Details

analyze1.0s (7.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0.1%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample10.3s (76.8%)

Results

4.6s	1615×	body	8192	exit
2.8s	4159×	body	1024	valid
955.0ms	1674×	body	1024	invalid
862.0ms	2025×	body	512	valid
304.0ms	1013×	body	256	valid
298.0ms	824×	body	512	invalid
172.0ms	189×	body	2048	valid
150.0ms	870×	body	128	valid
104.0ms	399×	body	256	invalid
57.0ms	399×	body	128	invalid

Compiler

Compiled 35 to 26 computations (25.7% saved)

simplify31.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

924×	`unswap-sqr_binary64`
427×	`associate-/l*_binary64`
271×	`*-commutative_binary64`
263×	`associate-/r*_binary64`
222×	`associate-/l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	16	17
2	26	15
3	39	15
4	63	15
5	120	15
6	276	15
7	708	15
8	1145	15
9	3095	15
10	4995	15

Stop Event

1×	node limit

Counts

1 → 2

prune2.0ms (0%)

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

60.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	60.8b	(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))

Compiler

Compiled 40 to 21 computations (47.5% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (cos.f64 x))
✓	4.6b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series4.0ms (0%)

Counts

2 → 4

Calls

2 calls:

2.0ms	(sqrt.f64 (cos.f64 x))
1.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

rewrite33.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

457×	`log1p-expm1-u_binary64`
457×	`expm1-log1p-u_binary64`
313×	`unpow-prod-down_binary64`
251×	`log-prod_binary64`
143×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	113	15
2	1290	15

Stop Event

1×	node limit

Counts

2 → 68

Calls

2 calls:

32.0ms	(sqrt.f64 (cos.f64 x))
32.0ms	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

simplify21.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

404×	`distribute-rgt-neg-in_binary64`
348×	`distribute-lft-neg-in_binary64`
285×	`unswap-sqr_binary64`
244×	`associate-l_binary64`
226×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	52
1	57	52
2	143	50
3	486	48
4	2303	48

Stop Event

1×	node limit

Counts

72 → 75

prune70.0ms (0.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	71	4	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	4	76

Error

38.2b

Counts

76 → 4

Alt Table

Status	Error	Program
	61.1b	(/.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
	60.8b	(/.f64 (fmod.f64 (exp.f64 x) (pow.f64 (pow.f64 (cos.f64 x) 1/6) 3)) (exp.f64 x))
▶	38.7b	(/.f64 (fmod.f64 (exp.f64 x) (+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
	61.1b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))

Compiler

Compiled 1297 to 554 computations (57.3% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) 2))
✓	0.9b	(pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) 2)
✓	1.4b	(cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
✓	49.8b	(fmod.f64 (exp.f64 x) (+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))))

series655.0ms (4.9%)

Counts

4 → 48

Calls

4 calls:

355.0ms	(log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) 2))
152.0ms	(cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
145.0ms	(pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) 2)
4.0ms	(fmod.f64 (exp.f64 x) (+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))))

rewrite48.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

709×	`prod-diff_binary64`
257×	`fma-def_binary64`
191×	`expm1-udef_binary64`
191×	`log1p-udef_binary64`
145×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	259	42
2	2865	42

Stop Event

1×	node limit

Counts

4 → 92

Calls

4 calls:

46.0ms	(log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) 2))
46.0ms	(pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) 2)
46.0ms	(cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))
46.0ms	(fmod.f64 (exp.f64 x) (+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))))))

simplify33.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

670×	`fma-neg_binary64`
375×	`distribute-rgt-neg-in_binary64`
356×	`distribute-lft-neg-in_binary64`
319×	`unswap-sqr_binary64`
231×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	982
1	189	640
2	586	586
3	2323	540

Stop Event

1×	node limit

Counts

140 → 122

prune115.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	155	4	159

Error

38.2b

Counts

159 → 4

Alt Table

Status	Error	Program
	61.1b	(/.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
▶	60.8b	(/.f64 (fmod.f64 (exp.f64 x) (pow.f64 (pow.f64 (cos.f64 x) 1/6) 3)) (exp.f64 x))
✓	38.7b	(/.f64 (fmod.f64 (exp.f64 x) (+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
	61.1b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))

Compiler

Compiled 3970 to 1722 computations (56.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (cos.f64 x) 1/6)
✓	0.1b	(pow.f64 (pow.f64 (cos.f64 x) 1/6) 3)
✓	4.6b	(fmod.f64 (exp.f64 x) (pow.f64 (pow.f64 (cos.f64 x) 1/6) 3))

series231.0ms (1.7%)

Counts

3 → 16

Calls

3 calls:

117.0ms	(pow.f64 (pow.f64 (cos.f64 x) 1/6) 3)
111.0ms	(pow.f64 (cos.f64 x) 1/6)
3.0ms	(fmod.f64 (exp.f64 x) (pow.f64 (pow.f64 (cos.f64 x) 1/6) 3))

rewrite40.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

700×	`log1p-expm1-u_binary64`
700×	`expm1-log1p-u_binary64`
145×	`expm1-udef_binary64`
145×	`log1p-udef_binary64`
86×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	187	21
2	2016	21

Stop Event

1×	node limit

Counts

3 → 61

Calls

3 calls:

39.0ms	(pow.f64 (cos.f64 x) 1/6)
39.0ms	(pow.f64 (pow.f64 (cos.f64 x) 1/6) 3)
39.0ms	(fmod.f64 (exp.f64 x) (pow.f64 (pow.f64 (cos.f64 x) 1/6) 3))

simplify29.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

588×	`distribute-rgt-neg-in_binary64`
416×	`fma-def_binary64`
384×	`cancel-sign-sub-inv_binary64`
355×	`associate-l_binary64`
329×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	144
1	91	144
2	233	140
3	813	136
4	3804	136

Stop Event

1×	node limit

Counts

77 → 74

prune41.0ms (0.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	74	4	78

Error

38.2b

Counts

78 → 4

Alt Table

Status	Error	Program
▶	61.1b	(/.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
✓	60.8b	(/.f64 (fmod.f64 (exp.f64 x) (pow.f64 (pow.f64 (cos.f64 x) 1/6) 3)) (exp.f64 x))
✓	38.7b	(/.f64 (fmod.f64 (exp.f64 x) (+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
	61.1b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))

Compiler

Compiled 1213 to 578 computations (52.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))
	0.0b	(sqrt.f64 (cos.f64 x))
✓	2.2b	(log.f64 (sqrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))
	4.6b	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

series274.0ms (2%)

Counts

2 → 0

Calls

2 calls:

269.0ms	(log.f64 (sqrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))
5.0ms	(sqrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))

rewrite40.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

638×	`log1p-expm1-u_binary64`
638×	`expm1-log1p-u_binary64`
364×	`log-prod_binary64`
145×	`log-pow_binary64`
140×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	165	27
2	1840	27

Stop Event

1×	node limit

Counts

2 → 56

Calls

2 calls:

38.0ms	(sqrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))
38.0ms	(log.f64 (sqrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

56 → 56

prune176.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	260	2	262
Fresh	0	1	1
Picked	1	0	1
Done	1	1	2
Total	262	4	266

Error

38.1b

Counts

266 → 4

Alt Table

Status	Error	Program
	61.0b	(/.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) (+.f64 (log.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) 2))) (log.f64 (sqrt.f64 (cbrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))))) (exp.f64 x))
	59.5b	(/.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))))) (log.f64 (+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))) (cbrt.f64 (exp.f64 (sqrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))))))))) (exp.f64 x))
✓	38.7b	(/.f64 (fmod.f64 (exp.f64 x) (+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (cos.f64 x))))))) (exp.f64 x))
	61.1b	(/.f64 (log.f64 (exp.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))) (exp.f64 x))

Compiler

Compiled 7433 to 2268 computations (69.5% saved)

regimes109.0ms (0.8%)

Accuracy

Total 0.7b remaining (1.9%)

Threshold costs 0.7b (1.9%)

Counts

59 → 1

Compiler

Compiled 1990 to 1272 computations (36.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	31
1	17	31

Stop Event

1×

saturated

end90.0ms (0.7%)

Compiler: Compiled 160 to 84 computations (47.5% saved)

Details

analyze1.0s (7.6%)

sample10.3s (76.8%)

simplify31.0ms (0.2%)

prune2.0ms (0%)

localize7.0ms (0%)

series4.0ms (0%)

rewrite33.0ms (0.2%)

simplify21.0ms (0.2%)

prune70.0ms (0.5%)

localize15.0ms (0.1%)

series655.0ms (4.9%)

rewrite48.0ms (0.4%)

simplify33.0ms (0.2%)

prune115.0ms (0.9%)

localize8.0ms (0.1%)

series231.0ms (1.7%)

rewrite40.0ms (0.3%)

simplify29.0ms (0.2%)

prune41.0ms (0.3%)

localize11.0ms (0.1%)

series274.0ms (2%)

rewrite40.0ms (0.3%)

simplify7.0ms (0%)

prune176.0ms (1.3%)

regimes109.0ms (0.8%)

simplify2.0ms (0%)

end90.0ms (0.7%)

Profiling