Details

analyze22.0ms (0.5%)

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)

sample2.7s (61.1%)

Results

1.5s	2062×	body	1024	valid
701.0ms	4629×	body	128	valid
411.0ms	1050×	body	512	valid
140.0ms	504×	body	256	valid
15.0ms	11×	body	2048	valid

Compiler

Compiled 40 to 28 computations (30% saved)

preprocess15.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	34
1	28	30
2	40	30
3	46	30
4	48	30
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify9.0ms (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`

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))

Compiler

Compiled 49 to 31 computations (36.7% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series38.0ms (0.8%)

Counts

3 → 52

Calls

18 calls:

7.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))	v	0
6.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))	v	-inf
6.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))	v	inf
2.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))	e	-inf
2.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))	e	inf

rewrite50.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

370×	`prod-diff_binary64`
254×	`fma-def_binary64`
187×	`expm1-udef_binary64`
187×	`log1p-udef_binary64`
166×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	208	27
2	2817	27

Stop Event

1×	node limit

Counts

3 → 81

simplify35.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

691×	`times-frac_binary64`
468×	`fma-def_binary64`
464×	`associate-/l*_binary64`
292×	`cancel-sign-sub-inv_binary64`
132×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	1173
1	403	1130
2	1559	1082

Stop Event

1×	node limit

Counts

133 → 120

prune85.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	116	4	120
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	116	5	121

Error

0.1b

Counts

121 → 5

Alt Table

Status	Error	Program
	35.7b	(/.f64 (cbrt.f64 (.f64 (pow.f64 e 3) (pow.f64 (sin.f64 v) 3))) (+.f64 1 (.f64 e (cos.f64 v))))
	1.1b	(/.f64 (pow.f64 (cbrt.f64 (.f64 e (sin.f64 v))) 3) (+.f64 1 (.f64 e (cos.f64 v))))
✓	0.1b	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
	1.0b	(pow.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (*.f64 e (sin.f64 v))) -1)
▶	0.2b	(*.f64 e (/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))

Compiler

Compiled 2568 to 1394 computations (45.7% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series64.0ms (1.4%)

Counts

3 → 72

Calls

18 calls:

8.0ms	(*.f64 e (/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))	v	0
6.0ms	(*.f64 e (/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))	v	-inf
6.0ms	(*.f64 e (/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))	v	inf
6.0ms	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))	v	-inf
5.0ms	(/.f64 1 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)))	v	inf

rewrite52.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

529×	`log-prod_binary64`
186×	`pow1/3_binary64`
181×	`expm1-udef_binary64`
181×	`log1p-udef_binary64`
171×	`pow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	42
1	207	39
2	2702	39

Stop Event

1×	node limit

Counts

3 → 115

simplify51.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

810×	`fma-def_binary64`
431×	`cancel-sign-sub-inv_binary64`
177×	`sub-neg_binary64`
158×	`distribute-rgt-neg-in_binary64`
147×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	2185
1	596	2112
2	2377	2043

Stop Event

1×	node limit

Counts

187 → 179

prune174.0ms (3.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	171	8	179
Fresh	3	0	3
Picked	1	0	1
Done	0	1	1
Total	175	9	184

Error

0.0b

Counts

184 → 9

Alt Table

Status	Error	Program
	1.1b	(/.f64 1 (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) e))
▶	0.2b	(*.f64 e (log1p.f64 (expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
	8.6b	(*.f64 e (cbrt.f64 (pow.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) 3)))
	4.5b	(.f64 e (.f64 (cbrt.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))) (cbrt.f64 (pow.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) -2))))
	35.7b	(cbrt.f64 (*.f64 (pow.f64 e 3) (pow.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) 3)))
✓	0.1b	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
	16.6b	(*.f64 e (-.f64 (exp.f64 (log1p.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))) 1))
	16.8b	(*.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)))))))
	0.5b	(/.f64 (sqrt.f64 e) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e)))

Compiler

Compiled 4200 to 2454 computations (41.6% saved)

localize10.0ms (0.2%)

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

series104.0ms (2.3%)

Counts

4 → 96

Calls

24 calls:

8.0ms	(expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))	v	-inf
6.0ms	(expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))	v	inf
6.0ms	(expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))	e	-inf
6.0ms	(*.f64 e (log1p.f64 (expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))	v	-inf
6.0ms	(*.f64 e (log1p.f64 (expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))	v	inf

rewrite57.0ms (1.3%)

Algorithm

1×	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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	53
1	198	53
2	2403	53

Stop Event

1×	node limit

Counts

4 → 114

simplify76.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	251	4002
1	832	3898
2	3553	3871

Stop Event

1×	node limit

Counts

210 → 152

prune142.0ms (3.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	152	9	161

Error

0.0b

Counts

161 → 9

Alt Table

Status	Error	Program
	1.1b	(/.f64 1 (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) e))
✓	0.2b	(*.f64 e (log1p.f64 (expm1.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))))
	8.6b	(*.f64 e (cbrt.f64 (pow.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) 3)))
	4.5b	(.f64 e (.f64 (cbrt.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))) (cbrt.f64 (pow.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) -2))))
	35.7b	(cbrt.f64 (*.f64 (pow.f64 e 3) (pow.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) 3)))
✓	0.1b	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
	16.6b	(*.f64 e (-.f64 (exp.f64 (log1p.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))) 1))
	16.8b	(*.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)))))))
▶	0.5b	(/.f64 (sqrt.f64 e) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e)))

Compiler

Compiled 4485 to 2592 computations (42.2% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series63.0ms (1.4%)

Counts

2 → 32

Calls

12 calls:

9.0ms	(/.f64 (sqrt.f64 e) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e)))	e	-inf
7.0ms	(/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e))	e	-inf
7.0ms	(/.f64 (sqrt.f64 e) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e)))	v	-inf
7.0ms	(/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e))	v	-inf
7.0ms	(/.f64 (sqrt.f64 e) (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) (sqrt.f64 e)))	v	inf

rewrite56.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

632×	`log-prod_binary64`
205×	`expm1-udef_binary64`
205×	`log1p-udef_binary64`
190×	`log-pow_binary64`
184×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	230	32
2	3205	32

Stop Event

1×	node limit

Counts

2 → 88

simplify35.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

674×	`times-frac_binary64`
583×	`fma-def_binary64`
433×	`associate-/l*_binary64`
287×	`cancel-sign-sub-inv_binary64`
127×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	1168
1	430	1087
2	1694	1024

Stop Event

1×	node limit

Counts

120 → 121

prune163.0ms (3.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	170	4	174
Fresh	5	1	6
Picked	1	0	1
Done	1	1	2
Total	177	6	183

Error

Counts

183 → 6

Alt Table

Status	Error	Program
	0.3b	(*.f64 (/.f64 e (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))) 1)
	0.4b	(.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))))
	8.6b	(*.f64 e (cbrt.f64 (pow.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) 3)))
	0.4b	(/.f64 (sqrt.f64 e) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 e)) (fma.f64 e (cos.f64 v) 1)) (sin.f64 v)))
✓	0.1b	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
	0.3b	(*.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) (/.f64 (sqrt.f64 e) (pow.f64 e -1/2)))

Compiler

Compiled 4085 to 2122 computations (48.1% saved)

regimes315.0ms (7%)

Accuracy

Total 0.1b remaining (74.8%)

Threshold costs 0.1b (74.8%)

Counts

104 → 1

Compiler

Compiled 4841 to 3395 computations (29.9% saved)

simplify3.0ms (0.1%)

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

Stop Event

1×

saturated

end90.0ms (2%)

Stop Event

1×

fuel

Compiler

Compiled 117 to 81 computations (30.8% saved)

Details

analyze22.0ms (0.5%)

sample2.7s (61.1%)

preprocess15.0ms (0.3%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series38.0ms (0.8%)

rewrite50.0ms (1.1%)

simplify35.0ms (0.8%)

prune85.0ms (1.9%)

localize9.0ms (0.2%)

series64.0ms (1.4%)

rewrite52.0ms (1.2%)

simplify51.0ms (1.1%)

prune174.0ms (3.9%)

localize10.0ms (0.2%)

series104.0ms (2.3%)

rewrite57.0ms (1.3%)

simplify76.0ms (1.7%)

prune142.0ms (3.2%)

localize11.0ms (0.2%)

series63.0ms (1.4%)

rewrite56.0ms (1.3%)

simplify35.0ms (0.8%)

prune163.0ms (3.6%)

regimes315.0ms (7%)

simplify3.0ms (0.1%)

end90.0ms (2%)

Profiling