Details

analyze1.5s (15.4%)

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)

sample5.1s (52.1%)

Results

3.5s	3532×	body	1024	valid
608.0ms	1419×	body	512	valid
443.0ms	2489×	body	128	valid
347.0ms	207×	body	2048	valid
186.0ms	609×	body	256	valid
1.0ms	1×	body	1024	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify7.0ms (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

prune3.0ms (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

13.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.4b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))

Compiler

Compiled 45 to 27 computations (40% saved)

localize8.0ms (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)))
✓	1.7b	(cos.f64 (+.f64 a b))

series58.0ms (0.6%)

Counts

3 → 68

Calls

3 calls:

46.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
8.0ms	(*.f64 r (sin.f64 b))
4.0ms	(cos.f64 (+.f64 a b))

rewrite12.0ms (0.1%)

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))

simplify64.0ms (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

prune167.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	116	8	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	8	125

Error

0.1b

Counts

125 → 8

Alt Table

Status	Error	Program
	13.4b	(/.f64 r (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b)))
	31.0b	(fma.f64 (/.f64 b (cos.f64 a)) r (fma.f64 (/.f64 (sin.f64 a) (pow.f64 (cos.f64 a) 2)) (.f64 b (.f64 b r)) (fma.f64 2/3 (/.f64 (.f64 (sin.f64 a) (.f64 r (pow.f64 b 4))) (pow.f64 (cos.f64 a) 2)) (fma.f64 (/.f64 (pow.f64 (sin.f64 a) 3) (pow.f64 (cos.f64 a) 4)) (.f64 r (pow.f64 b 4)) (.f64 (/.f64 (*.f64 (pow.f64 b 3) r) (cos.f64 a)) (+.f64 1/3 (/.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (cos.f64 a) 2))))))))
	13.4b	(.f64 (.f64 r (sin.f64 b)) (/.f64 1 (cos.f64 (+.f64 a b))))
	13.5b	(/.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)))))
	13.4b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 b a))))
	37.4b	(/.f64 (.f64 (.f64 r (sqrt.f64 (sin.f64 b))) (sqrt.f64 (sin.f64 b))) (cos.f64 (+.f64 a b)))
▶	0.3b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
	13.7b	(/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (*.f64 r (sin.f64 b))))

Compiler

Compiled 2639 to 942 computations (64.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series129.0ms (1.3%)

Counts

3 → 56

Calls

3 calls:

110.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
10.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
9.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 69

Calls

3 calls:

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

simplify128.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

805×	`fma-def_binary64`
381×	`cancel-sign-sub-inv_binary64`
294×	`fma-neg_binary64`
244×	`associate-r_binary64`
238×	`distribute-rgt-neg-in_binary64`

Counts

125 → 148

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	276	3123
1	736	2937
2	2768	2774
3	4842	2773
4	4998	2773
5	4952	2773

prune278.0ms (2.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	178	8	186
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	185	9	194

Error

0.0b

Counts

194 → 9

Alt Table

Status	Error	Program
	37.4b	(/.f64 (.f64 (.f64 r (sqrt.f64 (sin.f64 b))) (sqrt.f64 (sin.f64 b))) (cos.f64 (+.f64 a b)))
	0.7b	(/.f64 1 (/.f64 (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (/.f64 (sin.f64 a) 1)) r))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (.f64 (cos.f64 a) (cos.f64 b)))) (*.f64 (sin.f64 a) (sin.f64 b))))
	0.3b	(/.f64 r (/.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))) (sin.f64 b)))
	0.4b	(.f64 (.f64 r (sin.f64 b)) (/.f64 1 (-.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 b) (sin.f64 a)))))
	28.4b	(.f64 (/.f64 r (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))))))
	0.3b	(/.f64 (neg.f64 (.f64 (sin.f64 b) r)) (fma.f64 (cos.f64 a) (neg.f64 (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
	0.6b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 a)) (cbrt.f64 (cos.f64 a))) (.f64 (cbrt.f64 (cos.f64 a)) (cos.f64 b))) (*.f64 (sin.f64 a) (sin.f64 b))))

Compiler

Compiled 5201 to 1499 computations (71.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series189.0ms (1.9%)

Counts

3 → 64

Calls

3 calls:

114.0ms

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

64.0ms

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

10.0ms

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

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 92

Calls

3 calls:

10.0ms

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

7.0ms

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

3.0ms

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

simplify134.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

824×	`fma-def_binary64`
281×	`associate-r_binary64`
246×	`associate-l_binary64`
239×	`cancel-sign-sub-inv_binary64`
203×	`associate-/l*_binary64`

Counts

156 → 206

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	306	4746
1	792	4477
2	3048	4134
3	4766	4133
4	5029	4133

prune262.0ms (2.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	243	1	244
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	244	9	253

Error

0.0b

Counts

253 → 9

Alt Table

Status	Error	Program
	0.6b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 a)) (cbrt.f64 (cos.f64 a))) (.f64 (cbrt.f64 (cos.f64 a)) (cos.f64 b))) (*.f64 (sin.f64 a) (sin.f64 b))))
	31.6b	(.f64 (.f64 r (sqrt.f64 (sin.f64 b))) (/.f64 (sqrt.f64 (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (.f64 (cos.f64 a) (cos.f64 b)))) (*.f64 (sin.f64 a) (sin.f64 b))))
	0.3b	(/.f64 r (/.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))) (sin.f64 b)))
	0.4b	(.f64 (.f64 r (sin.f64 b)) (/.f64 1 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))))
	0.7b	(/.f64 1 (/.f64 (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (/.f64 (sin.f64 a) 1)) r))
✓	0.3b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
	28.4b	(.f64 (/.f64 r (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))))))
▶	0.3b	(/.f64 (neg.f64 (.f64 (sin.f64 b) r)) (fma.f64 (cos.f64 a) (neg.f64 (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))

Compiler

Compiled 7370 to 1944 computations (73.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series147.0ms (1.5%)

Counts

3 → 64

Calls

3 calls:

124.0ms

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

16.0ms

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

7.0ms

(*.f64 (sin.f64 b) r)

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`times-frac_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 73

Calls

3 calls:

4.0ms

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

3.0ms

(*.f64 (sin.f64 b) r)

0.0ms

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

simplify137.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

586×	`fma-def_binary64`
324×	`associate-/r/_binary64`
299×	`fma-neg_binary64`
288×	`associate-/l/_binary64`
237×	`cancel-sign-sub-inv_binary64`

Counts

137 → 170

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	249	4103
1	608	3920
2	2174	3862
3	4791	3862
4	4998	3862

prune230.0ms (2.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	214	3	217
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	216	10	226

Error

0.0b

Counts

226 → 10

Alt Table

Status	Error	Program
	0.4b	(.f64 (.f64 r (sin.f64 b)) (/.f64 1 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))))
	46.1b	(/.f64 (neg.f64 (.f64 (sin.f64 b) r)) (fma.f64 (cos.f64 a) (neg.f64 (cos.f64 b)) (.f64 (.f64 (sqrt.f64 (sin.f64 b)) (sqrt.f64 (sin.f64 a))) (.f64 (sqrt.f64 (sin.f64 b)) (sqrt.f64 (sin.f64 a))))))
	0.6b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 a)) (cbrt.f64 (cos.f64 a))) (.f64 (cbrt.f64 (cos.f64 a)) (cos.f64 b))) (*.f64 (sin.f64 a) (sin.f64 b))))
	31.5b	(/.f64 (neg.f64 (.f64 (sqrt.f64 (sin.f64 b)) (.f64 (sqrt.f64 (sin.f64 b)) r))) (fma.f64 (cos.f64 a) (neg.f64 (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
	0.5b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (cbrt.f64 (.f64 (.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (cos.f64 a) (cos.f64 b))) (.f64 (cos.f64 a) (cos.f64 b)))) (*.f64 (sin.f64 a) (sin.f64 b))))
	0.3b	(/.f64 r (/.f64 (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))) (sin.f64 b)))
✓	0.3b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
	28.4b	(.f64 (/.f64 r (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))))))
✓	0.3b	(/.f64 (neg.f64 (.f64 (sin.f64 b) r)) (fma.f64 (cos.f64 a) (neg.f64 (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
	0.3b	(.f64 (sin.f64 b) (/.f64 (neg.f64 r) (-.f64 (.f64 (sin.f64 a) (sin.f64 b)) (*.f64 (cos.f64 a) (cos.f64 b)))))

Compiler

Compiled 6032 to 1340 computations (77.8% saved)

regimes972.0ms (9.9%)

Accuracy

Total 0.3b remaining (78.3%)

Threshold costs 0.3b (78.3%)

Counts

206 → 1

Compiler

Compiled 18748 to 11334 computations (39.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	28
1	28	28
2	44	28
3	57	28
4	66	28
5	70	28
6	71	28
7	71	28

end159.0ms (1.6%)

Compiler: Compiled 287 to 165 computations (42.5% saved)

Details

analyze1.5s (15.4%)

sample5.1s (52.1%)

simplify7.0ms (0.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series58.0ms (0.6%)

rewrite12.0ms (0.1%)

simplify64.0ms (0.7%)

prune167.0ms (1.7%)

localize12.0ms (0.1%)

series129.0ms (1.3%)

rewrite18.0ms (0.2%)

simplify128.0ms (1.3%)

prune278.0ms (2.8%)

localize13.0ms (0.1%)

series189.0ms (1.9%)

rewrite27.0ms (0.3%)

simplify134.0ms (1.4%)

prune262.0ms (2.7%)

localize15.0ms (0.2%)

series147.0ms (1.5%)

rewrite12.0ms (0.1%)

simplify137.0ms (1.4%)

prune230.0ms (2.4%)

regimes972.0ms (9.9%)

simplify4.0ms (0%)

end159.0ms (1.6%)

Profiling