Details

analyze1.4s (15.9%)

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)

sample107.0ms (1.2%)

Algorithm

1×

intervals

Results

59.0ms	123×	body	1024	valid
9.0ms	36×	body	512	valid
7.0ms	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)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

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

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 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))

Compiler

Compiled 45 to 27 computations (40% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 r (sin.f64 b))
✓	0.2b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
✓	4.2b	(cos.f64 (+.f64 a b))

series64.0ms (0.7%)

Counts

3 → 68

Calls

3 calls:

48.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
11.0ms	(*.f64 r (sin.f64 b))
4.0ms	(cos.f64 (+.f64 a b))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

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 → 53

Calls

3 calls:

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

simplify60.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

558×	`fma-def_binary64`
517×	`associate-/r*_binary64`
394×	`associate-*l/_binary64`
321×	`associate-/l/_binary64`
308×	`associate-/r/_binary64`

Counts

121 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	200	2011
1	525	1879
2	2003	1831
3	5044	1831

prune122.0ms (1.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	111	13	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	13	125

Error

0.2b

Counts

125 → 13

Alt Table

Status	Error	Program
	17.1b	(/.f64 r (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b)))
▶	0.3b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
	17.3b	(/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 r (sin.f64 b))))
	17.1b	(/.f64 (*.f64 r (sin.f64 b)) (expm1.f64 (log1p.f64 (cos.f64 (+.f64 a b)))))
	17.4b	(/.f64 (.f64 r (sin.f64 b)) (.f64 (*.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) (cbrt.f64 (cos.f64 (+.f64 a b)))) (cbrt.f64 (cos.f64 (+.f64 a b)))))
	17.2b	(/.f64 (.f64 r (sin.f64 b)) (cbrt.f64 (.f64 (*.f64 (cos.f64 (+.f64 a b)) (cos.f64 (+.f64 a b))) (cos.f64 (+.f64 a b)))))
	17.7b	(/.f64 (.f64 (.f64 (cbrt.f64 (.f64 r (sin.f64 b))) (cbrt.f64 (.f64 r (sin.f64 b)))) (cbrt.f64 (*.f64 r (sin.f64 b)))) (cos.f64 (+.f64 a b)))
	17.1b	(.f64 (.f64 r (sin.f64 b)) (/.f64 1 (cos.f64 (+.f64 a b))))
	28.3b	(fma.f64 (/.f64 (sin.f64 b) (cos.f64 b)) r (/.f64 (.f64 (pow.f64 (sin.f64 b) 2) (.f64 a r)) (pow.f64 (cos.f64 b) 2)))
	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)))
	32.3b	(*.f64 (/.f64 r (sqrt.f64 (cos.f64 (+.f64 a b)))) (/.f64 (sin.f64 b) (sqrt.f64 (cos.f64 (+.f64 a b)))))
	37.7b	(cbrt.f64 (.f64 (.f64 (/.f64 (.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b))) (/.f64 (.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))) (/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))))
	40.8b	(/.f64 (.f64 (.f64 r (sqrt.f64 (sin.f64 b))) (sqrt.f64 (sin.f64 b))) (cos.f64 (+.f64 a b)))

Compiler

Compiled 2797 to 1004 computations (64.1% saved)

localize13.0ms (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)))
	0.1b	(*.f64 r (sin.f64 b))
✓	0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
✓	0.2b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

series138.0ms (1.6%)

Counts

3 → 64

Calls

3 calls:

113.0ms

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

16.0ms

(-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))

10.0ms

(*.f64 (sin.f64 a) (sin.f64 b))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

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 → 66

Calls

3 calls:

7.0ms

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

6.0ms

(*.f64 (sin.f64 a) (sin.f64 b))

4.0ms

(-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))

simplify130.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

824×	`fma-def_binary64`
381×	`fma-neg_binary64`
329×	`cancel-sign-sub-inv_binary64`
204×	`associate-r_binary64`
204×	`distribute-rgt-neg-in_binary64`

Counts

130 → 156

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	252	3500
1	691	3279
2	2584	3054
3	4578	3049
4	4996	3049
5	4923	3049

prune247.0ms (2.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	182	12	194
Fresh	12	0	12
Picked	1	0	1
Done	0	0	0
Total	195	12	207

Error

0.0b

Counts

207 → 12

Alt Table

Status	Error	Program
	0.4b	(/.f64 (.f64 r (sin.f64 b)) (expm1.f64 (log1p.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
	0.4b	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (/.f64 (sin.f64 a) 1)))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3)) (fma.f64 (sin.f64 b) (.f64 (sin.f64 a) (fma.f64 (sin.f64 b) (sin.f64 a) (.f64 (cos.f64 a) (cos.f64 b)))) (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)))))
	25.9b	(.f64 (sqrt.f64 (/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))) (sqrt.f64 (/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
	0.5b	(.f64 (/.f64 (.f64 r (sin.f64 b)) (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (.f64 (sin.f64 a) (sin.f64 b)) 3))) (+.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (+.f64 (.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))))))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (log.f64 (exp.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))))
▶	0.3b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))))
	31.7b	(/.f64 (.f64 (.f64 r (sqrt.f64 (sin.f64 b))) (sqrt.f64 (sin.f64 b))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
	0.9b	(.f64 (/.f64 r (.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))))))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (.f64 (cbrt.f64 (sin.f64 a)) (cbrt.f64 (sin.f64 a))) (*.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b)))))
	47.6b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (.f64 (sqrt.f64 (sin.f64 a)) (sqrt.f64 (sin.f64 b))) (*.f64 (sqrt.f64 (sin.f64 a)) (sqrt.f64 (sin.f64 b))))))
	0.4b	(.f64 (/.f64 (.f64 r (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))))

Compiler

Compiled 5721 to 1599 computations (72.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))))
✓	0.2b	(*.f64 (sin.f64 b) (sin.f64 a))
✓	0.3b	(pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)
✓	26.2b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))

series167.0ms (1.9%)

Counts

4 → 100

Calls

4 calls:

115.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))))
33.0ms	(pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)
10.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))
9.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

8.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))))
5.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))
4.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
3.0ms	(pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)

simplify130.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

398×	`cancel-sign-sub-inv_binary64`
328×	`fma-neg_binary64`
314×	`unswap-sqr_binary64`
291×	`associate-r_binary64`
237×	`associate-l_binary64`

Counts

192 → 182

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	297	4078
1	748	3860
2	3028	3622
3	4891	3621
4	5096	3621

prune433.0ms (4.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	176	6	182
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	181	13	194

Error

Counts

194 → 13

Alt Table

Status	Error	Program
	0.4b	(/.f64 r (/.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3))) (sin.f64 b)))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (log.f64 (exp.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))))
	23.3b	(/.f64 (.f64 (/.f64 r (sqrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))) (sin.f64 b)) (sqrt.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)))))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3)) (fma.f64 (sin.f64 b) (.f64 (sin.f64 a) (fma.f64 (sin.f64 b) (sin.f64 a) (.f64 (cos.f64 a) (cos.f64 b)))) (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)))))
	25.9b	(.f64 (sqrt.f64 (/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))) (sqrt.f64 (/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
	0.4b	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (.f64 (cbrt.f64 (sin.f64 a)) (cbrt.f64 (sin.f64 a))) (*.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b)))))
	15.3b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cbrt.f64 (sqrt.f64 (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3))) (cbrt.f64 (sqrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))))))
	0.4b	(.f64 (/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (pow.f64 (.f64 (sin.f64 a) (sin.f64 b)) 2))) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3))))
	31.7b	(/.f64 (.f64 (.f64 r (sqrt.f64 (sin.f64 b))) (sqrt.f64 (sin.f64 b))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
▶	0.4b	(/.f64 (.f64 r (sin.f64 b)) (expm1.f64 (log1p.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
	0.9b	(.f64 (/.f64 r (.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))))))
	0.5b	(.f64 (/.f64 (.f64 r (sin.f64 b)) (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3)) 3))) (+.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (+.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3))) (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))))))

Compiler

Compiled 6176 to 2343 computations (62.1% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
✓	0.2b	(/.f64 (.f64 r (sin.f64 b)) (expm1.f64 (log1p.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
✓	0.2b	(expm1.f64 (log1p.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))))
✓	0.3b	(log1p.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))

series1.1s (12.7%)

Counts

3 → 84

Calls

3 calls:

949.0ms

(log1p.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

155.0ms

(/.f64 (*.f64 r (sin.f64 b)) (expm1.f64 (log1p.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))

16.0ms

(expm1.f64 (log1p.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`

Counts

3 → 45

Calls

3 calls:

4.0ms

(/.f64 (*.f64 r (sin.f64 b)) (expm1.f64 (log1p.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))

1.0ms

(log1p.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

0.0ms

(expm1.f64 (log1p.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))

simplify110.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

686×	`fma-def_binary64`
316×	`associate-/l/_binary64`
184×	`fma-neg_binary64`
177×	`associate-/l*_binary64`
164×	`cancel-sign-sub-inv_binary64`

Counts

129 → 127

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	242	3909
1	669	3609
2	2573	3498
3	4829	3497
4	4986	3497

prune260.0ms (2.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	172	2	174
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	175	12	187

Error

Counts

187 → 12

Alt Table

Status	Error	Program
	0.5b	(/.f64 1 (/.f64 (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a))) (*.f64 (sin.f64 b) r)))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3)) (fma.f64 (sin.f64 b) (.f64 (sin.f64 a) (fma.f64 (sin.f64 b) (sin.f64 a) (.f64 (cos.f64 a) (cos.f64 b)))) (.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)))))
	25.9b	(.f64 (sqrt.f64 (/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))) (sqrt.f64 (/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (.f64 (cbrt.f64 (sin.f64 a)) (cbrt.f64 (sin.f64 a))) (*.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b)))))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (expm1.f64 (log.f64 (-.f64 (fma.f64 (cos.f64 b) (cos.f64 a) 1) (.f64 (sin.f64 b) (sin.f64 a))))))
	0.4b	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (log.f64 (exp.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.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)) (pow.f64 (.f64 (sin.f64 a) (sin.f64 b)) 2))) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3))))
	31.7b	(/.f64 (.f64 (.f64 r (sqrt.f64 (sin.f64 b))) (sqrt.f64 (sin.f64 b))) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
✓	0.4b	(/.f64 (.f64 r (sin.f64 b)) (expm1.f64 (log1p.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
	0.9b	(.f64 (/.f64 r (.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))))))
	0.5b	(.f64 (/.f64 (.f64 r (sin.f64 b)) (-.f64 (pow.f64 (.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3)) 3))) (+.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (+.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3))) (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))))))

Compiler

Compiled 5304 to 1638 computations (69.1% saved)

regimes1.0s (11.5%)

Accuracy

Total 0.3b remaining (85.4%)

Threshold costs 0.3b (85.4%)

Counts

207 → 1

Compiler

Compiled 20431 to 11939 computations (41.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	28
1	28	28
2	40	28
3	48	28
4	51	28
5	51	28

end1.0ms (0%)

Compiler: Compiled 20 to 13 computations (35% saved)

sample3.2s (36.1%)

Algorithm

1×

intervals

Results

1.8s	3555×	body	1024	valid
352.0ms	1360×	body	512	valid
226.0ms	198×	body	2048	valid
215.0ms	2338×	body	128	valid
96.0ms	549×	body	256	valid
0.0ms	1×	body	256	invalid

Compiler

Compiled 433 to 235 computations (45.7% saved)

Details

analyze1.4s (15.9%)

sample107.0ms (1.2%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize9.0ms (0.1%)

series64.0ms (0.7%)

rewrite15.0ms (0.2%)

simplify60.0ms (0.7%)

prune122.0ms (1.4%)

localize13.0ms (0.1%)

series138.0ms (1.6%)

rewrite21.0ms (0.2%)

simplify130.0ms (1.5%)

prune247.0ms (2.8%)

localize16.0ms (0.2%)

series167.0ms (1.9%)

rewrite24.0ms (0.3%)

simplify130.0ms (1.5%)

prune433.0ms (4.9%)

localize17.0ms (0.2%)

series1.1s (12.7%)

rewrite7.0ms (0.1%)

simplify110.0ms (1.2%)

prune260.0ms (2.9%)

regimes1.0s (11.5%)

simplify3.0ms (0%)

end1.0ms (0%)

sample3.2s (36.1%)

Profiling