Details

analyze23.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
12.5%	12.5%	75%	2
12.5%	12.5%	75%	3
18.7%	6.2%	75%	4
21.8%	3.1%	75%	5
23.4%	1.6%	75%	6
23.4%	1.6%	75%	7
24.2%	0.8%	75%	8
24.2%	0.8%	75%	9
24.6%	0.4%	75%	10
24.6%	0.4%	75%	11
24.8%	0.2%	75%	12
24.8%	0.2%	75%	13
24.9%	0.1%	75%	14

Compiler

Compiled 20 to 14 computations (30% saved)

sample3.4s (46.5%)

Results

1.8s	2081×	body	1024	valid
897.0ms	4663×	body	128	valid
500.0ms	1020×	body	512	valid
177.0ms	487×	body	256	valid
7.0ms	5×	body	2048	valid

Compiler

Compiled 53 to 37 computations (30.2% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`associate-/r/_binary64`
2×	`fma-def_binary64`
1×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	17	15
2	23	15
3	26	15
4	27	15
5	26	15

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

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))

Compiler

Compiled 47 to 28 computations (40.4% saved)

localize17.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
✓	0.1b	(*.f64 e (sin.f64 v))

series77.0ms (1.1%)

Counts

2 → 28

Calls

2 calls:

63.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
14.0ms	(*.f64 e (sin.f64 v))

rewrite75.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

877×	`log1p-expm1-u_binary64`
877×	`expm1-log1p-u_binary64`
90×	`add-sqr-sqrt_binary64`
82×	`add-cbrt-cube_binary64`
82×	`add-log-exp_binary64`

Counts

2 → 58

Calls

2 calls:

72.0ms	(/.f64 (*.f64 e (sin.f64 v)) (fma.f64 e (cos.f64 v) 1))
72.0ms	(*.f64 e (sin.f64 v))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	178	21
2	2238	21
3	5496	21
0	0	0
1	0	0

simplify102.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

688×	`times-frac_binary64`
456×	`associate-/l*_binary64`
414×	`fma-neg_binary64`
404×	`fma-def_binary64`
359×	`associate-/r*_binary64`

Counts

86 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	112	983
1	345	941
2	1320	901
3	4791	901
4	5067	901

prune153.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	81	8	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	8	90

Error

0.1b

Counts

90 → 8

Alt Table

Status	Error	Program
	25.2b	(.f64 (sqrt.f64 (.f64 e (sin.f64 v))) (.f64 (sqrt.f64 (.f64 e (sin.f64 v))) (/.f64 1 (fma.f64 e (cos.f64 v) 1))))
	1.2b	(.f64 (pow.f64 (cbrt.f64 (.f64 e (sin.f64 v))) 2) (.f64 (cbrt.f64 (.f64 e (sin.f64 v))) (/.f64 1 (fma.f64 e (cos.f64 v) 1))))
▶	0.2b	(.f64 (sin.f64 v) (.f64 e (/.f64 1 (fma.f64 e (cos.f64 v) 1))))
	0.3b	(*.f64 e (/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))
	33.8b	(/.f64 (cbrt.f64 (*.f64 (pow.f64 e 3) (pow.f64 (sin.f64 v) 3))) (fma.f64 e (cos.f64 v) 1))
	33.8b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 e (sin.f64 v)) 3)) (fma.f64 e (cos.f64 v) 1))
	1.3b	(/.f64 (pow.f64 (cbrt.f64 (*.f64 e (sin.f64 v))) 3) (fma.f64 e (cos.f64 v) 1))
	0.6b	(pow.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))) -1)

Compiler

Compiled 2128 to 1183 computations (44.4% saved)

localize19.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 e (/.f64 1 (fma.f64 e (cos.f64 v) 1)))
✓	0.0b	(/.f64 1 (fma.f64 e (cos.f64 v) 1))
✓	0.2b	(.f64 (sin.f64 v) (.f64 e (/.f64 1 (fma.f64 e (cos.f64 v) 1))))

series161.0ms (2.2%)

Counts

3 → 72

Calls

3 calls:

63.0ms	(.f64 (sin.f64 v) (.f64 e (/.f64 1 (fma.f64 e (cos.f64 v) 1))))
50.0ms	(*.f64 e (/.f64 1 (fma.f64 e (cos.f64 v) 1)))
47.0ms	(/.f64 1 (fma.f64 e (cos.f64 v) 1))

rewrite100.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

885×	`log1p-expm1-u_binary64`
885×	`expm1-log1p-u_binary64`
100×	`add-sqr-sqrt_binary64`
91×	`add-cbrt-cube_binary64`
91×	`add-log-exp_binary64`

Counts

3 → 67

Calls

3 calls:

97.0ms	(*.f64 e (/.f64 1 (fma.f64 e (cos.f64 v) 1)))
97.0ms	(/.f64 1 (fma.f64 e (cos.f64 v) 1))
97.0ms	(.f64 (sin.f64 v) (.f64 e (/.f64 1 (fma.f64 e (cos.f64 v) 1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	35
1	201	35
2	2329	35
3	5510	35
0	0	0
1	0	0

simplify140.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

679×	`fma-def_binary64`
538×	`fma-neg_binary64`
407×	`cancel-sign-sub-inv_binary64`
280×	`associate-/r/_binary64`
190×	`unswap-sqr_binary64`

Counts

139 → 139

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	201	2238
1	612	2160
2	2356	2109
3	4864	2109
4	5218	2109

prune263.0ms (3.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	138	9	147

Error

0.0b

Counts

147 → 9

Alt Table

Status	Error	Program
▶	0.3b	(*.f64 e (/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))
	1.3b	(*.f64 (sin.f64 v) (pow.f64 (cbrt.f64 (/.f64 e (fma.f64 e (cos.f64 v) 1))) 3))
	25.2b	(.f64 (sqrt.f64 (.f64 e (sin.f64 v))) (.f64 (sqrt.f64 (.f64 e (sin.f64 v))) (/.f64 1 (fma.f64 e (cos.f64 v) 1))))
	1.2b	(.f64 (pow.f64 (cbrt.f64 (.f64 e (sin.f64 v))) 2) (.f64 (cbrt.f64 (.f64 e (sin.f64 v))) (/.f64 1 (fma.f64 e (cos.f64 v) 1))))
	0.5b	(*.f64 (sin.f64 v) (pow.f64 (sqrt.f64 (/.f64 e (fma.f64 e (cos.f64 v) 1))) 2))
	33.8b	(/.f64 (cbrt.f64 (*.f64 (pow.f64 e 3) (pow.f64 (sin.f64 v) 3))) (fma.f64 e (cos.f64 v) 1))
	33.8b	(/.f64 (cbrt.f64 (pow.f64 (*.f64 e (sin.f64 v)) 3)) (fma.f64 e (cos.f64 v) 1))
	1.3b	(/.f64 (pow.f64 (cbrt.f64 (*.f64 e (sin.f64 v))) 3) (fma.f64 e (cos.f64 v) 1))
	0.6b	(pow.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))) -1)

Compiler

Compiled 3483 to 2116 computations (39.2% saved)

localize18.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 e (/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))
✓	0.2b	(/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))
✓	0.3b	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))

series157.0ms (2.1%)

Counts

3 → 72

Calls

3 calls:

62.0ms	(*.f64 e (/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))
56.0ms	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))
38.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))

rewrite97.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

528×	`log-prod_binary64`
263×	`pow2_binary64`
186×	`pow1/3_binary64`
181×	`expm1-udef_binary64`
181×	`log1p-udef_binary64`

Counts

3 → 116

Calls

3 calls:

91.0ms	(*.f64 e (/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))
91.0ms	(/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))
91.0ms	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	42
1	207	39
2	2523	39
3	5056	39
0	0	0
1	0	0

simplify135.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

815×	`fma-def_binary64`
494×	`fma-neg_binary64`
431×	`cancel-sign-sub-inv_binary64`
198×	`associate-/r/_binary64`
177×	`sub-neg_binary64`

Counts

188 → 179

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	2185
1	591	2112
2	2275	2043
3	4742	2043
4	5055	2043

prune353.0ms (4.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	172	7	179
Fresh	7	1	8
Picked	0	1	1
Done	0	0	0
Total	179	9	188

Error

0.0b

Counts

188 → 9

Alt Table

Status	Error	Program
	0.6b	(/.f64 1 (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) e))
	4.7b	(*.f64 e (cbrt.f64 (pow.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) 3)))
	12.3b	(*.f64 e (+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))))
	12.5b	(*.f64 e (/.f64 1 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))))))
	31.5b	(/.f64 (/.f64 e (sqrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))) (sqrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))
	25.2b	(.f64 (sqrt.f64 (.f64 e (sin.f64 v))) (.f64 (sqrt.f64 (.f64 e (sin.f64 v))) (/.f64 1 (fma.f64 e (cos.f64 v) 1))))
▶	0.2b	(*.f64 e (log1p.f64 (expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
✓	0.3b	(*.f64 e (/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))
	1.0b	(*.f64 e (pow.f64 (cbrt.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))) 3))

Compiler

Compiled 4203 to 2460 computations (41.5% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))
✓	0.1b	(*.f64 e (log1p.f64 (expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
✓	0.2b	(expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
✓	0.2b	(log1p.f64 (expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))))

series269.0ms (3.7%)

Counts

4 → 96

Calls

4 calls:

95.0ms	(expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
62.0ms	(*.f64 e (log1p.f64 (expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
56.0ms	(log1p.f64 (expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))))
55.0ms	(/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))

rewrite109.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

896×	`expm1-log1p-u_binary64`
895×	`log1p-expm1-u_binary64`
114×	`egg-rr`
97×	`add-sqr-sqrt_binary64`
88×	`add-cbrt-cube_binary64`

Counts

4 → 114

Calls

4 calls:

103.0ms	(/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))
103.0ms	(*.f64 e (log1p.f64 (expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
103.0ms	(expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
103.0ms	(log1p.f64 (expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	53
1	195	53
2	2311	53
3	5632	53
0	0	0
1	0	0

simplify159.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

541×	`cancel-sign-sub-inv_binary64`
270×	`fma-neg_binary64`
241×	`sub-neg_binary64`
235×	`associate-r_binary64`
222×	`fma-def_binary64`

Counts

210 → 151

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	251	4002
1	825	3898
2	3375	3871
3	4999	3871

prune295.0ms (4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	151	9	160

Error

0.0b

Counts

160 → 9

Alt Table

Status	Error	Program
	0.6b	(/.f64 1 (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) e))
	4.7b	(*.f64 e (cbrt.f64 (pow.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) 3)))
	12.3b	(*.f64 e (+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))))
	12.5b	(*.f64 e (/.f64 1 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))))))
	31.5b	(/.f64 (/.f64 e (sqrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))) (sqrt.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))
	25.2b	(.f64 (sqrt.f64 (.f64 e (sin.f64 v))) (.f64 (sqrt.f64 (.f64 e (sin.f64 v))) (/.f64 1 (fma.f64 e (cos.f64 v) 1))))
✓	0.2b	(*.f64 e (log1p.f64 (expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
✓	0.3b	(*.f64 e (/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))
	1.0b	(*.f64 e (pow.f64 (cbrt.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))) 3))

Compiler

Compiled 4360 to 2511 computations (42.4% saved)

regimes869.0ms (11.9%)

Accuracy

Total 0.1b remaining (68.8%)

Threshold costs 0.1b (68.8%)

Counts

137 → 1

Compiler

Compiled 6398 to 4442 computations (30.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	12	15
2	11	15

end278.0ms (3.8%)

Compiler: Compiled 196 to 132 computations (32.7% saved)

Details

analyze23.0ms (0.3%)

sample3.4s (46.5%)

simplify13.0ms (0.2%)

prune5.0ms (0.1%)

localize17.0ms (0.2%)

series77.0ms (1.1%)

rewrite75.0ms (1%)

simplify102.0ms (1.4%)

prune153.0ms (2.1%)

localize19.0ms (0.3%)

series161.0ms (2.2%)

rewrite100.0ms (1.4%)

simplify140.0ms (1.9%)

prune263.0ms (3.6%)

localize18.0ms (0.2%)

series157.0ms (2.1%)

rewrite97.0ms (1.3%)

simplify135.0ms (1.8%)

prune353.0ms (4.8%)

localize21.0ms (0.3%)

series269.0ms (3.7%)

rewrite109.0ms (1.5%)

simplify159.0ms (2.2%)

prune295.0ms (4%)

regimes869.0ms (11.9%)

simplify4.0ms (0%)

end278.0ms (3.8%)

Profiling