Details

analyze2.9s (22.9%)

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)

sample100.0ms (0.8%)

Algorithm

1×

intervals

Results

54.0ms	112×	body	1024	valid
11.0ms	10×	body	2048	valid
10.0ms	41×	body	512	valid
7.0ms	77×	body	128	valid
6.0ms	16×	body	256	valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify9.0ms (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

15.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.8b	(*.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 4 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 b)
✓	0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
✓	0.2b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
✓	2.5b	(cos.f64 (+.f64 a b))

rewrite55.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-cube-cbrt_binary64`
23×	`pow1_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`

Counts

4 → 153

Calls

4 calls:

15.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
13.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
11.0ms	(cos.f64 (+.f64 a b))
9.0ms	(sin.f64 b)

series313.0ms (2.4%)

Counts

4 → 56

Calls

4 calls:

197.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
110.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
4.0ms	(cos.f64 (+.f64 a b))
1.0ms	(sin.f64 b)

simplify129.0ms (1%)

Algorithm

1×	egg-herbie

Rules

410×	`unswap-sqr_binary64`
278×	`fma-neg_binary64`
255×	`cancel-sign-sub-inv_binary64`
248×	`associate-r_binary64`
212×	`associate-l_binary64`

Counts

209 → 339

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	290	3176
1	745	3002
2	2908	2962
3	4744	2962
4	4962	2962

prune235.0ms (1.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	325	14	339
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	326	14	340

Error

0.1b

Counts

340 → 14

Alt Table

Status	Error	Program
	15.8b	(/.f64 r (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b)))
▶	0.3b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a))))))
	0.4b	(.f64 r (/.f64 (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))) (fma.f64 (cos.f64 b) (cos.f64 a) (.f64 (sin.f64 b) (sin.f64 a))))))
	28.8b	(+.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)))
	0.5b	(.f64 r (/.f64 (sin.f64 b) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 b) (cos.f64 a)) 3) (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3)) (fma.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2) (.f64 (sin.f64 b) (.f64 (sin.f64 a) (fma.f64 (cos.f64 b) (cos.f64 a) (.f64 (sin.f64 b) (sin.f64 a)))))))))
	16.2b	(*.f64 r (/.f64 (sin.f64 b) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) 3)))
	31.7b	(+.f64 (/.f64 (.f64 b r) (cos.f64 a)) (/.f64 (.f64 (sin.f64 a) (*.f64 (pow.f64 b 2) r)) (pow.f64 (cos.f64 a) 2)))
	0.4b	(.f64 r (/.f64 (sin.f64 b) (/.f64 (-.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))))))))
	0.3b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
	15.8b	(.f64 r (.f64 (sin.f64 b) (/.f64 1 (cos.f64 (+.f64 a b)))))
	16.0b	(.f64 r (/.f64 (sin.f64 b) (.f64 (cbrt.f64 (pow.f64 (cos.f64 (+.f64 b a)) 2)) (cbrt.f64 (cos.f64 (+.f64 b a))))))
	15.8b	(*.f64 (/.f64 r (cos.f64 (+.f64 a b))) (sin.f64 b))
	15.9b	(/.f64 1 (/.f64 (cos.f64 (+.f64 b a)) (*.f64 (sin.f64 b) r)))
	37.1b	(*.f64 r (exp.f64 (log.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 b a))))))

Compiler

Compiled 5098 to 1775 computations (65.2% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sin.f64 b) (sin.f64 a))
✓	0.2b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a))))))
✓	0.2b	(/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 b) (sin.f64 a)))))
✓	51.7b	(fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a)))

rewrite62.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-cube-cbrt_binary64`
30×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
22×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`

Counts

4 → 167

Calls

4 calls:

15.0ms	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a))))))
13.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
13.0ms	(/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 b) (sin.f64 a)))))
9.0ms	(fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a)))

series676.0ms (5.3%)

Counts

4 → 100

Calls

4 calls:

364.0ms	(.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a))))))
177.0ms	(/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 b) (sin.f64 a)))))
107.0ms	(fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a)))
27.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

simplify158.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

660×	`unswap-sqr_binary64`
336×	`associate-r_binary64`
317×	`fma-neg_binary64`
288×	`associate-l_binary64`
188×	`associate-/l*_binary64`

Counts

267 → 423

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	341	7074
1	859	5049
2	3615	4800
3	5512	4800

prune350.0ms (2.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	413	10	423
Fresh	11	2	13
Picked	1	0	1
Done	0	0	0
Total	425	12	437

Error

0.0b

Counts

437 → 12

Alt Table

Status	Error	Program
	0.3b	(/.f64 (.f64 (sin.f64 b) r) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a)))))
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 b) (sin.f64 a))))))) (cbrt.f64 (.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 b) (sin.f64 a)))))))) (cbrt.f64 (.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a))))))))
▶	0.3b	(.f64 (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a))))) r)
	14.6b	(.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)))
	30.0b	(.f64 r (exp.f64 (log.f64 (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))))
	1.2b	(.f64 r (pow.f64 (cbrt.f64 (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a)))))) 3))
	0.3b	(.f64 (/.f64 r (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a))))) (sin.f64 b))
	1.2b	(.f64 r (.f64 (.f64 (cbrt.f64 (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 b) (sin.f64 a)))))) (cbrt.f64 (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 b) (sin.f64 a))))))) (cbrt.f64 (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a))))))))
	31.7b	(+.f64 (/.f64 (.f64 b r) (cos.f64 a)) (/.f64 (.f64 (sin.f64 a) (*.f64 (pow.f64 b 2) r)) (pow.f64 (cos.f64 a) 2)))
	30.9b	(.f64 r (-.f64 (exp.f64 (log1p.f64 (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))) 1))
	0.5b	(/.f64 1 (/.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 b) (sin.f64 a)))) (sin.f64 b)) r))
	16.0b	(.f64 r (/.f64 (sin.f64 b) (.f64 (cbrt.f64 (pow.f64 (cos.f64 (+.f64 b a)) 2)) (cbrt.f64 (cos.f64 (+.f64 b a))))))

Compiler

Compiled 10436 to 2151 computations (79.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (sin.f64 b) (sin.f64 a))
✓	0.2b	(.f64 (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a))))) r)
	0.2b	(/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 b) (sin.f64 a)))))
	51.7b	(fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a)))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1_binary64`
8×	`add-exp-log_binary64`
8×	`add-sqr-sqrt_binary64`
5×	`associate-*l/_binary64`
5×	`pow-prod-down_binary64`

Counts

1 → 42

Calls

1 calls:

13.0ms

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

series370.0ms (2.9%)

Counts

1 → 36

Calls

1 calls:

370.0ms

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

simplify106.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

836×	`associate-/l*_binary64`
396×	`fma-def_binary64`
395×	`associate-/r*_binary64`
290×	`unswap-sqr_binary64`
232×	`associate-*l/_binary64`

Counts

78 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	150	3007
1	392	2518
2	1416	2079
3	4977	2077
4	4954	2077

prune366.0ms (2.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	416	3	419
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	419	12	431

Error

0.0b

Counts

431 → 12

Alt Table

Status	Error	Program
	1.0b	(.f64 (/.f64 (/.f64 (sin.f64 b) (.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)))))) (cbrt.f64 (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 b) (sin.f64 a)))))) r)
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 b) (sin.f64 a))))))) (cbrt.f64 (.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 b) (sin.f64 a)))))))) (cbrt.f64 (.f64 r (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a))))))))
✓	0.3b	(.f64 (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a))))) r)
	0.3b	(/.f64 (sin.f64 b) (/.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))) r))
	1.2b	(.f64 r (pow.f64 (cbrt.f64 (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a)))))) 3))
▶	0.3b	(.f64 (/.f64 r (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a))))) (sin.f64 b))
	1.2b	(.f64 r (.f64 (.f64 (cbrt.f64 (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 b) (sin.f64 a)))))) (cbrt.f64 (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 b) (sin.f64 a))))))) (cbrt.f64 (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a))))))))
	31.7b	(+.f64 (/.f64 (.f64 b r) (cos.f64 a)) (/.f64 (.f64 (sin.f64 a) (*.f64 (pow.f64 b 2) r)) (pow.f64 (cos.f64 a) 2)))
	30.9b	(.f64 r (-.f64 (exp.f64 (log1p.f64 (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))) 1))
	0.5b	(/.f64 1 (/.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 b) (sin.f64 a)))) (sin.f64 b)) r))
	0.4b	(.f64 (.f64 (sin.f64 b) r) (/.f64 1 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))))
	16.0b	(.f64 r (/.f64 (sin.f64 b) (.f64 (cbrt.f64 (pow.f64 (cos.f64 (+.f64 b a)) 2)) (cbrt.f64 (cos.f64 (+.f64 b a))))))

Compiler

Compiled 10445 to 2145 computations (79.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (sin.f64 b) (sin.f64 a))
✓	0.2b	(/.f64 r (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 b) (sin.f64 a)))))
✓	0.2b	(.f64 (/.f64 r (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a))))) (sin.f64 b))
	51.7b	(fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a)))

rewrite36.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-cube-cbrt_binary64`
15×	`pow1_binary64`
14×	`add-exp-log_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cbrt-cube_binary64`

Counts

2 → 90

Calls

2 calls:

15.0ms

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

12.0ms

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

series787.0ms (6.2%)

Counts

2 → 72

Calls

2 calls:

460.0ms

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

326.0ms

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

simplify220.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

789×	`fma-def_binary64`
266×	`distribute-rgt-in_binary64`
248×	`associate-r_binary64`
232×	`distribute-lft-in_binary64`
214×	`unswap-sqr_binary64`

Counts

162 → 257

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	244	6309
1	622	5265
2	2643	4149
3	4941	4143
4	4939	4143

prune357.0ms (2.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	586	1	587
Fresh	2	8	10
Picked	0	1	1
Done	0	1	1
Total	588	11	599

Error

0.0b

Counts

599 → 11

Alt Table

Status	Error	Program
	1.0b	(.f64 (/.f64 (/.f64 (sin.f64 b) (.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)))))) (cbrt.f64 (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 b) (sin.f64 a)))))) r)
	1.4b	(.f64 (/.f64 (.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (cbrt.f64 r)) (.f64 (.f64 (cbrt.f64 (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 b) (sin.f64 a))))) (cbrt.f64 (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 b) (sin.f64 a)))))) (cbrt.f64 (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a))))))) (sin.f64 b))
✓	0.3b	(.f64 (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a))))) r)
	0.3b	(/.f64 (sin.f64 b) (/.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))) r))
	1.2b	(.f64 r (pow.f64 (cbrt.f64 (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a)))))) 3))
✓	0.3b	(.f64 (/.f64 r (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a))))) (sin.f64 b))
	1.2b	(.f64 r (.f64 (.f64 (cbrt.f64 (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 b) (sin.f64 a)))))) (cbrt.f64 (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 b) (sin.f64 a))))))) (cbrt.f64 (/.f64 (sin.f64 b) (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (*.f64 (sin.f64 b) (sin.f64 a))))))))
	30.9b	(.f64 r (-.f64 (exp.f64 (log1p.f64 (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))) 1))
	0.5b	(/.f64 1 (/.f64 (/.f64 (+.f64 (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (.f64 (sin.f64 b) (sin.f64 a)))) (fma.f64 (neg.f64 (sin.f64 b)) (sin.f64 a) (.f64 (sin.f64 b) (sin.f64 a)))) (sin.f64 b)) r))
	0.4b	(.f64 (.f64 (sin.f64 b) r) (/.f64 1 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))))
	16.0b	(.f64 r (/.f64 (sin.f64 b) (.f64 (cbrt.f64 (pow.f64 (cos.f64 (+.f64 b a)) 2)) (cbrt.f64 (cos.f64 (+.f64 b a))))))

Compiler

Compiled 9950 to 1943 computations (80.5% saved)

regimes2.3s (17.6%)

Accuracy

Total 0.3b remaining (81.6%)

Threshold costs 0.3b (81.6%)

Compiler

Compiled 35626 to 19997 computations (43.9% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`+-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	16	46
1	28	46
2	36	46
3	40	46
4	41	46
5	41	46

end1.0ms (0%)

Compiler: Compiled 31 to 15 computations (51.6% saved)

sample3.2s (24.9%)

Algorithm

1×

intervals

Results

1.7s	3541×	body	1024	valid
364.0ms	1327×	body	512	valid
213.0ms	191×	body	2048	valid
212.0ms	2364×	body	128	valid
131.0ms	577×	body	256	valid
0.0ms	1×	body	256	invalid

Compiler

Compiled 495 to 207 computations (58.2% saved)

Details

analyze2.9s (22.9%)

sample100.0ms (0.8%)

simplify9.0ms (0.1%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite55.0ms (0.4%)

series313.0ms (2.4%)

simplify129.0ms (1%)

prune235.0ms (1.8%)

localize18.0ms (0.1%)

rewrite62.0ms (0.5%)

series676.0ms (5.3%)

simplify158.0ms (1.2%)

prune350.0ms (2.7%)

localize18.0ms (0.1%)

rewrite17.0ms (0.1%)

series370.0ms (2.9%)

simplify106.0ms (0.8%)

prune366.0ms (2.9%)

localize18.0ms (0.1%)

rewrite36.0ms (0.3%)

series787.0ms (6.2%)

simplify220.0ms (1.7%)

prune357.0ms (2.8%)

regimes2.3s (17.6%)

simplify5.0ms (0%)

end1.0ms (0%)

sample3.2s (24.9%)

Profiling