Details

analyze991.0ms (20.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
12.5%	87.3%	0.2%	8
18.7%	81.1%	0.2%	9
22.6%	77.2%	0.2%	10
25%	74.9%	0.2%	11
39.4%	60.4%	0.2%	12
46.5%	53.2%	0.3%	13
48%	51.4%	0.6%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.3s (28.1%)

Results

1.2s	8256×	body	128	valid
81.0ms	741×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify37.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1016×	`fma-neg_binary64`
470×	`fma-def_binary64`
265×	`associate-/l*_binary64`
257×	`cancel-sign-sub-inv_binary64`
254×	`div-sub_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	24	13
2	57	13
3	114	13
4	218	13
5	414	13
6	805	13
7	1396	13
8	2763	13
9	4227	13
10	4909	13

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	6.9b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))
▶	4.5b	(*.f64 2 (/.f64 (/.f64 x z) (-.f64 y t)))

Compiler

Compiled 80 to 53 computations (33.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (/.f64 (/.f64 x z) (-.f64 y t)))
✓	4.2b	(/.f64 (/.f64 x z) (-.f64 y t))

series79.0ms (1.7%)

Counts

2 → 96

Calls

2 calls:

40.0ms	(*.f64 2 (/.f64 (/.f64 x z) (-.f64 y t)))
39.0ms	(/.f64 (/.f64 x z) (-.f64 y t))

rewrite56.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

395×	`prod-diff_binary64`
213×	`expm1-udef_binary64`
213×	`log1p-udef_binary64`
188×	`fma-def_binary64`
117×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	225	23
2	3270	23

Stop Event

1×	node limit

Counts

2 → 66

Calls

2 calls:

54.0ms	(*.f64 2 (/.f64 (/.f64 x z) (-.f64 y t)))
54.0ms	(/.f64 (/.f64 x z) (-.f64 y t))

simplify44.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

812×	`times-frac_binary64`
508×	`associate-/l*_binary64`
457×	`fma-def_binary64`
358×	`associate-/r*_binary64`
265×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	77	2208
1	270	2010
2	1116	1839

Stop Event

1×	node limit

Counts

162 → 103

prune88.0ms (1.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	95	10	105

Error

Counts

105 → 10

Alt Table

Status	Error	Program
	4.6b	(/.f64 2 (*.f64 (-.f64 y t) (/.f64 z x)))
	34.5b	(*.f64 (/.f64 x y) (/.f64 2 z))
	5.8b	(/.f64 (.f64 x 2) (.f64 z (-.f64 y t)))
	28.0b	(*.f64 (/.f64 (/.f64 x t) z) -2)
	29.1b	(.f64 2 (pow.f64 (sqrt.f64 (/.f64 x (.f64 z (-.f64 y t)))) 2))
	21.1b	(.f64 2 (.f64 (/.f64 1 (cbrt.f64 (pow.f64 (-.f64 y t) 2))) (/.f64 (/.f64 x z) (cbrt.f64 (-.f64 y t)))))
	5.8b	(.f64 2 (.f64 (/.f64 x 1) (/.f64 (/.f64 1 z) (-.f64 y t))))
	4.5b	(.f64 2 (.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (-.f64 y t)) (/.f64 (cbrt.f64 x) z)))
✓	4.5b	(*.f64 2 (/.f64 (/.f64 x z) (-.f64 y t)))
▶	4.5b	(.f64 2 (.f64 (/.f64 x z) (/.f64 1 (-.f64 y t))))

Compiler

Compiled 1966 to 938 computations (52.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 (/.f64 x z) (/.f64 1 (-.f64 y t))))
✓	0.0b	(/.f64 1 (-.f64 y t))
✓	4.3b	(*.f64 (/.f64 x z) (/.f64 1 (-.f64 y t)))

series76.0ms (1.6%)

Counts

3 → 120

Calls

3 calls:

37.0ms	(.f64 2 (.f64 (/.f64 x z) (/.f64 1 (-.f64 y t))))
32.0ms	(*.f64 (/.f64 x z) (/.f64 1 (-.f64 y t)))
7.0ms	(/.f64 1 (-.f64 y t))

rewrite56.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

386×	`prod-diff_binary64`
231×	`expm1-udef_binary64`
231×	`log1p-udef_binary64`
132×	`add-sqr-sqrt_binary64`
125×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	30
1	264	30
2	3673	30

Stop Event

1×	node limit

Counts

3 → 96

Calls

3 calls:

54.0ms	(.f64 2 (.f64 (/.f64 x z) (/.f64 1 (-.f64 y t))))
54.0ms	(/.f64 1 (-.f64 y t))
54.0ms	(*.f64 (/.f64 x z) (/.f64 1 (-.f64 y t)))

simplify49.0ms (1%)

Algorithm

1×	egg-herbie

Rules

812×	`times-frac_binary64`
515×	`fma-def_binary64`
506×	`associate-/l*_binary64`
360×	`associate-/r*_binary64`
272×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	102	2700
1	321	2484
2	1263	2265

Stop Event

1×	node limit

Counts

216 → 146

prune131.0ms (2.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	5	3	8
Picked	0	1	1
Done	1	0	1
Total	149	7	156

Error

Counts

156 → 7

Alt Table

Status	Error	Program
	5.8b	(/.f64 (.f64 x 2) (.f64 z (-.f64 y t)))
	4.4b	(*.f64 2 (/.f64 (/.f64 x (-.f64 y t)) z))
▶	4.3b	(*.f64 2 (/.f64 (/.f64 1 (-.f64 y t)) (/.f64 z x)))
	5.9b	(*.f64 2 (/.f64 x (/.f64 (-.f64 y t) (/.f64 1 z))))
	5.8b	(.f64 2 (.f64 (/.f64 x 1) (/.f64 (/.f64 1 z) (-.f64 y t))))
	4.5b	(.f64 2 (.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (-.f64 y t)) (/.f64 (cbrt.f64 x) z)))
✓	4.5b	(.f64 2 (.f64 (/.f64 x z) (/.f64 1 (-.f64 y t))))

Compiler

Compiled 2471 to 1223 computations (50.5% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (/.f64 (/.f64 1 (-.f64 y t)) (/.f64 z x)))
	0.0b	(/.f64 1 (-.f64 y t))
✓	4.1b	(/.f64 (/.f64 1 (-.f64 y t)) (/.f64 z x))

series69.0ms (1.4%)

Counts

2 → 96

Calls

2 calls:

35.0ms	(*.f64 2 (/.f64 (/.f64 1 (-.f64 y t)) (/.f64 z x)))
33.0ms	(/.f64 (/.f64 1 (-.f64 y t)) (/.f64 z x))

rewrite63.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

413×	`prod-diff_binary64`
235×	`log1p-udef_binary64`
134×	`add-sqr-sqrt_binary64`
127×	`log1p-expm1-u_binary64`
127×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	266	23
2	3773	23

Stop Event

1×	node limit

Counts

2 → 66

Calls

2 calls:

62.0ms	(*.f64 2 (/.f64 (/.f64 1 (-.f64 y t)) (/.f64 z x)))
62.0ms	(/.f64 (/.f64 1 (-.f64 y t)) (/.f64 z x))

simplify45.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

812×	`times-frac_binary64`
506×	`associate-/l*_binary64`
457×	`fma-def_binary64`
358×	`associate-/r*_binary64`
264×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	77	2208
1	270	2010
2	1116	1839

Stop Event

1×	node limit

Counts

162 → 104

prune90.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	143	7	150

Error

Counts

150 → 7

Alt Table

Status	Error	Program
	5.8b	(/.f64 (.f64 x 2) (.f64 z (-.f64 y t)))
▶	4.4b	(*.f64 2 (/.f64 (/.f64 x (-.f64 y t)) z))
✓	4.3b	(*.f64 2 (/.f64 (/.f64 1 (-.f64 y t)) (/.f64 z x)))
	5.9b	(*.f64 2 (/.f64 x (/.f64 (-.f64 y t) (/.f64 1 z))))
	5.8b	(.f64 2 (.f64 (/.f64 x 1) (/.f64 (/.f64 1 z) (-.f64 y t))))
	4.5b	(.f64 2 (.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (-.f64 y t)) (/.f64 (cbrt.f64 x) z)))
✓	4.5b	(.f64 2 (.f64 (/.f64 x z) (/.f64 1 (-.f64 y t))))

Compiler

Compiled 2555 to 1259 computations (50.7% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (/.f64 (/.f64 x (-.f64 y t)) z))
✓	0.0b	(/.f64 x (-.f64 y t))
✓	4.3b	(/.f64 (/.f64 x (-.f64 y t)) z)

series82.0ms (1.7%)

Counts

3 → 120

Calls

3 calls:

36.0ms	(*.f64 2 (/.f64 (/.f64 x (-.f64 y t)) z))
27.0ms	(/.f64 (/.f64 x (-.f64 y t)) z)
19.0ms	(/.f64 x (-.f64 y t))

rewrite65.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

395×	`prod-diff_binary64`
213×	`expm1-udef_binary64`
213×	`log1p-udef_binary64`
190×	`fma-def_binary64`
117×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	225	30
2	3272	30

Stop Event

1×	node limit

Counts

3 → 99

Calls

3 calls:

54.0ms	(*.f64 2 (/.f64 (/.f64 x (-.f64 y t)) z))
54.0ms	(/.f64 x (-.f64 y t))
54.0ms	(/.f64 (/.f64 x (-.f64 y t)) z)

simplify54.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

822×	`times-frac_binary64`
610×	`fma-def_binary64`
535×	`associate-/l*_binary64`
372×	`associate-/r*_binary64`
111×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	100	2814
1	332	2616
2	1295	2325

Stop Event

1×	node limit

Counts

219 → 150

prune106.0ms (2.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	150	7	157

Error

Counts

157 → 7

Alt Table

Status	Error	Program
	5.8b	(/.f64 (.f64 x 2) (.f64 z (-.f64 y t)))
✓	4.4b	(*.f64 2 (/.f64 (/.f64 x (-.f64 y t)) z))
✓	4.3b	(*.f64 2 (/.f64 (/.f64 1 (-.f64 y t)) (/.f64 z x)))
	5.9b	(*.f64 2 (/.f64 x (/.f64 (-.f64 y t) (/.f64 1 z))))
	5.8b	(.f64 2 (.f64 (/.f64 x 1) (/.f64 (/.f64 1 z) (-.f64 y t))))
	4.5b	(.f64 2 (.f64 (/.f64 x (-.f64 y t)) (/.f64 1 z)))
✓	4.5b	(.f64 2 (.f64 (/.f64 x z) (/.f64 1 (-.f64 y t))))

Compiler

Compiled 2540 to 1193 computations (53% saved)

regimes1.1s (22.7%)

Accuracy

Total 1.2b remaining (98.8%)

Threshold costs 0b (0%)

Counts

82 → 5

Compiler

Compiled 8912 to 6388 computations (28.3% saved)

bsearch2.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	128
1	45	128
2	57	128
3	63	128
4	67	128
5	68	128

Stop Event

1×

saturated

end116.0ms (2.4%)

Compiler: Compiled 285 to 149 computations (47.7% saved)

Details

analyze991.0ms (20.9%)

sample1.3s (28.1%)

simplify37.0ms (0.8%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series79.0ms (1.7%)

rewrite56.0ms (1.2%)

simplify44.0ms (0.9%)

prune88.0ms (1.9%)

localize7.0ms (0.1%)

series76.0ms (1.6%)

rewrite56.0ms (1.2%)

simplify49.0ms (1%)

prune131.0ms (2.8%)

localize7.0ms (0.1%)

series69.0ms (1.4%)

rewrite63.0ms (1.3%)

simplify45.0ms (0.9%)

prune90.0ms (1.9%)

localize6.0ms (0.1%)

series82.0ms (1.7%)

rewrite65.0ms (1.4%)

simplify54.0ms (1.1%)

prune106.0ms (2.2%)

regimes1.1s (22.7%)

bsearch2.0ms (0%)

simplify7.0ms (0.2%)

end116.0ms (2.4%)

Profiling