Details

analyze23.0ms (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)

sample2.9s (65.2%)

Results

1.5s	2062×	body	1024	valid
755.0ms	4629×	body	128	valid
445.0ms	1050×	body	512	valid
155.0ms	504×	body	256	valid
15.0ms	11×	body	2048	valid

Compiler

Compiled 40 to 28 computations (30% saved)

preprocess20.0ms (0.4%)

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)

simplify6.0ms (0.1%)

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 (0.9%)

Counts

3 → 52

Calls

18 calls:

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
6.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))	v	0
3.0ms	(/.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

rewrite49.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	207	27
2	2824	27

Stop Event

1×	node limit

Counts

3 → 81

simplify34.0ms (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
✓	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))))
	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))))

Compiler

Compiled 2568 to 1394 computations (45.7% saved)

localize10.0ms (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)))

series66.0ms (1.5%)

Counts

3 → 72

Calls

18 calls:

7.0ms	(*.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
6.0ms	(/.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	2681	39

Stop Event

1×	node limit

Counts

3 → 115

simplify50.0ms (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

prune168.0ms (3.8%)

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
	35.7b	(cbrt.f64 (*.f64 (pow.f64 e 3) (pow.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) 3)))
	16.6b	(*.f64 e (-.f64 (exp.f64 (log1p.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))) 1))
✓	0.1b	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
▶	0.3b	(/.f64 (neg.f64 e) (neg.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))
	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)))
	1.1b	(/.f64 1 (/.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) e))
	4.5b	(.f64 e (.f64 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 v) 2)) 1) (/.f64 (cbrt.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)))

Compiler

Compiled 4192 to 2459 computations (41.3% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series26.0ms (0.6%)

Counts

1 → 24

Calls

6 calls:

6.0ms	(/.f64 (neg.f64 e) (neg.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))	v	inf
6.0ms	(/.f64 (neg.f64 e) (neg.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))	v	-inf
6.0ms	(/.f64 (neg.f64 e) (neg.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))	v	0
3.0ms	(/.f64 (neg.f64 e) (neg.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))	e	0
2.0ms	(/.f64 (neg.f64 e) (neg.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))	e	-inf

rewrite43.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

924×	`log1p-expm1-u_binary64`
924×	`expm1-log1p-u_binary64`
115×	`add-sqr-sqrt_binary64`
113×	`*-un-lft-identity_binary64`
113×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	228	15
2	3234	15

Stop Event

1×	node limit

Counts

1 → 40

simplify28.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

674×	`times-frac_binary64`
454×	`associate-l_binary64`
422×	`associate-/l*_binary64`
358×	`associate-/r*_binary64`
303×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	901
1	316	867
2	1245	837

Stop Event

1×	node limit

Counts

64 → 64

prune100.0ms (2.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	119	7	126

Error

0.0b

Counts

126 → 7

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
✓	0.3b	(/.f64 (neg.f64 e) (neg.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))
	35.7b	(cbrt.f64 (*.f64 (pow.f64 e 3) (pow.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) 3)))
	9.1b	(/.f64 (neg.f64 e) (neg.f64 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) 3))))
▶	0.4b	(.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))))
	4.5b	(.f64 e (.f64 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 v) 2)) 1) (/.f64 (cbrt.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)))

Compiler

Compiled 2692 to 1527 computations (43.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))
✓	0.2b	(*.f64 (sqrt.f64 e) (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))
✓	0.3b	(.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))))

series98.0ms (2.2%)

Counts

3 → 56

Calls

18 calls:

9.0ms	(*.f64 (sqrt.f64 e) (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))	v	inf
8.0ms	(.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))))	v	inf
8.0ms	(.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))))	e	-inf
8.0ms	(*.f64 (sqrt.f64 e) (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))	v	0
7.0ms	(*.f64 (sqrt.f64 e) (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)))	v	-inf

rewrite50.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

566×	`log-prod_binary64`
193×	`expm1-udef_binary64`
193×	`log1p-udef_binary64`
183×	`pow3_binary64`
169×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	44
1	219	44
2	2741	44

Stop Event

1×	node limit

Counts

3 → 89

simplify54.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

428×	`cancel-sign-sub-inv_binary64`
205×	`associate-/r/_binary64`
197×	`fma-def_binary64`
182×	`sub-neg_binary64`
175×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	208	2164
1	675	2080
2	2740	2034

Stop Event

1×	node limit

Counts

145 → 148

prune123.0ms (2.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	148	7	155

Error

0.0b

Counts

155 → 7

Alt Table

Status	Error	Program
✓	0.1b	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
✓	0.3b	(/.f64 (neg.f64 e) (neg.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v))))
	35.7b	(cbrt.f64 (*.f64 (pow.f64 e 3) (pow.f64 (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1)) 3)))
	9.1b	(/.f64 (neg.f64 e) (neg.f64 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 e (cos.f64 v) 1) (sin.f64 v)) 3))))
✓	0.4b	(.f64 (sqrt.f64 e) (.f64 (sqrt.f64 e) (/.f64 (sin.f64 v) (fma.f64 e (cos.f64 v) 1))))
	4.5b	(.f64 e (.f64 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 v) 2)) 1) (/.f64 (cbrt.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)))

Compiler

Compiled 4100 to 2275 computations (44.5% saved)

regimes267.0ms (6.1%)

Accuracy

Total 0.1b remaining (76.1%)

Threshold costs 0.1b (76.1%)

Counts

89 → 1

Compiler

Compiled 4121 to 2915 computations (29.3% saved)

simplify2.0ms (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

Stop Event

1×

saturated

end110.0ms (2.5%)

Stop Event

1×

fuel

Compiler

Compiled 137 to 97 computations (29.2% saved)

Details

analyze23.0ms (0.5%)

sample2.9s (65.2%)

preprocess20.0ms (0.4%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series38.0ms (0.9%)

rewrite49.0ms (1.1%)

simplify34.0ms (0.8%)

prune85.0ms (1.9%)

localize10.0ms (0.2%)

series66.0ms (1.5%)

rewrite52.0ms (1.2%)

simplify50.0ms (1.1%)

prune168.0ms (3.8%)

localize9.0ms (0.2%)

series26.0ms (0.6%)

rewrite43.0ms (1%)

simplify28.0ms (0.6%)

prune100.0ms (2.3%)

localize9.0ms (0.2%)

series98.0ms (2.2%)

rewrite50.0ms (1.1%)

simplify54.0ms (1.2%)

prune123.0ms (2.8%)

regimes267.0ms (6.1%)

simplify2.0ms (0%)

end110.0ms (2.5%)

Profiling