saved)

Details

analyze17.6s (13.7%)

sample2.7s (2.1%)

simplify28.0ms (0%)

prune19.0ms (0%)

localize79.0ms (0.1%)

rewrite1.1s (0.9%)

series18.4s (14.3%)

simplify148.0ms (0.1%)

prune1.2s (0.9%)

localize62.0ms (0%)

rewrite507.0ms (0.4%)

series3.3s (2.6%)

simplify120.0ms (0.1%)

prune462.0ms (0.4%)

localize21.0ms (0%)

rewrite2.8s (2.2%)

series227.0ms (0.2%)

simplify264.0ms (0.2%)

prune1.2s (0.9%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0%)

prune1.0ms (0%)

regimes1.9s (1.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.3min (59.4%)

Profiling