Details

analyze1.2s (0.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
31.2%	68.6%	0.1%	8
40.6%	59.3%	0.1%	9
40.6%	59.3%	0.1%	10
46%	53.8%	0.1%	11
52.7%	47.2%	0.1%	12
52.7%	44.6%	2.8%	13
55.9%	40.6%	3.5%	14

Compiler

Compiled 24 to 22 computations (8.3% saved)

sample121.0ms (0.1%)

Algorithm

1×

intervals

Results

23.0ms	44×	body	1024	invalid
22.0ms	174×	body	128	valid
21.0ms	39×	body	1024	valid
10.0ms	25×	body	512	valid
8.0ms	15×	body	512	invalid
6.0ms	43×	body	128	invalid
5.0ms	5×	body	2048	valid
4.0ms	1×	body	4096	valid
4.0ms	15×	body	256	invalid
3.0ms	12×	body	256	valid

Compiler

Compiled 47 to 46 computations (2.1% saved)

simplify152.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4912	37
1	4912	37

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

30.3b

Counts

2 → 2

Compiler

Compiled 23 to 19 computations (17.4% saved)

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(*.f64 PI.f64 (/.f64 angle 180))
0.3b	(*.f64 PI.f64 (/.f64 angle 180))
0.1b	(.f64 (.f64 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))) (sin.f64 (.f64 PI.f64 (/.f64 angle 180)))) (cos.f64 (*.f64 PI.f64 (/.f64 angle 180))))
0.0b	(.f64 2 (-.f64 (.f64 b b) (*.f64 a a)))
0.7b	(-.f64 (.f64 b b) (.f64 a a))
9.5b	(.f64 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
21.6b	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
21.6b	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))

rewrite24.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
6×	`add-log-exp_binary64_458`
5×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
3×	`pow-prod-down_binary64_490` `associate-r_binary64_359` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
2×	`associate-l/_binary64_362` `flip3--_binary64_423` `associate-r/_binary64_361` `flip--_binary64_394`
1×	`sub-neg_binary64_412` `difference-of-squares_binary64_388` `-commutative_binary64_350` `associate-l*_binary64_360` `diff-log_binary64_511` `cancel-sign-sub-inv_binary64_385`

Counts

4 → 47

Calls

8 calls:

10.0ms	(.f64 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
4.0ms	(-.f64 (.f64 b b) (.f64 a a))
2.0ms	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))
2.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
0.0ms	(.f64 2 (-.f64 (.f64 b b) (*.f64 a a)))

series641.0ms (0.4%)

Counts

4 → 42

Calls

4 calls:

475.0ms	(.f64 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
101.0ms	(-.f64 (.f64 b b) (.f64 a a))
34.0ms	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))
30.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))

Compiler

Compiled 1720 to 1485 computations (13.7% saved)

simplify49.0ms (0%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5046	1907

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(*.f64 PI.f64 (/.f64 angle 180))
0.3b	(*.f64 PI.f64 (/.f64 angle 180))
0.1b	(.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 PI.f64 (/.f64 angle 180)))) (cos.f64 (*.f64 PI.f64 (/.f64 angle 180))))
0.0b	(*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))
0.7b	(-.f64 (pow.f64 b 2) (pow.f64 a 2))
9.5b	(.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
21.6b	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
21.6b	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))

rewrite39.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_441`
16×	`difference-of-squares_binary64_388`
13×	`unpow-prod-down_binary64_498`
11×	`*-un-lft-identity_binary64_419`
9×	`sqr-pow_binary64_391` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `unpow2_binary64_484` `pow1_binary64_480`
8×	`cancel-sign-sub-inv_binary64_385`
7×	`add-cube-cbrt_binary64_454`
6×	`add-log-exp_binary64_458`
3×	`pow-prod-down_binary64_490` `associate-r_binary64_359` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
2×	`associate-l/_binary64_362` `flip3--_binary64_423` `associate-r/_binary64_361` `distribute-lft-out--_binary64_371` `flip--_binary64_394`
1×	`sub-neg_binary64_412` `-commutative_binary64_350` `associate-l*_binary64_360` `diff-log_binary64_511`

Counts

4 → 71

Calls

8 calls:

17.0ms	(.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
10.0ms	(-.f64 (pow.f64 b 2) (pow.f64 a 2))
2.0ms	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))
2.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
0.0ms	(*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))

series645.0ms (0.4%)

Counts

4 → 42

Calls

4 calls:

480.0ms	(.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
103.0ms	(-.f64 (pow.f64 b 2) (pow.f64 a 2))
32.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
29.0ms	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))

Compiler

Compiled 1720 to 1517 computations (11.8% saved)

simplify93.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4943	2121
1	4943	2121

prune715.0ms (0.5%)

Pruning

75 alts after pruning (73 fresh and 2 done)

	Pruned	Kept	Total
New	129	73	202
Fresh	0	0	0
Picked	0	0	0
Done	0	2	2
Total	129	75	204

Error

27.8b

Counts

204 → 75

Compiler

Compiled 5229 to 3739 computations (28.5% saved)

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(pow.f64 (cos.f64 (*.f64 PI.f64 (/.f64 angle 180))) 3)
0.2b	(cbrt.f64 (pow.f64 (cos.f64 (*.f64 PI.f64 (/.f64 angle 180))) 3))
0.1b	(.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 PI.f64 (/.f64 angle 180)))) (cbrt.f64 (pow.f64 (cos.f64 (*.f64 PI.f64 (/.f64 angle 180))) 3)))
0.0b	(*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))
0.7b	(-.f64 (pow.f64 b 2) (pow.f64 a 2))
9.5b	(.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
21.6b	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
21.6b	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))

rewrite36.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_441`
16×	`difference-of-squares_binary64_388`
13×	`unpow-prod-down_binary64_498`
11×	`*-un-lft-identity_binary64_419`
9×	`sqr-pow_binary64_391` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `unpow2_binary64_484` `pow1_binary64_480`
8×	`cancel-sign-sub-inv_binary64_385`
7×	`add-cube-cbrt_binary64_454`
6×	`add-log-exp_binary64_458`
3×	`pow-prod-down_binary64_490` `associate-r_binary64_359` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
2×	`associate-l/_binary64_362` `flip3--_binary64_423` `associate-r/_binary64_361` `distribute-lft-out--_binary64_371` `flip--_binary64_394`
1×	`sub-neg_binary64_412` `-commutative_binary64_350` `associate-l*_binary64_360` `diff-log_binary64_511`

Counts

4 → 71

Calls

8 calls:

15.0ms	(.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
10.0ms	(-.f64 (pow.f64 b 2) (pow.f64 a 2))
2.0ms	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))
2.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
0.0ms	(*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))

series668.0ms (0.4%)

Counts

4 → 42

Calls

4 calls:

491.0ms	(.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
106.0ms	(-.f64 (pow.f64 b 2) (pow.f64 a 2))
36.0ms	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))
34.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))

Compiler

Compiled 1900 to 1697 computations (10.7% saved)

simplify90.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4943	2121
1	4943	2121

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

9.5b	(.f64 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
0.7b	(-.f64 (.f64 b b) (.f64 a a))
0.3b	(*.f64 PI.f64 (/.f64 angle 180))
0.0b	(.f64 2 (-.f64 (.f64 b b) (*.f64 a a)))
0.3b	(*.f64 PI.f64 (/.f64 angle 180))
0.7b	(-.f64 (.f64 b b) (.f64 a a))
9.5b	(.f64 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
21.6b	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))

rewrite32.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_441`
16×	`associate-r_binary64_359`
14×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
13×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
11×	`pow1_binary64_480`
10×	`times-frac_binary64_425`
6×	`add-log-exp_binary64_458`
5×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
4×	`pow-prod-down_binary64_490` `associate-l_binary64_360`
3×	`associate-*r/_binary64_361`
2×	`associate-l/_binary64_362` `unswap-sqr_binary64_387` `flip3--_binary64_423` `-commutative_binary64_350` `flip--_binary64_394`
1×	`sub-neg_binary64_412` `difference-of-squares_binary64_388` `div-inv_binary64_416` `diff-log_binary64_511` `cancel-sign-sub-inv_binary64_385` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 72

Calls

8 calls:

12.0ms	(.f64 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
8.0ms	(*.f64 PI.f64 (/.f64 angle 180))
4.0ms	(-.f64 (.f64 b b) (.f64 a a))
2.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
0.0ms	(.f64 2 (-.f64 (.f64 b b) (*.f64 a a)))

series577.0ms (0.4%)

Counts

4 → 35

Calls

4 calls:

433.0ms	(.f64 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
91.0ms	(-.f64 (.f64 b b) (.f64 a a))
31.0ms	(*.f64 PI.f64 (/.f64 angle 180))
22.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))

Compiler

Compiled 1192 to 1113 computations (6.6% saved)

simplify83.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4954	1733
1	4954	1733

localize29.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 PI.f64 (.f64 b b))
0.1b	(.f64 (.f64 (pow.f64 angle 3) 1/17496000) (pow.f64 PI.f64 3))
0.1b	(*.f64 (pow.f64 angle 3) 1/17496000)
0.1b	(.f64 (+.f64 (.f64 angle (.f64 1/90 (.f64 PI.f64 (.f64 b b)))) (+.f64 (.f64 (.f64 (.f64 (pow.f64 angle 3) 1/17496000) (pow.f64 PI.f64 3)) (-.f64 (.f64 a a) (.f64 b b))) (.f64 (.f64 angle (.f64 PI.f64 (.f64 a a))) -1/90))) (cos.f64 (*.f64 PI.f64 (/.f64 angle 180))))
7.8b	(.f64 angle (.f64 PI.f64 (*.f64 a a)))
8.8b	(.f64 angle (.f64 1/90 (.f64 PI.f64 (.f64 b b))))
14.8b	(.f64 (.f64 (.f64 (pow.f64 angle 3) 1/17496000) (pow.f64 PI.f64 3)) (-.f64 (.f64 a a) (*.f64 b b)))
21.6b	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))

rewrite50.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64_457`
50×	`prod-exp_binary64_468`
36×	`add-cbrt-cube_binary64_455`
29×	`pow1_binary64_480`
22×	`cbrt-unprod_binary64_452`
17×	`pow-prod-down_binary64_490`
7×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `pow-exp_binary64_487` `pow-to-exp_binary64_488` `associate-l*_binary64_360`
6×	`associate-r_binary64_359`
4×	`add-log-exp_binary64_458`
3×	`*-commutative_binary64_350`
2×	`sub-neg_binary64_412` `distribute-rgt-in_binary64_369` `associate-*r/_binary64_361` `distribute-lft-in_binary64_368` `cancel-sign-sub-inv_binary64_385`
1×	`difference-of-squares_binary64_388` `flip3--_binary64_423` `flip--_binary64_394`

Counts

4 → 88

Calls

8 calls:

16.0ms	(.f64 (.f64 (.f64 (pow.f64 angle 3) 1/17496000) (pow.f64 PI.f64 3)) (-.f64 (.f64 a a) (*.f64 b b)))
11.0ms	(.f64 angle (.f64 1/90 (.f64 PI.f64 (.f64 b b))))
8.0ms	(.f64 angle (.f64 PI.f64 (*.f64 a a)))
2.0ms	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))
0.0ms	(.f64 (+.f64 (.f64 angle (.f64 1/90 (.f64 PI.f64 (.f64 b b)))) (+.f64 (.f64 (.f64 (.f64 (pow.f64 angle 3) 1/17496000) (pow.f64 PI.f64 3)) (-.f64 (.f64 a a) (.f64 b b))) (.f64 (.f64 angle (.f64 PI.f64 (.f64 a a))) -1/90))) (cos.f64 (*.f64 PI.f64 (/.f64 angle 180))))

series740.0ms (0.5%)

Counts

4 → 32

Calls

4 calls:

507.0ms	(.f64 (.f64 (.f64 (pow.f64 angle 3) 1/17496000) (pow.f64 PI.f64 3)) (-.f64 (.f64 a a) (*.f64 b b)))
110.0ms	(.f64 angle (.f64 1/90 (.f64 PI.f64 (.f64 b b))))
89.0ms	(.f64 angle (.f64 PI.f64 (*.f64 a a)))
33.0ms	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))

Compiler

Compiled 2600 to 1938 computations (25.5% saved)

simplify62.0ms (0%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5134	2343

localize27.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 1/25194240000 (.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4)))
0.2b	(.f64 (.f64 angle angle) (pow.f64 PI.f64 2))
0.1b	(*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))
0.0b	(.f64 2 (-.f64 (.f64 b b) (*.f64 a a)))
3.0b	(.f64 (.f64 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))) (sin.f64 (.f64 PI.f64 (/.f64 angle 180)))) (+.f64 (-.f64 1 (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 PI.f64 2)))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4)))))
8.0b	(+.f64 (-.f64 1 (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 PI.f64 2)))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))))
9.5b	(.f64 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
21.6b	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))

rewrite55.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
10×	`associate-l/_binary64_362` `associate-r/_binary64_361`
9×	`pow-prod-down_binary64_490` `add-log-exp_binary64_458` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
6×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `associate-r*_binary64_359` `add-sqr-sqrt_binary64_441`
4×	`flip3-+_binary64_422` `frac-times_binary64_429` `flip3--_binary64_423` `flip-+_binary64_393` `flip--_binary64_394`
2×	`sum-log_binary64_510` `-commutative_binary64_350` `associate-l*_binary64_360` `associate-+l+_binary64_352`
1×	`sub-neg_binary64_412` `distribute-rgt-in_binary64_369` `associate-+l-_binary64_354` `distribute-lft-in_binary64_368` `diff-log_binary64_511` `cancel-sign-sub-inv_binary64_385` `+-commutative_binary64_349`

Counts

4 → 73

Calls

8 calls:

20.0ms	(.f64 (.f64 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))) (sin.f64 (.f64 PI.f64 (/.f64 angle 180)))) (+.f64 (-.f64 1 (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 PI.f64 2)))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4)))))
9.0ms	(.f64 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
9.0ms	(+.f64 (-.f64 1 (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 PI.f64 2)))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))))
2.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
0.0ms	(.f64 2 (-.f64 (.f64 b b) (*.f64 a a)))

series1.9s (1.2%)

Counts

4 → 45

Calls

4 calls:

1.3s	(.f64 (.f64 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))) (sin.f64 (.f64 PI.f64 (/.f64 angle 180)))) (+.f64 (-.f64 1 (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 PI.f64 2)))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4)))))
476.0ms	(.f64 (.f64 2 (-.f64 (.f64 b b) (.f64 a a))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
75.0ms	(+.f64 (-.f64 1 (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 PI.f64 2)))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))))
36.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))

Compiler

Compiled 3908 to 3154 computations (19.3% saved)

simplify92.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5272	6134

localize27.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 1/25194240000 (.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4)))
0.2b	(.f64 (.f64 angle angle) (pow.f64 PI.f64 2))
0.1b	(*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))
0.0b	(*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))
3.0b	(.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 PI.f64 (/.f64 angle 180)))) (+.f64 (-.f64 1 (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 PI.f64 2)))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4)))))
8.0b	(+.f64 (-.f64 1 (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 PI.f64 2)))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))))
9.5b	(.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
21.6b	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))

rewrite65.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
10×	`associate-l/_binary64_362` `associate-r/_binary64_361`
9×	`pow-prod-down_binary64_490` `add-log-exp_binary64_458` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
6×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `associate-r*_binary64_359` `add-sqr-sqrt_binary64_441`
4×	`flip3-+_binary64_422` `frac-times_binary64_429` `flip3--_binary64_423` `flip-+_binary64_393` `flip--_binary64_394`
2×	`sum-log_binary64_510` `-commutative_binary64_350` `associate-l*_binary64_360` `associate-+l+_binary64_352`
1×	`sub-neg_binary64_412` `distribute-rgt-in_binary64_369` `associate-+l-_binary64_354` `distribute-lft-in_binary64_368` `diff-log_binary64_511` `cancel-sign-sub-inv_binary64_385` `+-commutative_binary64_349`

Counts

4 → 73

Calls

8 calls:

28.0ms	(.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 PI.f64 (/.f64 angle 180)))) (+.f64 (-.f64 1 (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 PI.f64 2)))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4)))))
15.0ms	(.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
9.0ms	(+.f64 (-.f64 1 (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 PI.f64 2)))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))))
2.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
0.0ms	(*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))

series1.9s (1.2%)

Counts

4 → 45

Calls

4 calls:

1.3s	(.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 PI.f64 (/.f64 angle 180)))) (+.f64 (-.f64 1 (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 PI.f64 2)))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4)))))
492.0ms	(.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
79.0ms	(+.f64 (-.f64 1 (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 PI.f64 2)))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))))
38.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))

Compiler

Compiled 3908 to 3186 computations (18.5% saved)

simplify91.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5152	6134

prune8.0s (5.2%)

Pruning

290 alts after pruning (284 fresh and 6 done)

	Pruned	Kept	Total
New	359	217	576
Fresh	1	67	68
Picked	0	0	0
Done	1	6	7
Total	361	290	651

Error

27.1b

Counts

651 → 290

Compiler

Compiled 23341 to 16179 computations (30.7% saved)

localize23.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(cbrt.f64 (pow.f64 (log.f64 (exp.f64 (cos.f64 (*.f64 PI.f64 (/.f64 angle 180))))) 3))
0.1b	(.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 PI.f64 (/.f64 angle 180)))) (cbrt.f64 (pow.f64 (log.f64 (exp.f64 (cos.f64 (*.f64 PI.f64 (/.f64 angle 180))))) 3)))
0.1b	(exp.f64 (cos.f64 (*.f64 PI.f64 (/.f64 angle 180))))
0.0b	(*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))
0.7b	(-.f64 (pow.f64 b 2) (pow.f64 a 2))
9.5b	(.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
21.6b	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
21.6b	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))

rewrite38.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_441`
16×	`difference-of-squares_binary64_388`
13×	`unpow-prod-down_binary64_498`
11×	`*-un-lft-identity_binary64_419`
9×	`sqr-pow_binary64_391` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `unpow2_binary64_484` `pow1_binary64_480`
8×	`cancel-sign-sub-inv_binary64_385`
7×	`add-cube-cbrt_binary64_454`
6×	`add-log-exp_binary64_458`
3×	`pow-prod-down_binary64_490` `associate-r_binary64_359` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
2×	`associate-l/_binary64_362` `flip3--_binary64_423` `associate-r/_binary64_361` `distribute-lft-out--_binary64_371` `flip--_binary64_394`
1×	`sub-neg_binary64_412` `-commutative_binary64_350` `associate-l*_binary64_360` `diff-log_binary64_511`

Counts

4 → 71

Calls

8 calls:

17.0ms	(.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
9.0ms	(-.f64 (pow.f64 b 2) (pow.f64 a 2))
2.0ms	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))
2.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
0.0ms	(*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))

series671.0ms (0.4%)

Counts

4 → 42

Calls

4 calls:

494.0ms	(.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
107.0ms	(-.f64 (pow.f64 b 2) (pow.f64 a 2))
38.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
32.0ms	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))

Compiler

Compiled 2020 to 1817 computations (10% saved)

simplify100.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4943	2121
1	4943	2121

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

11.0b	(.f64 angle (.f64 1/90 (.f64 PI.f64 (-.f64 (.f64 b b) (*.f64 a a)))))
0.7b	(-.f64 (.f64 b b) (.f64 a a))
0.2b	(.f64 PI.f64 (-.f64 (.f64 b b) (*.f64 a a)))
0.2b	(.f64 1/90 (.f64 PI.f64 (-.f64 (.f64 b b) (.f64 a a))))
0.2b	(.f64 1/90 (.f64 PI.f64 (-.f64 (.f64 b b) (.f64 a a))))
0.2b	(.f64 PI.f64 (-.f64 (.f64 b b) (*.f64 a a)))
0.7b	(-.f64 (.f64 b b) (.f64 a a))
11.0b	(.f64 angle (.f64 1/90 (.f64 PI.f64 (-.f64 (.f64 b b) (*.f64 a a)))))

rewrite42.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
20×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
15×	`sub-neg_binary64_412` `cancel-sign-sub-inv_binary64_385`
12×	`associate-*r/_binary64_361`
10×	`pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `add-sqr-sqrt_binary64_441`
9×	`associate-l_binary64_360`
8×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
6×	`add-log-exp_binary64_458` `associate-r_binary64_359`
4×	`flip3--_binary64_423` `flip--_binary64_394`
3×	`*-commutative_binary64_350`
2×	`difference-of-squares_binary64_388`
1×	`unswap-sqr_binary64_387` `diff-log_binary64_511`

Counts

4 → 105

Calls

8 calls:

12.0ms	(.f64 angle (.f64 1/90 (.f64 PI.f64 (-.f64 (.f64 b b) (*.f64 a a)))))
10.0ms	(.f64 1/90 (.f64 PI.f64 (-.f64 (.f64 b b) (.f64 a a))))
7.0ms	(.f64 PI.f64 (-.f64 (.f64 b b) (*.f64 a a)))
4.0ms	(-.f64 (.f64 b b) (.f64 a a))
0.0ms	(.f64 1/90 (.f64 PI.f64 (-.f64 (.f64 b b) (.f64 a a))))

series710.0ms (0.5%)

Counts

4 → 51

Calls

4 calls:

315.0ms	(.f64 angle (.f64 1/90 (.f64 PI.f64 (-.f64 (.f64 b b) (*.f64 a a)))))
175.0ms	(.f64 1/90 (.f64 PI.f64 (-.f64 (.f64 b b) (.f64 a a))))
126.0ms	(.f64 PI.f64 (-.f64 (.f64 b b) (*.f64 a a)))
94.0ms	(-.f64 (.f64 b b) (.f64 a a))

Compiler

Compiled 1082 to 1056 computations (2.4% saved)

simplify53.0ms (0%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5734	2726

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 1/180 (.f64 PI.f64 angle))
0.2b	(*.f64 PI.f64 angle)
0.1b	(.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 1/180 (.f64 PI.f64 angle)))) (cos.f64 (.f64 PI.f64 (/.f64 angle 180))))
0.0b	(*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))
0.7b	(-.f64 (pow.f64 b 2) (pow.f64 a 2))
9.5b	(.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 1/180 (.f64 PI.f64 angle))))
21.6b	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))
22.0b	(sin.f64 (.f64 1/180 (.f64 PI.f64 angle)))

rewrite36.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_441`
16×	`difference-of-squares_binary64_388`
13×	`unpow-prod-down_binary64_498`
11×	`*-un-lft-identity_binary64_419`
9×	`sqr-pow_binary64_391` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `unpow2_binary64_484` `pow1_binary64_480`
8×	`cancel-sign-sub-inv_binary64_385`
7×	`add-cube-cbrt_binary64_454`
6×	`add-log-exp_binary64_458`
3×	`pow-prod-down_binary64_490` `associate-r_binary64_359` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
2×	`associate-l/_binary64_362` `flip3--_binary64_423` `associate-r/_binary64_361` `distribute-lft-out--_binary64_371` `flip--_binary64_394`
1×	`sub-neg_binary64_412` `-commutative_binary64_350` `associate-l*_binary64_360` `diff-log_binary64_511`

Counts

4 → 71

Calls

8 calls:

15.0ms	(.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 1/180 (.f64 PI.f64 angle))))
9.0ms	(-.f64 (pow.f64 b 2) (pow.f64 a 2))
2.0ms	(sin.f64 (.f64 1/180 (.f64 PI.f64 angle)))
2.0ms	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))
0.0ms	(*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))

series645.0ms (0.4%)

Counts

4 → 42

Calls

4 calls:

480.0ms	(.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 1/180 (.f64 PI.f64 angle))))
101.0ms	(-.f64 (pow.f64 b 2) (pow.f64 a 2))
33.0ms	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))
31.0ms	(sin.f64 (.f64 1/180 (.f64 PI.f64 angle)))

Compiler

Compiled 1720 to 1517 computations (11.8% saved)

simplify74.0ms (0%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4991	2121
1	4991	2121

localize37.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 PI.f64 (.f64 b b))
0.1b	(.f64 (.f64 (pow.f64 angle 3) 1/17496000) (pow.f64 PI.f64 3))
0.1b	(*.f64 (pow.f64 angle 3) 1/17496000)
0.1b	(.f64 (+.f64 (.f64 angle (.f64 1/90 (.f64 PI.f64 (.f64 b b)))) (+.f64 (+.f64 (.f64 (.f64 (.f64 (pow.f64 angle 3) 1/17496000) (pow.f64 PI.f64 3)) (.f64 a a)) (.f64 (pow.f64 angle 3) (.f64 (.f64 (pow.f64 PI.f64 3) (.f64 b b)) -1/17496000))) (.f64 (.f64 angle (.f64 PI.f64 (.f64 a a))) -1/90))) (cos.f64 (.f64 PI.f64 (/.f64 angle 180))))
8.8b	(.f64 angle (.f64 1/90 (.f64 PI.f64 (.f64 b b))))
13.7b	(.f64 (.f64 (.f64 (pow.f64 angle 3) 1/17496000) (pow.f64 PI.f64 3)) (.f64 a a))
14.2b	(.f64 (pow.f64 angle 3) (.f64 (.f64 (pow.f64 PI.f64 3) (.f64 b b)) -1/17496000))
21.6b	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))

rewrite63.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

193×	`add-exp-log_binary64_457`
163×	`prod-exp_binary64_468`
53×	`add-cbrt-cube_binary64_455`
35×	`cbrt-unprod_binary64_452`
28×	`pow-exp_binary64_487` `pow-to-exp_binary64_488`
23×	`pow1_binary64_480`
16×	`associate-l_binary64_360`
13×	`pow-prod-down_binary64_490`
8×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
4×	`add-log-exp_binary64_458`
3×	`unpow-prod-down_binary64_498` `associate-r_binary64_359` `*-commutative_binary64_350` `cube-prod_binary64_447`
1×	`unpow3_binary64_485` `cube-mult_binary64_449` `sqr-pow_binary64_391`

Counts

4 → 124

Calls

8 calls:

14.0ms	(.f64 (pow.f64 angle 3) (.f64 (.f64 (pow.f64 PI.f64 3) (.f64 b b)) -1/17496000))
13.0ms	(.f64 (.f64 (.f64 (pow.f64 angle 3) 1/17496000) (pow.f64 PI.f64 3)) (.f64 a a))
11.0ms	(.f64 angle (.f64 1/90 (.f64 PI.f64 (.f64 b b))))
2.0ms	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))
0.0ms	(.f64 (+.f64 (.f64 angle (.f64 1/90 (.f64 PI.f64 (.f64 b b)))) (+.f64 (+.f64 (.f64 (.f64 (.f64 (pow.f64 angle 3) 1/17496000) (pow.f64 PI.f64 3)) (.f64 a a)) (.f64 (pow.f64 angle 3) (.f64 (.f64 (pow.f64 PI.f64 3) (.f64 b b)) -1/17496000))) (.f64 (.f64 angle (.f64 PI.f64 (.f64 a a))) -1/90))) (cos.f64 (.f64 PI.f64 (/.f64 angle 180))))

series529.0ms (0.3%)

Counts

4 → 23

Calls

4 calls:

184.0ms	(.f64 (.f64 (.f64 (pow.f64 angle 3) 1/17496000) (pow.f64 PI.f64 3)) (.f64 a a))
181.0ms	(.f64 (pow.f64 angle 3) (.f64 (.f64 (pow.f64 PI.f64 3) (.f64 b b)) -1/17496000))
124.0ms	(.f64 angle (.f64 1/90 (.f64 PI.f64 (.f64 b b))))
40.0ms	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))

Compiler

Compiled 2416 to 1780 computations (26.3% saved)

simplify90.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5323	2845

localize31.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))
0.0b	(sqrt.f64 (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
0.0b	(sqrt.f64 (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
0.0b	(.f64 2 (-.f64 (.f64 b b) (*.f64 a a)))
2.4b	(.f64 (.f64 (sqrt.f64 (sin.f64 (.f64 PI.f64 (/.f64 angle 180)))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a)))) (sqrt.f64 (sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))))
8.0b	(+.f64 (-.f64 1 (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 PI.f64 2)))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))))
21.6b	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
21.6b	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))

rewrite38.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
9×	`add-log-exp_binary64_458`
6×	`-un-lft-identity_binary64_419` `pow-prod-down_binary64_490` `add-cube-cbrt_binary64_454` `associate-r*_binary64_359` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `add-sqr-sqrt_binary64_441`
4×	`associate-*r/_binary64_361`
3×	`sqrt-prod_binary64_435`
2×	`associate-*l/_binary64_362` `sum-log_binary64_510` `associate-+l+_binary64_352`
1×	`flip3-+_binary64_422` `sub-neg_binary64_412` `associate-+l-_binary64_354` `flip3--_binary64_423` `-commutative_binary64_350` `associate-l*_binary64_360` `flip-+_binary64_393` `diff-log_binary64_511` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385` `+-commutative_binary64_349`

Counts

4 → 55

Calls

8 calls:

17.0ms	(.f64 (.f64 (sqrt.f64 (sin.f64 (.f64 PI.f64 (/.f64 angle 180)))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a)))) (sqrt.f64 (sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))))
9.0ms	(+.f64 (-.f64 1 (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 PI.f64 2)))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))))
2.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
2.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
0.0ms	(.f64 2 (-.f64 (.f64 b b) (*.f64 a a)))

series650.0ms (0.4%)

Counts

4 → 32

Calls

4 calls:

490.0ms	(.f64 (.f64 (sqrt.f64 (sin.f64 (.f64 PI.f64 (/.f64 angle 180)))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a)))) (sqrt.f64 (sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))))
80.0ms	(+.f64 (-.f64 1 (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 PI.f64 2)))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))))
41.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
39.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))

Compiler

Compiled 2432 to 2007 computations (17.5% saved)

simplify74.0ms (0%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5011	2372

prune14.8s (9.7%)

Pruning

478 alts after pruning (469 fresh and 9 done)

	Pruned	Kept	Total
New	415	201	616
Fresh	11	268	279
Picked	0	0	0
Done	2	9	11
Total	428	478	906

Error

27.0b

Counts

906 → 478

Compiler

Compiled 30520 to 21553 computations (29.4% saved)

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 PI.f64 angle)
0.2b	(*.f64 PI.f64 angle)
0.1b	(.f64 (.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 1/180 (.f64 PI.f64 angle)))) (cos.f64 (.f64 1/180 (*.f64 PI.f64 angle))))
0.0b	(*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))
0.7b	(-.f64 (pow.f64 b 2) (pow.f64 a 2))
9.5b	(.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 1/180 (.f64 PI.f64 angle))))
22.0b	(sin.f64 (.f64 1/180 (.f64 PI.f64 angle)))
22.0b	(cos.f64 (.f64 1/180 (.f64 PI.f64 angle)))

rewrite37.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_441`
16×	`difference-of-squares_binary64_388`
13×	`unpow-prod-down_binary64_498`
11×	`*-un-lft-identity_binary64_419`
9×	`sqr-pow_binary64_391` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `unpow2_binary64_484` `pow1_binary64_480`
8×	`cancel-sign-sub-inv_binary64_385`
7×	`add-cube-cbrt_binary64_454`
6×	`add-log-exp_binary64_458`
3×	`pow-prod-down_binary64_490` `associate-r_binary64_359` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
2×	`associate-l/_binary64_362` `flip3--_binary64_423` `associate-r/_binary64_361` `distribute-lft-out--_binary64_371` `flip--_binary64_394`
1×	`sub-neg_binary64_412` `-commutative_binary64_350` `associate-l*_binary64_360` `diff-log_binary64_511`

Counts

4 → 71

Calls

8 calls:

15.0ms	(.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 1/180 (.f64 PI.f64 angle))))
10.0ms	(-.f64 (pow.f64 b 2) (pow.f64 a 2))
2.0ms	(sin.f64 (.f64 1/180 (.f64 PI.f64 angle)))
2.0ms	(cos.f64 (.f64 1/180 (.f64 PI.f64 angle)))
0.0ms	(*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))

series629.0ms (0.4%)

Counts

4 → 42

Calls

4 calls:

464.0ms	(.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (.f64 1/180 (.f64 PI.f64 angle))))
102.0ms	(-.f64 (pow.f64 b 2) (pow.f64 a 2))
31.0ms	(sin.f64 (.f64 1/180 (.f64 PI.f64 angle)))
31.0ms	(cos.f64 (.f64 1/180 (.f64 PI.f64 angle)))

Compiler

Compiled 1720 to 1499 computations (12.8% saved)

simplify73.0ms (0%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4981	2121
1	4981	2121

localize7.0ms (0%)

Local error

Found 6 expressions with local error:

8.8b	(.f64 angle (.f64 1/90 (.f64 PI.f64 (.f64 b b))))
0.2b	(.f64 1/90 (.f64 PI.f64 (*.f64 b b)))
0.2b	(.f64 PI.f64 (.f64 b b))
0.2b	(.f64 PI.f64 (.f64 b b))
0.2b	(.f64 1/90 (.f64 PI.f64 (*.f64 b b)))
8.8b	(.f64 angle (.f64 1/90 (.f64 PI.f64 (.f64 b b))))

rewrite32.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
19×	`pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
9×	`associate-l_binary64_360`
7×	`add-sqr-sqrt_binary64_441`
6×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
3×	`add-log-exp_binary64_458` `associate-r_binary64_359` `*-commutative_binary64_350`
1×	`unswap-sqr_binary64_387`

Counts

3 → 64

Calls

6 calls:

10.0ms	(.f64 angle (.f64 1/90 (.f64 PI.f64 (.f64 b b))))
8.0ms	(.f64 PI.f64 (.f64 b b))
8.0ms	(.f64 1/90 (.f64 PI.f64 (*.f64 b b)))
0.0ms	(.f64 PI.f64 (.f64 b b))
0.0ms	(.f64 1/90 (.f64 PI.f64 (*.f64 b b)))

series159.0ms (0.1%)

Counts

3 → 12

Calls

3 calls:

97.0ms	(.f64 angle (.f64 1/90 (.f64 PI.f64 (.f64 b b))))
34.0ms	(.f64 1/90 (.f64 PI.f64 (*.f64 b b)))
27.0ms	(.f64 PI.f64 (.f64 b b))

Compiler

Compiled 216 to 240 computations (-11.1% saved)

simplify62.0ms (0%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5360	961

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(pow.f64 (cos.f64 (*.f64 PI.f64 (/.f64 angle 180))) 3)
0.2b	(cbrt.f64 (pow.f64 (cos.f64 (*.f64 PI.f64 (/.f64 angle 180))) 3))
0.1b	(.f64 (.f64 (.f64 2 (.f64 b b)) (sin.f64 (.f64 PI.f64 (/.f64 angle 180)))) (cbrt.f64 (pow.f64 (cos.f64 (.f64 PI.f64 (/.f64 angle 180))) 3)))
0.0b	(.f64 2 (.f64 b b))
0.3b	(*.f64 PI.f64 (/.f64 angle 180))
5.5b	(.f64 (.f64 2 (.f64 b b)) (sin.f64 (.f64 PI.f64 (/.f64 angle 180))))
21.6b	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
21.6b	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))

rewrite27.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_441` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
16×	`associate-r_binary64_359`
15×	`pow1_binary64_480`
13×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
10×	`times-frac_binary64_425`
8×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
7×	`pow-prod-down_binary64_490`
4×	`add-log-exp_binary64_458` `associate-l_binary64_360`
2×	`unswap-sqr_binary64_387` `*-commutative_binary64_350`
1×	`div-inv_binary64_416` `associate-*r/_binary64_361` `div-exp_binary64_470` `cbrt-undiv_binary64_453`

Counts

4 → 67

Calls

8 calls:

9.0ms	(.f64 (.f64 2 (.f64 b b)) (sin.f64 (.f64 PI.f64 (/.f64 angle 180))))
7.0ms	(*.f64 PI.f64 (/.f64 angle 180))
2.0ms	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))
2.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
0.0ms	(.f64 2 (.f64 b b))

series271.0ms (0.2%)

Counts

4 → 24

Calls

4 calls:

178.0ms	(.f64 (.f64 2 (.f64 b b)) (sin.f64 (.f64 PI.f64 (/.f64 angle 180))))
33.0ms	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))
31.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
29.0ms	(*.f64 PI.f64 (/.f64 angle 180))

Compiler

Compiled 960 to 868 computations (9.6% saved)

simplify63.0ms (0%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5158	1528

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(pow.f64 (cos.f64 (*.f64 PI.f64 (/.f64 angle 180))) 3)
0.2b	(cbrt.f64 (pow.f64 (cos.f64 (*.f64 PI.f64 (/.f64 angle 180))) 3))
0.1b	(.f64 (exp.f64 (log.f64 (.f64 (sin.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 2 (-.f64 (.f64 b b) (.f64 a a)))))) (cbrt.f64 (pow.f64 (cos.f64 (*.f64 PI.f64 (/.f64 angle 180))) 3)))
0.0b	(.f64 2 (-.f64 (.f64 b b) (*.f64 a a)))
9.5b	(.f64 (sin.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))
9.7b	(log.f64 (.f64 (sin.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a)))))
21.6b	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
21.6b	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))

rewrite29.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary64_457` `pow1_binary64_480`
9×	`add-cbrt-cube_binary64_455`
8×	`distribute-rgt-in_binary64_369` `associate-*r/_binary64_361` `distribute-lft-in_binary64_368`
6×	`pow-prod-down_binary64_490` `prod-exp_binary64_468`
5×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
4×	`sub-neg_binary64_412` `add-log-exp_binary64_458` `cancel-sign-sub-inv_binary64_385`
3×	`rem-log-exp_binary64_460` `cbrt-unprod_binary64_452` `log-pow_binary64_508` `associate-l_binary64_360`
2×	`flip3--_binary64_423` `flip--_binary64_394` `log-div_binary64_506`
1×	`associate-r_binary64_359` `log-prod_binary64_505` `*-commutative_binary64_350`

Counts

4 → 58

Calls

8 calls:

10.0ms	(.f64 (sin.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))
9.0ms	(log.f64 (.f64 (sin.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a)))))
2.0ms	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))
2.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
0.0ms	(.f64 2 (-.f64 (.f64 b b) (*.f64 a a)))

series1.2s (0.8%)

Counts

4 → 42

Calls

4 calls:

636.0ms	(log.f64 (.f64 (sin.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a)))))
473.0ms	(.f64 (sin.f64 (.f64 PI.f64 (/.f64 angle 180))) (.f64 2 (-.f64 (.f64 b b) (*.f64 a a))))
35.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
33.0ms	(cos.f64 (*.f64 PI.f64 (/.f64 angle 180)))

Compiler

Compiled 2922 to 2493 computations (14.7% saved)

simplify77.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	6144	3752

localize30.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (.f64 angle angle) (pow.f64 PI.f64 2))
0.1b	(*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))
0.0b	(pow.f64 (+.f64 (-.f64 1 (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 PI.f64 2)))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4)))) 3)
0.0b	(*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))
4.3b	(cbrt.f64 (pow.f64 (+.f64 (-.f64 1 (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 PI.f64 2)))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4)))) 3))
8.0b	(+.f64 (-.f64 1 (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 PI.f64 2)))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))))
9.5b	(.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
21.6b	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))

rewrite49.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64_450`
9×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
8×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
3×	`pow-prod-down_binary64_490` `unpow-prod-down_binary64_498` `associate-r_binary64_359` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `cube-prod_binary64_447`
2×	`flip3-+_binary64_422` `associate-l/_binary64_362` `cbrt-div_binary64_451` `sum-log_binary64_510` `cube-div_binary64_448` `associate-r/_binary64_361` `flip-+_binary64_393` `associate-+l+_binary64_352`
1×	`pow1/3_binary64_501` `sub-neg_binary64_412` `unpow3_binary64_485` `cube-mult_binary64_449` `associate-+l-_binary64_354` `sqr-pow_binary64_391` `flip3--_binary64_423` `rem-cbrt-cube_binary64_443` `-commutative_binary64_350` `associate-l*_binary64_360` `diff-log_binary64_511` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385` `+-commutative_binary64_349`

Counts

4 → 65

Calls

8 calls:

15.0ms	(.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
13.0ms	(cbrt.f64 (pow.f64 (+.f64 (-.f64 1 (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 PI.f64 2)))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4)))) 3))
9.0ms	(+.f64 (-.f64 1 (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 PI.f64 2)))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))))
2.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))
0.0ms	(*.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2)))

series694.0ms (0.5%)

Counts

4 → 32

Calls

4 calls:

509.0ms	(.f64 (.f64 2 (-.f64 (pow.f64 b 2) (pow.f64 a 2))) (sin.f64 (*.f64 PI.f64 (/.f64 angle 180))))
76.0ms	(cbrt.f64 (pow.f64 (+.f64 (-.f64 1 (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 PI.f64 2)))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4)))) 3))
71.0ms	(+.f64 (-.f64 1 (.f64 1/64800 (.f64 (.f64 angle angle) (pow.f64 PI.f64 2)))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))))
38.0ms	(sin.f64 (*.f64 PI.f64 (/.f64 angle 180)))

Compiler

Compiled 2228 to 1929 computations (13.4% saved)

simplify83.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5106	3204

prune17.0s (11.2%)

Pruning

663 alts after pruning (651 fresh and 12 done)

	Pruned	Kept	Total
New	278	199	477
Fresh	12	452	464
Picked	0	0	0
Done	2	12	14
Total	292	663	955

Error

24.3b

Counts

955 → 663

Compiler

Compiled 10407 to 6659 computations (36% saved)

simplify770.0ms (0.5%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4975	55173
1	4975	55173

regimes25.9s (17%)

Compiler: Compiled 287617 to 227099 computations (21% saved)

bsearch42.0ms (0%)

Compiler: Compiled 7 to 8 computations (-14.3% saved)

regimes10.4s (6.8%)

Compiler: Compiled 117795 to 93409 computations (20.7% saved)

bsearch97.0ms (0.1%)

Steps

Iters	Range		Point
8	-3.273924119565461e+140	-6.335553167868901e+136	-3.2279412078330076e+140

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes9.1s (6%)

Compiler: Compiled 112793 to 88885 computations (21.2% saved)

bsearch0.0ms (0%)

regimes6.8s (4.5%)

Compiler: Compiled 85581 to 67406 computations (21.2% saved)

bsearch0.0ms (0%)

regimes7.0s (4.6%)

Compiler: Compiled 86612 to 68363 computations (21.1% saved)

bsearch0.0ms (0%)

regimes615.0ms (0.4%)

Compiler: Compiled 5667 to 5002 computations (11.7% saved)

bsearch0.0ms (0%)

regimes595.0ms (0.4%)

Compiler: Compiled 5437 to 4812 computations (11.5% saved)

bsearch0.0ms (0%)

regimes250.0ms (0.2%)

Compiler: Compiled 1272 to 1253 computations (1.5% saved)

bsearch0.0ms (0%)

regimes54.0ms (0%)

Compiler: Compiled 255 to 282 computations (-10.6% saved)

bsearch0.0ms (0%)

regimes108.0ms (0.1%)

Compiler: Compiled 177 to 216 computations (-22% saved)

bsearch155.0ms (0.1%)

Steps

Iters	Range		Point
10	5.966992575762436e-83	4.161259190511269e-73	4.581974872422141e-78
9	-4.441584539569119e-38	-1.0772125890844552e-45	-1.3709945349245143e-42

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes102.0ms (0.1%)

Compiler: Compiled 150 to 189 computations (-26% saved)

bsearch149.0ms (0.1%)

Steps

Iters	Range		Point
10	5.966992575762436e-83	4.161259190511269e-73	1.3157802113335384e-73
9	-4.441584539569119e-38	-1.0772125890844552e-45	-4.5461182162760603e-39

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes97.0ms (0.1%)

Compiler: Compiled 123 to 162 computations (-31.7% saved)

bsearch158.0ms (0.1%)

Steps

Iters	Range		Point
10	5.966992575762436e-83	4.161259190511269e-73	1.4256809634928402e-75
9	-4.441584539569119e-38	-1.0772125890844552e-45	-1.985360085628856e-44

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes88.0ms (0.1%)

Compiler: Compiled 96 to 135 computations (-40.6% saved)

bsearch152.0ms (0.1%)

Steps

Iters	Range		Point
10	5.966992575762436e-83	4.161259190511269e-73	1.8484039207807332e-73
9	-4.441584539569119e-38	-1.0772125890844552e-45	-2.0922304355887315e-41

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes82.0ms (0.1%)

Compiler: Compiled 69 to 108 computations (-56.5% saved)

bsearch155.0ms (0.1%)

Steps

Iters	Range		Point
10	5.966992575762436e-83	4.161259190511269e-73	1.8484039207807332e-73
9	-4.441584539569119e-38	-1.0772125890844552e-45	-4.3833796797803637e-38

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes30.0ms (0%)

Compiler: Compiled 42 to 81 computations (-92.9% saved)

bsearch0.0ms (0%)

regimes26.0ms (0%)

Accuracy

Total 3.7b remaining (12.7%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch24.0ms (0%)

Compiler: Compiled 482 to 381 computations (21% saved)

simplify11.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	237	727
1	237	727

end0.0ms (0%)

sample32.1s (21%)

Algorithm

1×

intervals

Results

824.0ms	1471×	body	1024	valid
695.0ms	1269×	body	1024	invalid
660.0ms	5152×	body	128	valid
297.0ms	755×	body	512	valid
279.0ms	74×	body	4096	valid
250.0ms	604×	body	512	invalid
170.0ms	1294×	body	128	invalid
161.0ms	174×	body	2048	valid
103.0ms	374×	body	256	valid
88.0ms	328×	body	256	invalid

Compiler

Compiled 29358 to 22962 computations (21.8% saved)

Pareto

0.87680879944856