Details

analyze445.0ms (7.9%)

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
25%	74.9%	0.1%	6
37.4%	62.4%	0.1%	7
56.2%	43.7%	0.1%	8
56.2%	43.7%	0.1%	9
65.5%	34.3%	0.1%	10
76.5%	23.4%	0.1%	11
76.5%	23.4%	0.1%	12
81.9%	17.9%	0.1%	13
87.8%	12.1%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.9s (52.1%)

Results

1.6s	2175×	body	1024	valid
729.0ms	4538×	body	128	valid
436.0ms	1020×	body	512	valid
160.0ms	521×	body	256	valid
3.0ms	2×	body	2048	valid

Compiler

Compiled 26 to 18 computations (30.8% saved)

preprocess36.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

516×	`fma-def_binary64`
380×	`fma-neg_binary64`
130×	`cancel-sign-sub-inv_binary64`
69×	`sub-neg_binary64`
64×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	56
1	53	56
2	104	56
3	167	56
4	263	56
5	435	56
6	743	56
7	1134	56
8	1663	56
9	1904	56
10	1930	56
0	3	3

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

171×	`fma-def_binary64`
87×	`fma-neg_binary64`
37×	`cancel-sign-sub-inv_binary64`
23×	`distribute-rgt-neg-in_binary64`
20×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	17	14
2	32	14
3	49	14
4	76	14
5	124	14
6	205	14
7	306	14
8	408	14
9	524	14
10	582	14
11	588	14

Stop Event

1×

saturated

Counts

1 → 1

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
✓	0.1b	(*.f64 z (sin.f64 y))
✓	0.1b	(*.f64 x (cos.f64 y))

series29.0ms (0.5%)

Counts

3 → 84

Calls

21 calls:

2.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))	x	-inf
2.0ms	(*.f64 x (cos.f64 y))	y	inf
2.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))	x	inf
2.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))	x	0
2.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))	z	inf

rewrite73.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

518×	`log-prod_binary64`
391×	`fma-def_binary64`
206×	`egg-rr`
190×	`fma-neg_binary64`
184×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	198	26
2	2648	26

Stop Event

1×	node limit

Counts

3 → 206

simplify58.0ms (1%)

Algorithm

1×	egg-herbie

Rules

651×	`fma-neg_binary64`
345×	`*-commutative_binary64`
249×	`distribute-lft-neg-in_binary64`
243×	`distribute-rgt-neg-in_binary64`
229×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	57	850
1	172	841
2	525	822
3	1952	819
4	4821	819

Stop Event

1×	node limit

Counts

290 → 231

prune167.0ms (3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	222	9	231
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	223	9	232

Error

0.0b

Counts

232 → 9

Alt Table

Status	Error	Program
	31.6b	(fma.f64 (.f64 (neg.f64 z) (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y)) (.f64 x (cos.f64 y)))
	36.2b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 (sin.f64 y) (neg.f64 z)))
▶	0.2b	(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))
	48.1b	(fma.f64 (+.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))) (-.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))) (+.f64 (fma.f64 z (neg.f64 (sin.f64 y)) (.f64 z (sin.f64 y))) (fma.f64 z (neg.f64 (sin.f64 y)) (.f64 z (sin.f64 y)))))
	29.1b	(/.f64 1 (/.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) (-.f64 (pow.f64 (.f64 x (cos.f64 y)) 2) (pow.f64 (*.f64 z (sin.f64 y)) 2))))
	0.9b	(-.f64 (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 3) (.f64 z (sin.f64 y)))
	0.4b	(fma.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (.f64 (cbrt.f64 (cos.f64 y)) x) (.f64 (sin.f64 y) (neg.f64 z)))
	0.9b	(fma.f64 (.f64 (cos.f64 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 (sin.f64 y) (neg.f64 z)))
	40.8b	(/.f64 1 (/.f64 (fma.f64 (.f64 z (sin.f64 y)) (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) (pow.f64 (.f64 x (cos.f64 y)) 2)) (-.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (*.f64 z (sin.f64 y)) 3))))

Compiler

Compiled 5248 to 1213 computations (76.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))
	0.1b	(*.f64 z (sin.f64 y))
✓	0.1b	(fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y))))
✓	53.7b	(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))

series61.0ms (1.1%)

Counts

3 → 84

Calls

21 calls:

6.0ms	(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))	z	inf
5.0ms	(fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y))))	z	inf
4.0ms	(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))	x	inf
4.0ms	(fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y))))	z	-inf
4.0ms	(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))	z	-inf

rewrite53.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

897×	`expm1-log1p-u_binary64`
708×	`prod-diff_binary64`
114×	`add-sqr-sqrt_binary64`
104×	`log1p-expm1-u_binary64`
103×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	64
1	220	51
2	2745	51

Stop Event

1×	node limit

Counts

3 → 68

simplify43.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

760×	`fma-def_binary64`
433×	`cancel-sign-sub-inv_binary64`
408×	`fma-neg_binary64`
399×	`associate-l_binary64`
325×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	726
1	127	720
2	359	708
3	1157	704
4	4458	704

Stop Event

1×	node limit

Counts

152 → 89

prune101.0ms (1.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	113	9	122

Error

0.0b

Counts

122 → 9

Alt Table

Status	Error	Program
	31.6b	(fma.f64 (.f64 (neg.f64 z) (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y)) (.f64 x (cos.f64 y)))
	36.2b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 (sin.f64 y) (neg.f64 z)))
✓	0.2b	(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))
	48.1b	(fma.f64 (+.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))) (-.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))) (+.f64 (fma.f64 z (neg.f64 (sin.f64 y)) (.f64 z (sin.f64 y))) (fma.f64 z (neg.f64 (sin.f64 y)) (.f64 z (sin.f64 y)))))
	29.1b	(/.f64 1 (/.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) (-.f64 (pow.f64 (.f64 x (cos.f64 y)) 2) (pow.f64 (*.f64 z (sin.f64 y)) 2))))
	0.9b	(-.f64 (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 3) (.f64 z (sin.f64 y)))
▶	0.4b	(fma.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (.f64 (cbrt.f64 (cos.f64 y)) x) (.f64 (sin.f64 y) (neg.f64 z)))
	0.9b	(fma.f64 (.f64 (cos.f64 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 (sin.f64 y) (neg.f64 z)))
	40.8b	(/.f64 1 (/.f64 (fma.f64 (.f64 z (sin.f64 y)) (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) (pow.f64 (.f64 x (cos.f64 y)) 2)) (-.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (*.f64 z (sin.f64 y)) 3))))

Compiler

Compiled 2737 to 821 computations (70% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sin.f64 y) (neg.f64 z))
✓	0.1b	(*.f64 (cbrt.f64 (cos.f64 y)) x)
✓	0.3b	(pow.f64 (cbrt.f64 (cos.f64 y)) 2)
✓	0.3b	(cbrt.f64 (cos.f64 y))

series189.0ms (3.3%)

Counts

4 → 72

Calls

18 calls:

23.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) x)	y	inf
22.0ms	(cbrt.f64 (cos.f64 y))	y	-inf
20.0ms	(pow.f64 (cbrt.f64 (cos.f64 y)) 2)	y	inf
20.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) x)	x	0
19.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) x)	x	inf

rewrite49.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

889×	`log1p-expm1-u_binary64`
889×	`expm1-log1p-u_binary64`
118×	`add-sqr-sqrt_binary64`
109×	`add-cbrt-cube_binary64`
108×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	241	27
2	2842	27

Stop Event

1×	node limit

Counts

4 → 73

simplify36.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

770×	`fma-neg_binary64`
347×	`distribute-rgt-neg-in_binary64`
337×	`distribute-lft-neg-in_binary64`
277×	`fma-def_binary64`
216×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	77	682
1	225	670
2	671	649
3	2587	649

Stop Event

1×	node limit

Counts

145 → 107

prune156.0ms (2.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	138	9	147

Error

0.0b

Counts

147 → 9

Alt Table

Status	Error	Program
	31.6b	(fma.f64 (.f64 (neg.f64 z) (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y)) (.f64 x (cos.f64 y)))
	36.2b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 (sin.f64 y) (neg.f64 z)))
✓	0.2b	(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))
	48.1b	(fma.f64 (+.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))) (-.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))) (+.f64 (fma.f64 z (neg.f64 (sin.f64 y)) (.f64 z (sin.f64 y))) (fma.f64 z (neg.f64 (sin.f64 y)) (.f64 z (sin.f64 y)))))
	29.1b	(/.f64 1 (/.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))) (-.f64 (pow.f64 (.f64 x (cos.f64 y)) 2) (pow.f64 (*.f64 z (sin.f64 y)) 2))))
	0.9b	(-.f64 (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 3) (.f64 z (sin.f64 y)))
	0.5b	(fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 3) 2) (.f64 (cbrt.f64 (cos.f64 y)) x) (.f64 (sin.f64 y) (neg.f64 z)))
	0.9b	(fma.f64 (.f64 (cos.f64 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 (sin.f64 y) (neg.f64 z)))
▶	0.3b	(fma.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)) (.f64 (cbrt.f64 (cos.f64 y)) x) (.f64 (sin.f64 y) (neg.f64 z)))

Compiler

Compiled 3201 to 1235 computations (61.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (cbrt.f64 (cos.f64 y)) x)
✓	0.3b	(pow.f64 (cos.f64 y) 2)
	0.3b	(cbrt.f64 (cos.f64 y))
✓	0.3b	(cbrt.f64 (pow.f64 (cos.f64 y) 2))

series66.0ms (1.2%)

Counts

2 → 16

Calls

6 calls:

33.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))	y	inf
28.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))	y	-inf
1.0ms	(cbrt.f64 (pow.f64 (cos.f64 y) 2))	y	0
1.0ms	(pow.f64 (cos.f64 y) 2)	y	-inf
1.0ms	(pow.f64 (cos.f64 y) 2)	y	inf

rewrite34.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

434×	`log1p-expm1-u_binary64`
434×	`expm1-log1p-u_binary64`
281×	`unpow-prod-down_binary64`
215×	`log-prod_binary64`
132×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	14
1	119	14
2	1269	14

Stop Event

1×	node limit

Counts

2 → 65

simplify33.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

568×	`associate-l_binary64`
465×	`associate-r_binary64`
460×	`fma-def_binary64`
437×	`unswap-sqr_binary64`
305×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	165
1	91	159
2	251	157
3	854	153
4	4371	153

Stop Event

1×	node limit

Counts

81 → 79

prune150.0ms (2.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	135	8	143

Error

0.0b

Counts

143 → 8

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))
	48.1b	(fma.f64 (+.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))) (-.f64 (sqrt.f64 (.f64 x (cos.f64 y))) (sqrt.f64 (.f64 z (sin.f64 y)))) (+.f64 (fma.f64 z (neg.f64 (sin.f64 y)) (.f64 z (sin.f64 y))) (fma.f64 z (neg.f64 (sin.f64 y)) (.f64 z (sin.f64 y)))))
	0.3b	(fma.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)) (.f64 (log1p.f64 (expm1.f64 (cbrt.f64 (cos.f64 y)))) x) (.f64 (sin.f64 y) (neg.f64 z)))
	31.6b	(fma.f64 (.f64 (neg.f64 z) (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y)) (.f64 x (cos.f64 y)))
	0.5b	(fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 3) 2) (.f64 (cbrt.f64 (cos.f64 y)) x) (.f64 (sin.f64 y) (neg.f64 z)))
	0.9b	(fma.f64 (.f64 (cos.f64 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 (sin.f64 y) (neg.f64 z)))
✓	0.3b	(fma.f64 (cbrt.f64 (pow.f64 (cos.f64 y) 2)) (.f64 (cbrt.f64 (cos.f64 y)) x) (.f64 (sin.f64 y) (neg.f64 z)))
	0.9b	(-.f64 (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 3) (.f64 z (sin.f64 y)))

Compiler

Compiled 2941 to 1160 computations (60.6% saved)

regimes733.0ms (13%)

Accuracy

Total 0.1b remaining (71.5%)

Threshold costs 0.1b (71.5%)

Counts

169 → 1

Compiler

Compiled 13472 to 8216 computations (39% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
2×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	13	14
2	21	14
3	26	14
4	31	14
5	33	14

Stop Event

1×

saturated

end127.0ms (2.3%)

Stop Event

1×

fuel

Compiler

Compiled 202 to 117 computations (42.1% saved)

Iter	Nodes	Cost
0	9	14
1	17	14
2	32	14
3	49	14
4	76	14
5	124	14
6	205	14
7	306	14
8	408	14
9	524	14
10	582	14
11	588	14

Iter	Nodes	Cost
0	9	14
1	17	14
2	32	14
3	49	14
4	76	14
5	124	14
6	205	14
7	306	14
8	408	14
9	524	14
10	582	14
11	588	14

Details

analyze445.0ms (7.9%)

sample2.9s (52.1%)

preprocess36.0ms (0.6%)

simplify13.0ms (0.2%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series29.0ms (0.5%)

rewrite73.0ms (1.3%)

simplify58.0ms (1%)

prune167.0ms (3%)

localize11.0ms (0.2%)

series61.0ms (1.1%)

rewrite53.0ms (0.9%)

simplify43.0ms (0.8%)

prune101.0ms (1.8%)

localize15.0ms (0.3%)

series189.0ms (3.3%)

rewrite49.0ms (0.9%)

simplify36.0ms (0.6%)

prune156.0ms (2.8%)

localize12.0ms (0.2%)

series66.0ms (1.2%)

rewrite34.0ms (0.6%)

simplify33.0ms (0.6%)

prune150.0ms (2.7%)

regimes733.0ms (13%)

simplify2.0ms (0%)

end127.0ms (2.3%)

Profiling

Iter	Nodes	Cost
0	9	14
1	17	14
2	32	14
3	49	14
4	76	14
5	124	14
6	205	14
7	306	14
8	408	14
9	524	14
10	582	14
11	588	14