Details

analyze1.2s (13.4%)

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
0%	99.9%	0.1%	6
6.2%	93.6%	0.1%	7
9.4%	90.5%	0.1%	8
14%	85.8%	0.1%	9
19.5%	80.4%	0.1%	10
20.7%	79.2%	0.1%	11
22%	77.8%	0.1%	12
23.5%	76.4%	0.1%	13
23.8%	76%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample66.0ms (0.7%)

Algorithm

1×

intervals

Results

31.0ms	99×	body	1024	valid
10.0ms	50×	body	512	valid
5.0ms	10×	body	2048	valid
5.0ms	81×	body	128	valid
2.0ms	16×	body	256	valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`associate-/r/_binary64`
1×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	13	14
2	17	14
3	20	14
4	21	14
5	21	14

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

14.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	14.3b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.2b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
3.9b	(cos.f64 (+.f64 a b))

rewrite67.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 47

Calls

3 calls:

5.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
4.0ms	(*.f64 r (sin.f64 b))
4.0ms	(cos.f64 (+.f64 a b))

Compiler

Compiled 706 to 152 computations (78.5% saved)

series128.0ms (1.4%)

Error

12.8b

Counts

3 → 34

Calls

3 calls:

62.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
21.0ms	(cos.f64 (+.f64 a b))
18.0ms	(*.f64 r (sin.f64 b))

Compiler

Compiled 1428 to 849 computations (40.5% saved)

simplify100.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

449×	`associate-/r*_binary64`
371×	`associate-*l/_binary64`
329×	`*-commutative_binary64`
294×	`associate-*r/_binary64`
293×	`associate-/l/_binary64`

Counts

81 → 62

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	166	1453
1	439	1331
2	1605	1299
3	4534	1299
4	4752	1299
5	4961	1299

prune71.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	54	8	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	8	63

Error

0.2b

Counts

63 → 8

Alt Table

Status	Error	Program
	15.0b	(/.f64 (.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (*.f64 (sin.f64 b) (cbrt.f64 r))) (cos.f64 (+.f64 a b)))
	14.5b	(/.f64 (*.f64 r (sin.f64 b)) (log.f64 (exp.f64 (cos.f64 (+.f64 b a)))))
	14.4b	(/.f64 r (/.f64 (cos.f64 (+.f64 b a)) (sin.f64 b)))
▶	0.3b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))))
	14.7b	(.f64 (/.f64 r (.f64 (cbrt.f64 (cos.f64 (+.f64 b a))) (cbrt.f64 (cos.f64 (+.f64 b a))))) (/.f64 (sin.f64 b) (cbrt.f64 (cos.f64 (+.f64 b a)))))
	14.3b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 b a))))
	14.7b	(/.f64 1 (/.f64 (cos.f64 (+.f64 b a)) (*.f64 (sin.f64 b) r)))
	29.8b	(*.f64 (/.f64 r (sqrt.f64 (cos.f64 (+.f64 b a)))) (/.f64 (sin.f64 b) (sqrt.f64 (cos.f64 (+.f64 b a)))))

Compiler

Compiled 1105 to 431 computations (61% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.1b	(-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))
0.2b	(*.f64 (sin.f64 b) (sin.f64 a))
0.2b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))))

rewrite143.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

14×	`add-sqr-sqrt_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

4 → 76

Calls

4 calls:

9.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))))
5.0ms	(-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))
5.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
4.0ms	(*.f64 r (sin.f64 b))

Compiler

Compiled 1877 to 293 computations (84.4% saved)

series214.0ms (2.3%)

Error

0.2b

Counts

4 → 44

Calls

4 calls:

101.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))))
30.0ms	(-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))
27.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
22.0ms	(*.f64 r (sin.f64 b))

Compiler

Compiled 2266 to 1286 computations (43.2% saved)

simplify146.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

359×	`associate-/l/_binary64`
338×	`associate-/r/_binary64`
337×	`cancel-sign-sub-inv_binary64`
229×	`associate-r_binary64`
223×	`distribute-rgt-neg-in_binary64`

Counts

120 → 76

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	232	2810
1	636	2586
2	2407	2358
3	4537	2358
4	4992	2358
5	4984	2358

prune96.0ms (1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	67	9	76
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	73	11	84

Error

0.0b

Counts

84 → 11

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (.f64 (cbrt.f64 (sin.f64 b)) (cbrt.f64 (sin.f64 b))) (*.f64 (sin.f64 a) (cbrt.f64 (sin.f64 b))))))
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))))
▶	0.3b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (sin.f64 b) 2))) (+.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))))
	0.4b	(.f64 (/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (sin.f64 b) 2)))) (+.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a))))
	0.4b	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a)))
	1.2b	(/.f64 (.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (.f64 (sin.f64 b) (cbrt.f64 r))) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))))
	0.4b	(.f64 (/.f64 (.f64 (sin.f64 b) r) (-.f64 (pow.f64 (.f64 (cos.f64 b) (cos.f64 a)) 3) (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3))) (+.f64 (.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (cos.f64 b) (cos.f64 a))) (+.f64 (.f64 (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (sin.f64 b) (sin.f64 a))) (.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))))))
	14.7b	(.f64 (/.f64 r (.f64 (cbrt.f64 (cos.f64 (+.f64 b a))) (cbrt.f64 (cos.f64 (+.f64 b a))))) (/.f64 (sin.f64 b) (cbrt.f64 (cos.f64 (+.f64 b a)))))
	1.2b	(.f64 (.f64 (cbrt.f64 (/.f64 r (-.f64 (/.f64 (.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a)))) (cbrt.f64 (/.f64 r (-.f64 (/.f64 (.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a))))) (cbrt.f64 (/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a)))))
	0.4b	(.f64 r (/.f64 1 (-.f64 (/.f64 (.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a))))
	29.8b	(*.f64 (/.f64 r (sqrt.f64 (cos.f64 (+.f64 b a)))) (/.f64 (sin.f64 b) (sqrt.f64 (cos.f64 (+.f64 b a)))))

Compiler

Compiled 2082 to 750 computations (64% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (sin.f64 b) 2))) (+.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))))
0.3b	(pow.f64 (sin.f64 a) 2)
0.3b	(pow.f64 (cos.f64 b) 2)
0.4b	(/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (sin.f64 b) 2))) (+.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a))))

rewrite380.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

43×	`times-frac_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`
20×	`add-exp-log_binary64`

Counts

4 → 121

Calls

4 calls:

14.0ms	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (sin.f64 b) 2))) (+.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))))
13.0ms	(/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (sin.f64 b) 2))) (+.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a))))
3.0ms	(pow.f64 (sin.f64 a) 2)
2.0ms	(pow.f64 (cos.f64 b) 2)

Compiler

Compiled 6860 to 2713 computations (60.5% saved)

series363.0ms (4%)

Error

0.0b

Counts

4 → 34

Calls

4 calls:

210.0ms	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (sin.f64 b) 2))) (+.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))))
85.0ms	(/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (sin.f64 b) 2))) (+.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a))))
15.0ms	(pow.f64 (sin.f64 a) 2)
11.0ms	(pow.f64 (cos.f64 b) 2)

Compiler

Compiled 2785 to 1599 computations (42.6% saved)

simplify271.0ms (3%)

Algorithm

1×	egg-herbie

Rules

258×	`associate-/l*_binary64`
247×	`associate-r_binary64`
247×	`associate-l_binary64`
233×	`cancel-sign-sub-inv_binary64`
228×	`unswap-sqr_binary64`

Counts

155 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	321	8332
1	845	7453
2	3472	6630
3	4826	6630
4	5000	6630
5	4975	6630

prune264.0ms (2.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	120	5	125
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	126	10	136

Error

Counts

136 → 10

Alt Table

Status	Error	Program
	0.9b	(/.f64 (.f64 r (sin.f64 b)) (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 (pow.f64 (cos.f64 b) 2) (pow.f64 (cos.f64 a) 2)) (.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (sin.f64 a) 2)))) (cbrt.f64 (-.f64 (.f64 (pow.f64 (cos.f64 b) 2) (pow.f64 (cos.f64 a) 2)) (.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (sin.f64 a) 2))))) (/.f64 (cbrt.f64 (-.f64 (.f64 (pow.f64 (cos.f64 b) 2) (pow.f64 (cos.f64 a) 2)) (.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (sin.f64 a) 2)))) (+.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))))))
▶	0.3b	(/.f64 (.f64 (sin.f64 b) r) (/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (sin.f64 b) 2))) (+.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))))
	0.4b	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a)))
	1.2b	(/.f64 (.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (.f64 (sin.f64 b) (cbrt.f64 r))) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))))
	0.4b	(.f64 (/.f64 (.f64 (sin.f64 b) r) (-.f64 (pow.f64 (.f64 (cos.f64 b) (cos.f64 a)) 3) (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3))) (+.f64 (.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (cos.f64 b) (cos.f64 a))) (+.f64 (.f64 (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (sin.f64 b) (sin.f64 a))) (.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))))))
	0.4b	(/.f64 (sin.f64 b) (.f64 1 (/.f64 (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))) r)))
	14.7b	(.f64 (/.f64 r (.f64 (cbrt.f64 (cos.f64 (+.f64 b a))) (cbrt.f64 (cos.f64 (+.f64 b a))))) (/.f64 (sin.f64 b) (cbrt.f64 (cos.f64 (+.f64 b a)))))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (.f64 (/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 b) 2) (pow.f64 (cos.f64 a) 2)) (.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (sin.f64 a) 2))) (+.f64 (pow.f64 (.f64 (cos.f64 b) (cos.f64 a)) 3) (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3))) (+.f64 (.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (cos.f64 b) (cos.f64 a))) (-.f64 (.f64 (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (sin.f64 b) (sin.f64 a))) (.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))))))
	0.4b	(.f64 (/.f64 r (-.f64 (.f64 (pow.f64 (cos.f64 b) 2) (pow.f64 (cos.f64 a) 2)) (.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (sin.f64 a) 2)))) (.f64 (sin.f64 b) (+.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))))
	29.8b	(*.f64 (/.f64 r (sqrt.f64 (cos.f64 (+.f64 b a)))) (/.f64 (sin.f64 b) (sqrt.f64 (cos.f64 (+.f64 b a)))))

Compiler

Compiled 5619 to 2287 computations (59.3% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (.f64 (sin.f64 b) r) (/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (sin.f64 b) 2))) (+.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))))
0.3b	(pow.f64 (sin.f64 a) 2)
0.3b	(pow.f64 (cos.f64 b) 2)
0.4b	(/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (sin.f64 b) 2))) (+.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a))))

rewrite381.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

43×	`times-frac_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`
20×	`add-exp-log_binary64`

Counts

4 → 121

Calls

4 calls:

15.0ms	(/.f64 (.f64 (sin.f64 b) r) (/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (sin.f64 b) 2))) (+.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))))
12.0ms	(/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (sin.f64 b) 2))) (+.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a))))
3.0ms	(pow.f64 (sin.f64 a) 2)
2.0ms	(pow.f64 (cos.f64 b) 2)

Compiler

Compiled 6860 to 2713 computations (60.5% saved)

series375.0ms (4.1%)

Error

Counts

4 → 34

Calls

4 calls:

211.0ms	(/.f64 (.f64 (sin.f64 b) r) (/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (sin.f64 b) 2))) (+.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))))
87.0ms	(/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (sin.f64 b) 2))) (+.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a))))
14.0ms	(pow.f64 (sin.f64 a) 2)
11.0ms	(pow.f64 (cos.f64 b) 2)

Compiler

Compiled 2778 to 1598 computations (42.5% saved)

simplify227.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

257×	`associate-/l*_binary64`
249×	`associate-r_binary64`
246×	`associate-l_binary64`
233×	`cancel-sign-sub-inv_binary64`
231×	`unswap-sqr_binary64`

Counts

155 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	321	8312
1	842	7454
2	3480	6631
3	4842	6631
4	4977	6631

prune248.0ms (2.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	125	10	135

Error

Counts

135 → 10

Alt Table

Status	Error	Program
	0.9b	(/.f64 (.f64 r (sin.f64 b)) (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 (pow.f64 (cos.f64 b) 2) (pow.f64 (cos.f64 a) 2)) (.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (sin.f64 a) 2)))) (cbrt.f64 (-.f64 (.f64 (pow.f64 (cos.f64 b) 2) (pow.f64 (cos.f64 a) 2)) (.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (sin.f64 a) 2))))) (/.f64 (cbrt.f64 (-.f64 (.f64 (pow.f64 (cos.f64 b) 2) (pow.f64 (cos.f64 a) 2)) (.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (sin.f64 a) 2)))) (+.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))))))
	0.3b	(/.f64 (.f64 (sin.f64 b) r) (/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (sin.f64 b) 2))) (+.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))))
	0.4b	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a)))
	1.2b	(/.f64 (.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (.f64 (sin.f64 b) (cbrt.f64 r))) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))))
	0.4b	(.f64 (/.f64 (.f64 (sin.f64 b) r) (-.f64 (pow.f64 (.f64 (cos.f64 b) (cos.f64 a)) 3) (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3))) (+.f64 (.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (cos.f64 b) (cos.f64 a))) (+.f64 (.f64 (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (sin.f64 b) (sin.f64 a))) (.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))))))
	0.4b	(/.f64 (sin.f64 b) (.f64 1 (/.f64 (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))) r)))
	14.7b	(.f64 (/.f64 r (.f64 (cbrt.f64 (cos.f64 (+.f64 b a))) (cbrt.f64 (cos.f64 (+.f64 b a))))) (/.f64 (sin.f64 b) (cbrt.f64 (cos.f64 (+.f64 b a)))))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (.f64 (/.f64 (-.f64 (.f64 (pow.f64 (cos.f64 b) 2) (pow.f64 (cos.f64 a) 2)) (.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (sin.f64 a) 2))) (+.f64 (pow.f64 (.f64 (cos.f64 b) (cos.f64 a)) 3) (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3))) (+.f64 (.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (cos.f64 b) (cos.f64 a))) (-.f64 (.f64 (.f64 (sin.f64 b) (sin.f64 a)) (.f64 (sin.f64 b) (sin.f64 a))) (.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))))))
	0.3b	(.f64 (/.f64 (sin.f64 b) (-.f64 (.f64 (pow.f64 (cos.f64 b) 2) (pow.f64 (cos.f64 a) 2)) (.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (sin.f64 a) 2)))) (.f64 (+.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a))) r))
	29.8b	(*.f64 (/.f64 r (sqrt.f64 (cos.f64 (+.f64 b a)))) (/.f64 (sin.f64 b) (sqrt.f64 (cos.f64 (+.f64 b a)))))

Compiler

Compiled 5180 to 2062 computations (60.2% saved)

regimes2.0s (22.2%)

Accuracy

Total 0.3b remaining (85.2%)

Threshold costs 0.3b (85.2%)

Compiler

Compiled 41316 to 22802 computations (44.8% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	21	26
2	31	26
3	37	26
4	41	26
5	42	26
6	42	26

end1.0ms (0%)

Compiler: Compiled 19 to 12 computations (36.8% saved)

sample2.3s (24.7%)

Algorithm

1×

intervals

Results

986.0ms	3455×	body	1024	valid
273.0ms	1392×	body	512	valid
156.0ms	2369×	body	128	valid
118.0ms	200×	body	2048	valid
78.0ms	584×	body	256	valid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 440 to 240 computations (45.5% saved)

Details

analyze1.2s (13.4%)

sample66.0ms (0.7%)

simplify8.0ms (0.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite67.0ms (0.7%)

series128.0ms (1.4%)

simplify100.0ms (1.1%)

prune71.0ms (0.8%)

localize13.0ms (0.1%)

rewrite143.0ms (1.6%)

series214.0ms (2.3%)

simplify146.0ms (1.6%)

prune96.0ms (1%)

localize25.0ms (0.3%)

rewrite380.0ms (4.2%)

series363.0ms (4%)

simplify271.0ms (3%)

prune264.0ms (2.9%)

localize25.0ms (0.3%)

rewrite381.0ms (4.2%)

series375.0ms (4.1%)

simplify227.0ms (2.5%)

prune248.0ms (2.7%)

regimes2.0s (22.2%)

simplify4.0ms (0%)

end1.0ms (0%)

sample2.3s (24.7%)

Profiling