Details

analyze323.0ms (6.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample2.9s (56.2%)

Results

1.5s	2133×	body	2048	valid
444.0ms	1112×	body	1024	valid
432.0ms	1572×	body	512	valid
271.0ms	2583×	body	128	valid
159.0ms	766×	body	256	valid
60.0ms	90×	body	4096	valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify20.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

424×	`fma-def_binary64`
293×	`fma-neg_binary64`
86×	`div-sub_binary64`
74×	`associate-/l*_binary64`
63×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	40	12
4	73	12
5	127	12
6	192	12
7	317	12
8	621	12
9	1140	12
10	1700	12
11	1829	12

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

34.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	34.9b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.6b	(-.f64 1 (cos.f64 x))
✓	16.4b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series5.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

3.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
2.0ms	(-.f64 1 (cos.f64 x))

rewrite56.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

818×	`log1p-expm1-u_binary64`
818×	`expm1-log1p-u_binary64`
259×	`prod-diff_binary64`
102×	`egg-rr`
76×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	153	18
2	2128	18

Stop Event

1×	node limit

Counts

2 → 102

Calls

2 calls:

53.0ms	(-.f64 1 (cos.f64 x))
53.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

simplify32.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

588×	`associate-l_binary64`
468×	`fma-def_binary64`
434×	`associate-r_binary64`
413×	`unswap-sqr_binary64`
387×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	224
1	97	220
2	266	214
3	901	212
4	4446	212

Stop Event

1×	node limit

Counts

118 → 119

prune120.0ms (2.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	111	8	119
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	8	120

Error

0.0b

Counts

120 → 8

Alt Table

Status	Error	Program
	34.9b	(/.f64 (pow.f64 (-.f64 1 (cos.f64 x)) 1) (*.f64 x x))
	34.2b	(+.f64 (fma.f64 (sqrt.f64 (pow.f64 x -2)) (sqrt.f64 (pow.f64 x -2)) (neg.f64 (.f64 (.f64 (cos.f64 x) (pow.f64 x -2)) 1))) (fma.f64 (neg.f64 (.f64 (cos.f64 x) (pow.f64 x -2))) 1 (.f64 (*.f64 (cos.f64 x) (pow.f64 x -2)) 1)))
	28.3b	1/2
▶	17.4b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
	17.4b	(/.f64 (.f64 (.f64 (sin.f64 x) (sin.f64 x)) (/.f64 1 (+.f64 1 (cos.f64 x)))) (*.f64 x x))
	34.9b	(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
	41.2b	(+.f64 (fma.f64 1 (pow.f64 x -2) (neg.f64 (.f64 (cos.f64 x) (pow.f64 x -2)))) (fma.f64 (neg.f64 (sqrt.f64 (.f64 (cos.f64 x) (pow.f64 x -2)))) (sqrt.f64 (.f64 (cos.f64 x) (pow.f64 x -2))) (.f64 (cos.f64 x) (pow.f64 x -2))))
	33.6b	(pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)

Compiler

Compiled 3203 to 1862 computations (41.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
✓	0.2b	(*.f64 (sin.f64 x) (sin.f64 x))
✓	0.4b	(+.f64 1 (cos.f64 x))
✓	16.7b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

series28.0ms (0.6%)

Counts

4 → 40

Calls

4 calls:

12.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
10.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
4.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
1.0ms	(+.f64 1 (cos.f64 x))

rewrite57.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

456×	`prod-diff_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
145×	`egg-rr`
114×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	46
1	229	30
2	3474	30

Stop Event

1×	node limit

Counts

4 → 145

Calls

4 calls:

55.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
55.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
55.0ms	(+.f64 1 (cos.f64 x))
55.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

simplify41.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

920×	`times-frac_binary64`
452×	`fma-neg_binary64`
209×	`*-commutative_binary64`
187×	`fma-def_binary64`
167×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	54	564
1	155	556
2	460	496
3	1638	496
4	4511	496

Stop Event

1×	node limit

Counts

185 → 179

prune124.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	176	3	179
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	181	6	187

Error

Counts

187 → 6

Alt Table

Status	Error	Program
	28.3b	1/2
	17.4b	(/.f64 (.f64 (sin.f64 x) (.f64 (sin.f64 x) (exp.f64 (neg.f64 (log1p.f64 (cos.f64 x)))))) (*.f64 x x))
	17.5b	(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (.f64 x x)))
▶	16.9b	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
	34.9b	(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
	33.6b	(pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)

Compiler

Compiled 3083 to 1672 computations (45.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (sin.f64 x) 2)
✓	0.3b	(*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2))
	0.4b	(+.f64 1 (cos.f64 x))
✓	16.3b	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))

series19.0ms (0.4%)

Counts

3 → 12

Calls

3 calls:

12.0ms	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
3.0ms	(*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2))
3.0ms	(pow.f64 (sin.f64 x) 2)

rewrite56.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

519×	`log-prod_binary64`
191×	`fma-def_binary64`
184×	`expm1-udef_binary64`
184×	`log1p-udef_binary64`
166×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	38
1	233	30
2	2938	30

Stop Event

1×	node limit

Counts

3 → 117

Calls

3 calls:

49.0ms	(pow.f64 (sin.f64 x) 2)
49.0ms	(*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2))
49.0ms	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))

simplify29.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-def_binary64`
649×	`cancel-sign-sub-inv_binary64`
390×	`fma-neg_binary64`
211×	`*-commutative_binary64`
145×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	192
1	121	184
2	355	176
3	1276	174
4	4863	174

Stop Event

1×	node limit

Counts

129 → 140

prune118.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	179	6	185

Error

Counts

185 → 6

Alt Table

Status	Error	Program
	28.3b	1/2
▶	17.4b	(/.f64 (.f64 (sin.f64 x) (.f64 (sin.f64 x) (exp.f64 (neg.f64 (log1p.f64 (cos.f64 x)))))) (*.f64 x x))
	17.5b	(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (.f64 x x)))
✓	16.9b	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
	34.9b	(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))
	33.6b	(pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x) 2)

Compiler

Compiled 3247 to 1888 computations (41.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sin.f64 x) (exp.f64 (neg.f64 (log1p.f64 (cos.f64 x)))))
✓	0.2b	(.f64 (sin.f64 x) (.f64 (sin.f64 x) (exp.f64 (neg.f64 (log1p.f64 (cos.f64 x))))))
✓	0.3b	(log1p.f64 (cos.f64 x))
✓	16.7b	(/.f64 (.f64 (sin.f64 x) (.f64 (sin.f64 x) (exp.f64 (neg.f64 (log1p.f64 (cos.f64 x)))))) (*.f64 x x))

series554.0ms (10.9%)

Counts

4 → 48

Calls

4 calls:

150.0ms	(/.f64 (.f64 (sin.f64 x) (.f64 (sin.f64 x) (exp.f64 (neg.f64 (log1p.f64 (cos.f64 x)))))) (*.f64 x x))
135.0ms	(.f64 (sin.f64 x) (.f64 (sin.f64 x) (exp.f64 (neg.f64 (log1p.f64 (cos.f64 x))))))
134.0ms	(log1p.f64 (cos.f64 x))
134.0ms	(*.f64 (sin.f64 x) (exp.f64 (neg.f64 (log1p.f64 (cos.f64 x)))))

rewrite59.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

644×	`log-prod_binary64`
189×	`expm1-udef_binary64`
189×	`log1p-udef_binary64`
175×	`log-pow_binary64`
143×	`log-div_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	63
1	229	49
2	3265	39

Stop Event

1×	node limit

Counts

4 → 132

Calls

4 calls:

57.0ms	(*.f64 (sin.f64 x) (exp.f64 (neg.f64 (log1p.f64 (cos.f64 x)))))
57.0ms	(.f64 (sin.f64 x) (.f64 (sin.f64 x) (exp.f64 (neg.f64 (log1p.f64 (cos.f64 x))))))
57.0ms	(log1p.f64 (cos.f64 x))
57.0ms	(/.f64 (.f64 (sin.f64 x) (.f64 (sin.f64 x) (exp.f64 (neg.f64 (log1p.f64 (cos.f64 x)))))) (*.f64 x x))

simplify43.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

672×	`fma-neg_binary64`
478×	`times-frac_binary64`
313×	`fma-def_binary64`
305×	`distribute-rgt-neg-in_binary64`
290×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	956
1	224	714
2	704	634
3	2618	546

Stop Event

1×	node limit

Counts

180 → 171

prune117.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	171	6	177

Error

Counts

177 → 6

Alt Table

Status	Error	Program
	16.5b	(pow.f64 (/.f64 (sqrt.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))) x) 2)
	17.5b	(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x 2)) (.f64 x x)))
✓	17.4b	(/.f64 (.f64 (sin.f64 x) (.f64 (sin.f64 x) (exp.f64 (neg.f64 (log1p.f64 (cos.f64 x)))))) (*.f64 x x))
✓	16.9b	(/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (+.f64 1 (cos.f64 x)) (pow.f64 x 2)))
	0.1b	(.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (.f64 1/2 x)) x))
	34.9b	(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 x)))) (*.f64 x x))

Compiler

Compiled 3150 to 1841 computations (41.6% saved)

regimes303.0ms (6%)

Accuracy

Total 0.1b remaining (84.5%)

Threshold costs 0.1b (84.5%)

Counts

117 → 1

Compiler

Compiled 4311 to 2914 computations (32.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	11	17

Stop Event

1×

saturated

end88.0ms (1.7%)

Compiler: Compiled 101 to 70 computations (30.7% saved)

Details

analyze323.0ms (6.3%)

sample2.9s (56.2%)

simplify20.0ms (0.4%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series5.0ms (0.1%)

rewrite56.0ms (1.1%)

simplify32.0ms (0.6%)

prune120.0ms (2.4%)

localize10.0ms (0.2%)

series28.0ms (0.6%)

rewrite57.0ms (1.1%)

simplify41.0ms (0.8%)

prune124.0ms (2.4%)

localize12.0ms (0.2%)

series19.0ms (0.4%)

rewrite56.0ms (1.1%)

simplify29.0ms (0.6%)

prune118.0ms (2.3%)

localize11.0ms (0.2%)

series554.0ms (10.9%)

rewrite59.0ms (1.2%)

simplify43.0ms (0.8%)

prune117.0ms (2.3%)

regimes303.0ms (6%)

simplify2.0ms (0%)

end88.0ms (1.7%)

Profiling