Details

analyze523.0ms (7.8%)

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
37.4%	62.4%	0.1%	7
43.7%	56.2%	0.1%	8
43.7%	56.2%	0.1%	9
65.5%	34.3%	0.1%	10
70.2%	29.6%	0.1%	11
70.2%	29.6%	0.1%	12
81.9%	17.9%	0.1%	13
84.6%	15.2%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.8s (41.5%)

Results

1.5s	2064×	body	1024	valid
764.0ms	4718×	body	128	valid
389.0ms	977×	body	512	valid
140.0ms	486×	body	256	valid
16.0ms	11×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	13	12
2	16	12

Stop Event

1×

saturated

Counts

1 → 2

prune5.0ms (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	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))

Compiler

Compiled 42 to 23 computations (45.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series23.0ms (0.3%)

Counts

3 → 64

Calls

3 calls:

15.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
6.0ms	(*.f64 z (cos.f64 y))
2.0ms	(cos.f64 y)

rewrite44.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

689×	`log1p-expm1-u_binary64`
689×	`expm1-log1p-u_binary64`
201×	`prod-diff_binary64`
147×	`log1p-udef_binary64`
81×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	156	21
2	1869	21

Stop Event

1×	node limit

Counts

3 → 56

Calls

3 calls:

43.0ms	(cos.f64 y)
43.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
43.0ms	(*.f64 z (cos.f64 y))

simplify44.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

474×	`fma-neg_binary64`
354×	`sub-neg_binary64`
257×	`*-commutative_binary64`
244×	`distribute-rgt-neg-in_binary64`
241×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	48	644
1	133	637
2	397	620
3	1542	619
4	4110	619

Stop Event

1×	node limit

Counts

120 → 80

prune56.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	74	6	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	7	81

Error

0.1b

Counts

81 → 7

Alt Table

Status	Error	Program
	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (log.f64 (+.f64 1 (expm1.f64 (cos.f64 y))))))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3))))
▶	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (log.f64 (exp.f64 (cos.f64 y)))))
	0.3b	(fma.f64 x (sin.f64 y) (*.f64 z (pow.f64 (cbrt.f64 (cos.f64 y)) 3)))
	31.0b	(pow.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)
	1.3b	(pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 3)

Compiler

Compiled 1210 to 526 computations (56.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (cos.f64 y))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (log.f64 (exp.f64 (cos.f64 y)))))
✓	0.1b	(*.f64 z (log.f64 (exp.f64 (cos.f64 y))))
✓	0.3b	(log.f64 (exp.f64 (cos.f64 y)))

series25.0ms (0.4%)

Counts

4 → 76

Calls

4 calls:

13.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (log.f64 (exp.f64 (cos.f64 y)))))
7.0ms	(*.f64 z (log.f64 (exp.f64 (cos.f64 y))))
2.0ms	(exp.f64 (cos.f64 y))
2.0ms	(log.f64 (exp.f64 (cos.f64 y)))

rewrite48.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

751×	`log1p-expm1-u_binary64`
751×	`expm1-log1p-u_binary64`
201×	`prod-diff_binary64`
89×	`add-sqr-sqrt_binary64`
81×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	178	26
2	2055	26

Stop Event

1×	node limit

Counts

4 → 77

Calls

4 calls:

47.0ms	(exp.f64 (cos.f64 y))
47.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (log.f64 (exp.f64 (cos.f64 y)))))
47.0ms	(*.f64 z (log.f64 (exp.f64 (cos.f64 y))))
47.0ms	(log.f64 (exp.f64 (cos.f64 y)))

simplify34.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-neg_binary64`
355×	`distribute-rgt-neg-in_binary64`
340×	`distribute-lft-neg-in_binary64`
224×	`cancel-sign-sub-inv_binary64`
216×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	752
1	176	741
2	547	716
3	2205	708

Stop Event

1×	node limit

Counts

153 → 109

prune128.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	108	8	116

Error

0.1b

Counts

116 → 8

Alt Table

Status	Error	Program
	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3))))
▶	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (log.f64 (pow.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3) 1/3))))
	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (log.f64 (+.f64 1 (expm1.f64 (cos.f64 y))))))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
	0.3b	(fma.f64 x (sin.f64 y) (*.f64 z (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3)))))
	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (log.f64 (log.f64 (exp.f64 (exp.f64 (cos.f64 y)))))))
	31.0b	(pow.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)
	1.3b	(pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 3)

Compiler

Compiled 1707 to 783 computations (54.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3) 1/3)
✓	0.1b	(*.f64 z (log.f64 (pow.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3) 1/3)))
✓	0.3b	(log.f64 (pow.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3) 1/3))
✓	0.8b	(pow.f64 (exp.f64 (cos.f64 y)) 3)

series1.8s (26.2%)

Counts

4 → 44

Calls

4 calls:

1.1s	(*.f64 z (log.f64 (pow.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3) 1/3)))
456.0ms	(log.f64 (pow.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3) 1/3))
195.0ms	(pow.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3) 1/3)
10.0ms	(pow.f64 (exp.f64 (cos.f64 y)) 3)

rewrite44.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

736×	`log1p-expm1-u_binary64`
736×	`expm1-log1p-u_binary64`
150×	`log1p-udef_binary64`
87×	`add-sqr-sqrt_binary64`
82×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	218	22
2	2105	22

Stop Event

1×	node limit

Counts

4 → 75

Calls

4 calls:

43.0ms	(pow.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3) 1/3)
43.0ms	(*.f64 z (log.f64 (pow.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3) 1/3)))
43.0ms	(log.f64 (pow.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3) 1/3))
43.0ms	(pow.f64 (exp.f64 (cos.f64 y)) 3)

simplify39.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

579×	`unswap-sqr_binary64`
380×	`associate-r_binary64`
380×	`associate-l_binary64`
291×	`cancel-sign-sub-inv_binary64`
287×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	890
1	243	663
2	788	425
3	3610	422

Stop Event

1×	node limit

Counts

119 → 109

prune127.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	109	8	117

Error

0.1b

Counts

117 → 8

Alt Table

Status	Error	Program
	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3))))
✓	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (log.f64 (pow.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3) 1/3))))
▶	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (log.f64 (+.f64 1 (expm1.f64 (cos.f64 y))))))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
	0.3b	(fma.f64 x (sin.f64 y) (*.f64 z (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3)))))
	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (log.f64 (log.f64 (exp.f64 (exp.f64 (cos.f64 y)))))))
	31.0b	(pow.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)
	1.3b	(pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 3)

Compiler

Compiled 2080 to 1170 computations (43.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 z (log.f64 (+.f64 1 (expm1.f64 (cos.f64 y)))))
✓	0.3b	(log.f64 (+.f64 1 (expm1.f64 (cos.f64 y))))
✓	0.6b	(+.f64 1 (expm1.f64 (cos.f64 y)))
✓	0.6b	(expm1.f64 (cos.f64 y))

series500.0ms (7.4%)

Counts

4 → 60

Calls

4 calls:

360.0ms	(*.f64 z (log.f64 (+.f64 1 (expm1.f64 (cos.f64 y)))))
134.0ms	(log.f64 (+.f64 1 (expm1.f64 (cos.f64 y))))
3.0ms	(expm1.f64 (cos.f64 y))
2.0ms	(+.f64 1 (expm1.f64 (cos.f64 y)))

rewrite49.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

701×	`log1p-expm1-u_binary64`
701×	`expm1-log1p-u_binary64`
163×	`prod-diff_binary64`
135×	`log1p-udef_binary64`
99×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	164	19
2	1896	19

Stop Event

1×	node limit

Counts

4 → 99

Calls

4 calls:

47.0ms	(*.f64 z (log.f64 (+.f64 1 (expm1.f64 (cos.f64 y)))))
47.0ms	(log.f64 (+.f64 1 (expm1.f64 (cos.f64 y))))
47.0ms	(+.f64 1 (expm1.f64 (cos.f64 y)))
47.0ms	(expm1.f64 (cos.f64 y))

simplify57.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

759×	`fma-neg_binary64`
276×	`*-commutative_binary64`
243×	`fma-def_binary64`
227×	`associate-+l-_binary64`
212×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	518
1	201	503
2	574	467
3	2022	459
4	4830	459

Stop Event

1×	node limit

Counts

159 → 131

prune136.0ms (2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	131	8	139

Error

0.1b

Counts

139 → 8

Alt Table

Status	Error	Program
	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (cbrt.f64 (pow.f64 (cos.f64 y) 3))))
✓	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (log.f64 (pow.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3) 1/3))))
✓	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (log.f64 (+.f64 1 (expm1.f64 (cos.f64 y))))))
✓	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
	0.3b	(fma.f64 x (sin.f64 y) (*.f64 z (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 y)) 3)))))
	0.2b	(fma.f64 x (sin.f64 y) (*.f64 z (log.f64 (log.f64 (exp.f64 (exp.f64 (cos.f64 y)))))))
	31.0b	(pow.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)
	1.3b	(pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 3)

Compiler

Compiled 2210 to 1112 computations (49.7% saved)

regimes120.0ms (1.8%)

Accuracy

Total 0.1b remaining (41.8%)

Threshold costs 0.1b (41.8%)

Counts

27 → 1

Compiler

Compiled 1680 to 1074 computations (36.1% 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

end129.0ms (1.9%)

Compiler: Compiled 138 to 98 computations (29% saved)

Details

analyze523.0ms (7.8%)

sample2.8s (41.5%)

simplify6.0ms (0.1%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

series23.0ms (0.3%)

rewrite44.0ms (0.7%)

simplify44.0ms (0.6%)

prune56.0ms (0.8%)

localize10.0ms (0.1%)

series25.0ms (0.4%)

rewrite48.0ms (0.7%)

simplify34.0ms (0.5%)

prune128.0ms (1.9%)

localize15.0ms (0.2%)

series1.8s (26.2%)

rewrite44.0ms (0.7%)

simplify39.0ms (0.6%)

prune127.0ms (1.9%)

localize11.0ms (0.2%)

series500.0ms (7.4%)

rewrite49.0ms (0.7%)

simplify57.0ms (0.8%)

prune136.0ms (2%)

regimes120.0ms (1.8%)

simplify2.0ms (0%)

end129.0ms (1.9%)

Profiling