Details

analyze1.4s (13.8%)

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
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)

sample707.0ms (7%)

Algorithm

1×

intervals

Results

661.0ms	123×	body	1024	valid
9.0ms	36×	body	512	valid
6.0ms	74×	body	128	valid
4.0ms	4×	body	2048	valid
3.0ms	19×	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`
1×	`+-commutative_binary64`
1×	`associate-*r/_binary64`
1×	`associate-*l/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	13	14
2	16	14
3	20	14
4	21	14
5	21	14

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

17.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.1b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))

Compiler

Compiled 45 to 28 computations (37.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
✓	0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
✓	4.2b	(cos.f64 (+.f64 a b))

series102.0ms (1%)

Counts

3 → 52

Calls

3 calls:

69.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
29.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
4.0ms	(cos.f64 (+.f64 a b))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
19×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`

Counts

3 → 73

Calls

3 calls:

6.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
3.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
3.0ms	(cos.f64 (+.f64 a b))

simplify73.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

696×	`fma-def_binary64`
561×	`associate-/r*_binary64`
437×	`associate-*l/_binary64`
281×	`associate-/r/_binary64`
239×	`associate-/l/_binary64`

Counts

125 → 172

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	244	2790
1	620	2642
2	2288	2580
3	5317	2580

prune178.0ms (1.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	159	13	172
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	160	13	173

Error

0.2b

Counts

173 → 13

Alt Table

Status	Error	Program
	17.1b	(/.f64 (*.f64 (sin.f64 b) r) (cos.f64 (+.f64 a b)))
	17.4b	(.f64 (.f64 r (/.f64 1 (*.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) (cbrt.f64 (cos.f64 (+.f64 a b)))))) (/.f64 (sin.f64 b) (cbrt.f64 (cos.f64 (+.f64 a b)))))
	28.3b	(+.f64 (/.f64 (.f64 (sin.f64 b) r) (cos.f64 b)) (/.f64 (.f64 (pow.f64 (sin.f64 b) 2) (*.f64 a r)) (pow.f64 (cos.f64 b) 2)))
	42.2b	(.f64 (.f64 r (sqrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))) (sqrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))))
▶	0.4b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
	17.7b	(.f64 (.f64 r (*.f64 (cbrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) (cbrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))))) (cbrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))))
	17.1b	(*.f64 r (/.f64 (sin.f64 b) (expm1.f64 (log1p.f64 (cos.f64 (+.f64 a b))))))
	34.2b	(.f64 r (+.f64 (/.f64 (.f64 (sin.f64 a) (pow.f64 b 2)) (pow.f64 (cos.f64 a) 2)) (+.f64 (.f64 2/3 (/.f64 (.f64 (sin.f64 a) (pow.f64 b 4)) (pow.f64 (cos.f64 a) 2))) (+.f64 (/.f64 (.f64 (pow.f64 (sin.f64 a) 3) (pow.f64 b 4)) (pow.f64 (cos.f64 a) 4)) (+.f64 (/.f64 (.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 b 3)) (pow.f64 (cos.f64 a) 3)) (+.f64 (*.f64 1/3 (/.f64 (pow.f64 b 3) (cos.f64 a))) (/.f64 b (cos.f64 a))))))))
	37.7b	(cbrt.f64 (.f64 (.f64 (.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) (.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))) (*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))))
	42.2b	(.f64 r (.f64 (sqrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) (sqrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))))
	28.6b	(.f64 r (cbrt.f64 (/.f64 (.f64 (.f64 (sin.f64 b) (sin.f64 b)) (sin.f64 b)) (.f64 (*.f64 (cos.f64 (+.f64 a b)) (cos.f64 (+.f64 a b))) (cos.f64 (+.f64 a b))))))
	17.1b	(*.f64 r (/.f64 (sin.f64 b) (log1p.f64 (expm1.f64 (cos.f64 (+.f64 a b))))))
	32.3b	(.f64 (.f64 r (/.f64 1 (sqrt.f64 (cos.f64 (+.f64 a b))))) (/.f64 (sin.f64 b) (sqrt.f64 (cos.f64 (+.f64 a b)))))

Compiler

Compiled 4261 to 1433 computations (66.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
✓	0.2b	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
✓	0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
✓	0.3b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))

series222.0ms (2.2%)

Counts

4 → 80

Calls

4 calls:

125.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
70.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
17.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
10.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
20×	`associate-r_binary64`
19×	`times-frac_binary64`

Counts

4 → 110

Calls

4 calls:

10.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
6.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
4.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
4.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

simplify148.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

386×	`fma-neg_binary64`
323×	`cancel-sign-sub-inv_binary64`
292×	`associate-r_binary64`
268×	`associate-l_binary64`
198×	`distribute-rgt-neg-in_binary64`

Counts

190 → 251

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	331	5599
1	870	5281
2	3258	5029
3	4530	5023
4	4971	5023

prune304.0ms (3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	237	14	251
Fresh	10	2	12
Picked	1	0	1
Done	0	0	0
Total	248	16	264

Error

0.0b

Counts

264 → 16

Alt Table

Status	Error	Program
	12.0b	(.f64 r (cbrt.f64 (pow.f64 (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))) 3)))
	1.2b	(.f64 (.f64 r (.f64 (cbrt.f64 (sin.f64 b)) (cbrt.f64 (sin.f64 b)))) (/.f64 (cbrt.f64 (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
	0.4b	(.f64 r (.f64 (/.f64 (sin.f64 b) (-.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (.f64 (.f64 (sin.f64 a) (sin.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))))
	32.6b	(.f64 (.f64 r (sqrt.f64 (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))))) (sqrt.f64 (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))))
▶	0.4b	(.f64 r (/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b))))))
	0.7b	(.f64 r (log1p.f64 (expm1.f64 (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))))
	33.2b	(.f64 (sqrt.f64 r) (.f64 (sqrt.f64 r) (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))))
	23.3b	(.f64 (.f64 r (/.f64 1 (sqrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))))) (/.f64 (sin.f64 b) (sqrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))))
	1.3b	(.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (.f64 (cbrt.f64 r) (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
	0.4b	(/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))
	0.4b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)))))
	23.8b	(.f64 (.f64 r (/.f64 (.f64 (cbrt.f64 (sin.f64 b)) (cbrt.f64 (sin.f64 b))) (sqrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))))) (/.f64 (cbrt.f64 (sin.f64 b)) (sqrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
	1.3b	(.f64 (.f64 r (/.f64 (.f64 (cbrt.f64 (sin.f64 b)) (cbrt.f64 (sin.f64 b))) (.f64 (cbrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))) (cbrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))))) (/.f64 (cbrt.f64 (sin.f64 b)) (cbrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))))
	42.2b	(.f64 r (.f64 (sqrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) (sqrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))))
	28.3b	(+.f64 (/.f64 (.f64 (sin.f64 b) r) (cos.f64 b)) (/.f64 (.f64 (pow.f64 (sin.f64 b) 2) (*.f64 a r)) (pow.f64 (cos.f64 b) 2)))
	0.9b	(.f64 (.f64 r (/.f64 1 (.f64 (cbrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))) (cbrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))))) (/.f64 (sin.f64 b) (cbrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))

Compiler

Compiled 8115 to 2184 computations (73.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b))))
✓	0.2b	(/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))
	0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
✓	0.3b	(.f64 r (/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b))))))

series210.0ms (2.1%)

Counts

3 → 84

Calls

3 calls:

124.0ms

(*.f64 r (/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b))))))

70.0ms

(/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))

15.0ms

(fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b))))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
19×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
19×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`

Counts

3 → 73

Calls

3 calls:

5.0ms

(*.f64 r (/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b))))))

3.0ms

(/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))

0.0ms

(fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b))))

simplify131.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

711×	`fma-def_binary64`
566×	`associate-/r*_binary64`
285×	`associate-/r/_binary64`
240×	`associate-/l/_binary64`
199×	`associate-r_binary64`

Counts

157 → 174

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	250	4914
1	627	4622
2	2345	4559
3	4948	4558
4	4980	4558

prune270.0ms (2.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	216	6	222
Fresh	8	7	15
Picked	1	0	1
Done	0	0	0
Total	225	13	238

Error

0.0b

Counts

238 → 13

Alt Table

Status	Error	Program
	12.0b	(.f64 r (cbrt.f64 (pow.f64 (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))) 3)))
	1.2b	(.f64 (.f64 r (.f64 (cbrt.f64 (sin.f64 b)) (cbrt.f64 (sin.f64 b)))) (/.f64 (cbrt.f64 (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
	0.4b	(.f64 r (/.f64 (sin.f64 b) (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b))))))))
	23.3b	(.f64 (.f64 r (/.f64 1 (sqrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))))) (/.f64 (sin.f64 b) (sqrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))))
	1.3b	(.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (.f64 (cbrt.f64 r) (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
	0.4b	(/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))
	0.9b	(.f64 (/.f64 r (.f64 (cbrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))) (cbrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))))) (/.f64 (sin.f64 b) (cbrt.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))))
	23.8b	(.f64 (.f64 r (/.f64 (.f64 (cbrt.f64 (sin.f64 b)) (cbrt.f64 (sin.f64 b))) (sqrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))))) (/.f64 (cbrt.f64 (sin.f64 b)) (sqrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
	1.3b	(.f64 (.f64 r (/.f64 (.f64 (cbrt.f64 (sin.f64 b)) (cbrt.f64 (sin.f64 b))) (.f64 (cbrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))) (cbrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))))) (/.f64 (cbrt.f64 (sin.f64 b)) (cbrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))))
	32.7b	(.f64 r (.f64 (sqrt.f64 (/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b)))))) (sqrt.f64 (/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b))))))))
	31.4b	(cbrt.f64 (pow.f64 (/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))) 3))
	0.4b	(.f64 r (/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3))))))
▶	0.3b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))

Compiler

Compiled 6998 to 1868 computations (73.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
✓	0.1b	(*.f64 (sin.f64 b) r)
✓	0.2b	(*.f64 (sin.f64 b) (sin.f64 a))
✓	0.2b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))

series149.0ms (1.5%)

Counts

4 → 52

Calls

4 calls:

116.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
15.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
10.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
7.0ms	(*.f64 (sin.f64 b) r)

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

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 → 86

Calls

4 calls:

8.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
4.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
3.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
3.0ms	(*.f64 (sin.f64 b) r)

simplify107.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

458×	`fma-neg_binary64`
407×	`cancel-sign-sub-inv_binary64`
346×	`associate-/l/_binary64`
238×	`distribute-rgt-neg-in_binary64`
225×	`associate-r_binary64`

Counts

138 → 197

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	279	3318
1	756	3067
2	2829	3007
3	4911	2999
4	5087	2999

prune258.0ms (2.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	193	4	197
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	198	12	210

Error

0.0b

Counts

210 → 12

Alt Table

Status	Error	Program
	23.8b	(.f64 (.f64 r (/.f64 (.f64 (cbrt.f64 (sin.f64 b)) (cbrt.f64 (sin.f64 b))) (sqrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))))) (/.f64 (cbrt.f64 (sin.f64 b)) (sqrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
	0.4b	(/.f64 (.f64 (sin.f64 b) r) (log1p.f64 (expm1.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))))
	0.4b	(.f64 r (/.f64 (sin.f64 b) (expm1.f64 (log1p.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b))))))))
	23.3b	(.f64 (.f64 r (/.f64 1 (sqrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))))) (/.f64 (sin.f64 b) (sqrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))))
	1.3b	(.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (.f64 (cbrt.f64 r) (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
	0.4b	(/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))
	0.5b	(/.f64 (.f64 (sin.f64 b) r) (log.f64 (exp.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
	0.3b	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3))))
	12.0b	(.f64 r (cbrt.f64 (pow.f64 (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))) 3)))
	0.9b	(.f64 (/.f64 r (.f64 (cbrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))) (cbrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))))) (/.f64 (sin.f64 b) (cbrt.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))))
	32.7b	(.f64 r (.f64 (sqrt.f64 (/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b)))))) (sqrt.f64 (/.f64 (sin.f64 b) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 a) (sin.f64 b))))))))
	0.3b	(.f64 (sin.f64 b) (/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))

Compiler

Compiled 5347 to 1352 computations (74.7% saved)

regimes2.5s (24.7%)

Accuracy

Total 0.3b remaining (86.4%)

Threshold costs 0.3b (86.4%)

Counts

293 → 1

Compiler

Compiled 37415 to 20324 computations (45.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`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	23	26
2	31	26
3	36	26
4	38	26
5	38	26

end1.0ms (0%)

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

sample3.2s (31.9%)

Algorithm

1×

intervals

Results

1.8s	3555×	body	1024	valid
356.0ms	1360×	body	512	valid
260.0ms	198×	body	2048	valid
247.0ms	2338×	body	128	valid
98.0ms	549×	body	256	valid
0.0ms	1×	body	256	invalid

Compiler

Compiled 364 to 202 computations (44.5% saved)

Details

analyze1.4s (13.8%)

sample707.0ms (7%)

simplify8.0ms (0.1%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series102.0ms (1%)

rewrite16.0ms (0.2%)

simplify73.0ms (0.7%)

prune178.0ms (1.8%)

localize15.0ms (0.1%)

series222.0ms (2.2%)

rewrite33.0ms (0.3%)

simplify148.0ms (1.5%)

prune304.0ms (3%)

localize12.0ms (0.1%)

series210.0ms (2.1%)

rewrite16.0ms (0.2%)

simplify131.0ms (1.3%)

prune270.0ms (2.7%)

localize12.0ms (0.1%)

series149.0ms (1.5%)

rewrite23.0ms (0.2%)

simplify107.0ms (1.1%)

prune258.0ms (2.5%)

regimes2.5s (24.7%)

simplify3.0ms (0%)

end1.0ms (0%)

sample3.2s (31.9%)

Profiling