Details

analyze613.0ms (13.5%)

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

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.3s (50.2%)

Results

953.0ms	1379×	body	1024	valid
897.0ms	5866×	body	128	valid
264.0ms	682×	body	512	valid
122.0ms	325×	body	256	valid
6.0ms	4×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	14	12
2	23	12
3	29	12

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 42 to 24 computations (42.9% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series11.0ms (0.2%)

Counts

2 → 40

Calls

2 calls:

10.0ms	(fma.f64 z (cos.f64 y) x)
1.0ms	(sin.f64 y)

rewrite35.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

595×	`log1p-expm1-u_binary64`
595×	`expm1-log1p-u_binary64`
317×	`log-prod_binary64`
129×	`expm1-udef_binary64`
129×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	136	10
2	1608	10

Stop Event

1×	node limit

Counts

2 → 51

Calls

2 calls:

34.0ms	(sin.f64 y)
34.0ms	(fma.f64 z (cos.f64 y) x)

simplify37.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

698×	`cancel-sign-sub-inv_binary64`
340×	`fma-neg_binary64`
309×	`sub-neg_binary64`
270×	`unswap-sqr_binary64`
227×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	341
1	128	336
2	385	322
3	1453	321
4	4006	321

Stop Event

1×	node limit

Counts

91 → 70

prune42.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	5	71

Error

0.0b

Counts

71 → 5

Alt Table

Status	Error	Program
	38.1b	(+.f64 (sin.f64 y) (cbrt.f64 (pow.f64 (fma.f64 z (cos.f64 y) x) 3)))
✓	0.1b	(+.f64 (sin.f64 y) (fma.f64 z (cos.f64 y) x))
	33.2b	(+.f64 (sin.f64 y) (pow.f64 (sqrt.f64 (fma.f64 z (cos.f64 y) x)) 2))
▶	1.1b	(+.f64 (sin.f64 y) (pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) x)) 3))
	32.2b	(+.f64 (sin.f64 y) (-.f64 (exp.f64 (log1p.f64 (fma.f64 z (cos.f64 y) x))) 1))

Compiler

Compiled 1078 to 446 computations (58.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sin.f64 y)
	0.1b	(fma.f64 z (cos.f64 y) x)
✓	0.6b	(cbrt.f64 (fma.f64 z (cos.f64 y) x))
✓	0.8b	(pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) x)) 3)

series141.0ms (3.1%)

Counts

2 → 40

Calls

2 calls:

100.0ms	(pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) x)) 3)
42.0ms	(cbrt.f64 (fma.f64 z (cos.f64 y) x))

rewrite38.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

684×	`log1p-expm1-u_binary64`
684×	`expm1-log1p-u_binary64`
141×	`expm1-udef_binary64`
141×	`log1p-udef_binary64`
89×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	178	16
2	1890	16

Stop Event

1×	node limit

Counts

2 → 64

Calls

2 calls:

37.0ms	(cbrt.f64 (fma.f64 z (cos.f64 y) x))
37.0ms	(pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) x)) 3)

simplify39.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

729×	`fma-def_binary64`
376×	`cancel-sign-sub-inv_binary64`
290×	`unswap-sqr_binary64`
207×	`associate-r_binary64`
158×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	164	1414
1	521	1389
2	1841	1343

Stop Event

1×	node limit

Counts

104 → 113

prune111.0ms (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	181	2	183
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	182	6	188

Error

0.0b

Counts

188 → 6

Alt Table

Status	Error	Program
▶	18.4b	(+.f64 (sin.f64 y) (fma.f64 (cbrt.f64 (.f64 z z)) (.f64 (cbrt.f64 z) (cos.f64 y)) x))
	38.1b	(+.f64 (sin.f64 y) (cbrt.f64 (pow.f64 (fma.f64 z (cos.f64 y) x) 3)))
✓	0.1b	(+.f64 (sin.f64 y) (fma.f64 z (cos.f64 y) x))
	33.2b	(+.f64 (sin.f64 y) (pow.f64 (sqrt.f64 (fma.f64 z (cos.f64 y) x)) 2))
✓	1.1b	(+.f64 (sin.f64 y) (pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) x)) 3))
	29.6b	(+.f64 (sin.f64 y) (fma.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (cos.f64 y)) x))

Compiler

Compiled 4033 to 2027 computations (49.7% saved)

localize24.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cbrt.f64 z) (cos.f64 y))
✓	0.2b	(fma.f64 (cbrt.f64 (.f64 z z)) (.f64 (cbrt.f64 z) (cos.f64 y)) x)
✓	0.6b	(cbrt.f64 z)
✓	31.8b	(cbrt.f64 (*.f64 z z))

series170.0ms (3.8%)

Counts

4 → 39

Calls

4 calls:

126.0ms	(fma.f64 (cbrt.f64 (.f64 z z)) (.f64 (cbrt.f64 z) (cos.f64 y)) x)
29.0ms	(*.f64 (cbrt.f64 z) (cos.f64 y))
11.0ms	(cbrt.f64 z)
4.0ms	(cbrt.f64 (*.f64 z z))

rewrite50.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

785×	`log1p-expm1-u_binary64`
785×	`expm1-log1p-u_binary64`
99×	`prod-diff_binary64`
94×	`add-sqr-sqrt_binary64`
87×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	34
1	193	26
2	2219	26

Stop Event

1×	node limit

Counts

4 → 87

Calls

4 calls:

48.0ms	(*.f64 (cbrt.f64 z) (cos.f64 y))
48.0ms	(fma.f64 (cbrt.f64 (.f64 z z)) (.f64 (cbrt.f64 z) (cos.f64 y)) x)
48.0ms	(cbrt.f64 z)
48.0ms	(cbrt.f64 (*.f64 z z))

simplify39.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

559×	`fma-neg_binary64`
339×	`sub-neg_binary64`
315×	`*-commutative_binary64`
249×	`distribute-rgt-neg-in_binary64`
246×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	370
1	122	359
2	420	338
3	1828	333
4	4616	333

Stop Event

1×	node limit

Counts

126 → 109

prune100.0ms (2.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	108	7	115

Error

Counts

115 → 7

Alt Table

Status	Error	Program
▶	0.7b	(+.f64 (sin.f64 y) (fma.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 (pow.f64 (cbrt.f64 z) 2))) (cbrt.f64 (cbrt.f64 z))) (*.f64 (cbrt.f64 z) (cos.f64 y)) x))
✓	1.1b	(+.f64 (sin.f64 y) (pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) x)) 3))
✓	18.4b	(+.f64 (sin.f64 y) (fma.f64 (cbrt.f64 (.f64 z z)) (.f64 (cbrt.f64 z) (cos.f64 y)) x))
	38.1b	(+.f64 (sin.f64 y) (cbrt.f64 (pow.f64 (fma.f64 z (cos.f64 y) x) 3)))
✓	0.1b	(+.f64 (sin.f64 y) (fma.f64 z (cos.f64 y) x))
	33.2b	(+.f64 (sin.f64 y) (pow.f64 (sqrt.f64 (fma.f64 z (cos.f64 y) x)) 2))
	29.6b	(+.f64 (sin.f64 y) (fma.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (cos.f64 y)) x))

Compiler

Compiled 1986 to 784 computations (60.5% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (cbrt.f64 z))
✓	0.5b	(pow.f64 (cbrt.f64 z) 2)
	0.6b	(cbrt.f64 z)
✓	0.6b	(cbrt.f64 (pow.f64 (cbrt.f64 z) 2))

series186.0ms (4.1%)

Counts

3 → 24

Calls

3 calls:

92.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 z) 2))
72.0ms	(cbrt.f64 (cbrt.f64 z))
22.0ms	(pow.f64 (cbrt.f64 z) 2)

rewrite41.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

447×	`log1p-expm1-u_binary64`
447×	`expm1-log1p-u_binary64`
364×	`unpow-prod-down_binary64`
229×	`log-prod_binary64`
148×	`egg-rr`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	134	19
2	1362	18

Stop Event

1×	node limit

Counts

3 → 148

Calls

3 calls:

39.0ms	(cbrt.f64 (cbrt.f64 z))
39.0ms	(pow.f64 (cbrt.f64 z) 2)
39.0ms	(cbrt.f64 (pow.f64 (cbrt.f64 z) 2))

simplify72.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

581×	`sqr-pow_binary64`
540×	`unswap-sqr_binary64`
352×	`fma-def_binary64`
348×	`*-commutative_binary64`
224×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	17	396
1	45	396
2	95	396
3	256	396
4	990	280
5	2063	280
6	2236	280
7	2519	280
8	2920	280
9	3363	280
10	3950	280
11	4693	280

Stop Event

1×	node limit

Counts

172 → 155

prune193.0ms (4.3%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	247	0	247
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	247	7	254

Error

Counts

254 → 7

Alt Table

Status	Error	Program
✓	0.7b	(+.f64 (sin.f64 y) (fma.f64 (.f64 (.f64 (cbrt.f64 z) (cbrt.f64 (pow.f64 (cbrt.f64 z) 2))) (cbrt.f64 (cbrt.f64 z))) (*.f64 (cbrt.f64 z) (cos.f64 y)) x))
✓	1.1b	(+.f64 (sin.f64 y) (pow.f64 (cbrt.f64 (fma.f64 z (cos.f64 y) x)) 3))
✓	18.4b	(+.f64 (sin.f64 y) (fma.f64 (cbrt.f64 (.f64 z z)) (.f64 (cbrt.f64 z) (cos.f64 y)) x))
	38.1b	(+.f64 (sin.f64 y) (cbrt.f64 (pow.f64 (fma.f64 z (cos.f64 y) x) 3)))
✓	0.1b	(+.f64 (sin.f64 y) (fma.f64 z (cos.f64 y) x))
	33.2b	(+.f64 (sin.f64 y) (pow.f64 (sqrt.f64 (fma.f64 z (cos.f64 y) x)) 2))
	29.6b	(+.f64 (sin.f64 y) (fma.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (cos.f64 y)) x))

Compiler

Compiled 6836 to 2894 computations (57.7% saved)

regimes171.0ms (3.8%)

Accuracy

Total 0.0b remaining (53.2%)

Threshold costs 0.0b (53.2%)

Counts

33 → 1

Compiler

Compiled 2176 to 1430 computations (34.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	9	12

Stop Event

1×

saturated

end101.0ms (2.2%)

Compiler: Compiled 132 to 86 computations (34.8% saved)

Details

analyze613.0ms (13.5%)

sample2.3s (50.2%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series11.0ms (0.2%)

rewrite35.0ms (0.8%)

simplify37.0ms (0.8%)

prune42.0ms (0.9%)

localize9.0ms (0.2%)

series141.0ms (3.1%)

rewrite38.0ms (0.8%)

simplify39.0ms (0.9%)

prune111.0ms (2.4%)

localize24.0ms (0.5%)

series170.0ms (3.8%)

rewrite50.0ms (1.1%)

simplify39.0ms (0.9%)

prune100.0ms (2.2%)

localize15.0ms (0.3%)

series186.0ms (4.1%)

rewrite41.0ms (0.9%)

simplify72.0ms (1.6%)

prune193.0ms (4.3%)

regimes171.0ms (3.8%)

simplify2.0ms (0%)

end101.0ms (2.2%)

Profiling