Details

analyze1.2s (24.5%)

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
0%	99.8%	0.2%	8
2.3%	97.4%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
29.7%	70%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.1s (22.7%)

Results

981.0ms	8253×	body	128	valid
103.0ms	743×	body	128	invalid
1.0ms	2×	body	1024	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify22.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

734×	`fma-def_binary64`
533×	`div-sub_binary64`
511×	`fma-neg_binary64`
499×	`times-frac_binary64`
213×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	19	16
2	40	14
3	85	14
4	194	14
5	394	14
6	832	14
7	2375	14

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.1b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	11.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
✓	1.0b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

series52.0ms (1%)

Counts

2 → 96

Calls

2 calls:

34.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
18.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

rewrite54.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

365×	`fma-def_binary64`
224×	`expm1-udef_binary64`
224×	`log1p-udef_binary64`
200×	`fma-neg_binary64`
193×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	227	24
2	3413	24

Stop Event

1×	node limit

Counts

2 → 77

Calls

2 calls:

52.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
52.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

simplify52.0ms (1%)

Algorithm

1×	egg-herbie

Rules

774×	`fma-def_binary64`
656×	`times-frac_binary64`
494×	`cancel-sign-sub-inv_binary64`
325×	`sub-neg_binary64`
153×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	2936
1	568	2936
2	1962	2292

Stop Event

1×	node limit

Counts

173 → 153

prune133.0ms (2.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	148	5	153
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	150	5	155

Error

Counts

155 → 5

Alt Table

Status	Error	Program
	11.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (.f64 y t) (-.f64 z a)))
	35.1b	(fma.f64 y (.f64 (sqrt.f64 (-.f64 z t)) (.f64 (sqrt.f64 (-.f64 z t)) (/.f64 1 (-.f64 z a)))) x)
▶	1.1b	(fma.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a))) x)
	29.7b	(/.f64 (-.f64 (.f64 (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))) (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t)))) (.f64 x x)) (-.f64 (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))) x))
	2.9b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))

Compiler

Compiled 3562 to 1243 computations (65.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 z a))
✓	0.0b	(-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a)))
✓	0.0b	(/.f64 z (-.f64 z a))
✓	1.0b	(fma.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a))) x)

series83.0ms (1.7%)

Counts

4 → 135

Calls

4 calls:

42.0ms	(fma.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a))) x)
18.0ms	(-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a)))
15.0ms	(/.f64 t (-.f64 z a))
9.0ms	(/.f64 z (-.f64 z a))

rewrite70.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

308×	`fma-neg_binary64`
250×	`expm1-udef_binary64`
250×	`log1p-udef_binary64`
169×	`egg-rr`
136×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	38
1	255	38
2	4065	38

Stop Event

1×	node limit

Counts

4 → 169

Calls

4 calls:

67.0ms	(/.f64 t (-.f64 z a))
67.0ms	(-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a)))
67.0ms	(/.f64 z (-.f64 z a))
67.0ms	(fma.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a))) x)

simplify65.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

820×	`fma-def_binary64`
661×	`times-frac_binary64`
513×	`cancel-sign-sub-inv_binary64`
346×	`sub-neg_binary64`
153×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	3858
1	608	3849
2	2105	3428

Stop Event

1×	node limit

Counts

304 → 273

prune203.0ms (4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	272	1	273
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	273	5	278

Error

Counts

278 → 5

Alt Table

Status	Error	Program
✓	1.1b	(fma.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a))) x)
	29.7b	(/.f64 (-.f64 (.f64 (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))) (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t)))) (.f64 x x)) (-.f64 (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))) x))
▶	2.9b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
	11.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 z a)) x) (/.f64 (.f64 y t) (-.f64 z a)))
	31.2b	(fma.f64 y (/.f64 (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 z a))) (sqrt.f64 (-.f64 z a))) x)

Compiler

Compiled 6394 to 2000 computations (68.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
✓	0.0b	(/.f64 y (-.f64 z a))
✓	10.3b	(*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t))

series82.0ms (1.6%)

Counts

3 → 132

Calls

3 calls:

39.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
29.0ms	(*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t))
13.0ms	(/.f64 y (-.f64 z a))

rewrite64.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

258×	`fma-neg_binary64`
250×	`expm1-udef_binary64`
250×	`log1p-udef_binary64`
136×	`add-sqr-sqrt_binary64`
131×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	255	34
2	3956	34

Stop Event

1×	node limit

Counts

3 → 113

Calls

3 calls:

62.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
62.0ms	(/.f64 y (-.f64 z a))
62.0ms	(*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t))

simplify62.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-def_binary64`
679×	`times-frac_binary64`
528×	`cancel-sign-sub-inv_binary64`
278×	`sub-neg_binary64`
143×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	179	3947
1	585	3704
2	1905	3086

Stop Event

1×	node limit

Counts

245 → 212

prune142.0ms (2.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	211	1	212
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	213	4	217

Error

Counts

217 → 4

Alt Table

Status	Error	Program
✓	1.1b	(fma.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a))) x)
✓	2.9b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
	31.2b	(fma.f64 y (/.f64 (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 z a))) (sqrt.f64 (-.f64 z a))) x)
▶	11.8b	(+.f64 x (/.f64 1 (/.f64 (-.f64 z a) (*.f64 y (-.f64 z t)))))

Compiler

Compiled 4944 to 1622 computations (67.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 1 (/.f64 (-.f64 z a) (*.f64 y (-.f64 z t)))))
✓	0.0b	(*.f64 y (-.f64 z t))
✓	0.6b	(/.f64 1 (/.f64 (-.f64 z a) (*.f64 y (-.f64 z t))))
✓	11.7b	(/.f64 (-.f64 z a) (*.f64 y (-.f64 z t)))

series102.0ms (2%)

Counts

4 → 192

Calls

4 calls:

41.0ms	(+.f64 x (/.f64 1 (/.f64 (-.f64 z a) (*.f64 y (-.f64 z t)))))
27.0ms	(/.f64 (-.f64 z a) (*.f64 y (-.f64 z t)))
27.0ms	(/.f64 1 (/.f64 (-.f64 z a) (*.f64 y (-.f64 z t))))
7.0ms	(*.f64 y (-.f64 z t))

rewrite69.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

280×	`log1p-udef_binary64`
156×	`add-sqr-sqrt_binary64`
153×	`egg-rr`
149×	`add-cbrt-cube_binary64`
149×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	55
1	299	49
2	4647	49

Stop Event

1×	node limit

Counts

4 → 153

Calls

4 calls:

66.0ms	(+.f64 x (/.f64 1 (/.f64 (-.f64 z a) (*.f64 y (-.f64 z t)))))
66.0ms	(*.f64 y (-.f64 z t))
66.0ms	(/.f64 1 (/.f64 (-.f64 z a) (*.f64 y (-.f64 z t))))
66.0ms	(/.f64 (-.f64 z a) (*.f64 y (-.f64 z t)))

simplify84.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

753×	`cancel-sign-sub-inv_binary64`
445×	`sub-neg_binary64`
211×	`associate--l+_binary64`
204×	`fma-neg_binary64`
180×	`associate--r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	216	5131
1	756	4808
2	2716	4225

Stop Event

1×	node limit

Counts

345 → 274

prune171.0ms (3.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	274	0	274
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	274	4	278

Error

Counts

278 → 4

Alt Table

Status	Error	Program
✓	1.1b	(fma.f64 y (-.f64 (/.f64 z (-.f64 z a)) (/.f64 t (-.f64 z a))) x)
✓	2.9b	(+.f64 x (*.f64 (/.f64 y (-.f64 z a)) (-.f64 z t)))
	31.2b	(fma.f64 y (/.f64 (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 z a))) (sqrt.f64 (-.f64 z a))) x)
✓	11.8b	(+.f64 x (/.f64 1 (/.f64 (-.f64 z a) (*.f64 y (-.f64 z t)))))

Compiler

Compiled 6605 to 2246 computations (66% saved)

regimes1.0s (20.9%)

Accuracy

Total 1.2b remaining (98.7%)

Threshold costs 0b (0%)

Counts

162 → 1

Compiler

Compiled 20428 to 12833 computations (37.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	20	16
2	27	16
3	31	16
4	33	16

Stop Event

1×

saturated

end56.0ms (1.1%)

Compiler: Compiled 106 to 63 computations (40.6% saved)

Details

analyze1.2s (24.5%)

sample1.1s (22.7%)

simplify22.0ms (0.4%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series52.0ms (1%)

rewrite54.0ms (1.1%)

simplify52.0ms (1%)

prune133.0ms (2.7%)

localize8.0ms (0.2%)

series83.0ms (1.7%)

rewrite70.0ms (1.4%)

simplify65.0ms (1.3%)

prune203.0ms (4%)

localize7.0ms (0.1%)

series82.0ms (1.6%)

rewrite64.0ms (1.3%)

simplify62.0ms (1.2%)

prune142.0ms (2.8%)

localize8.0ms (0.2%)

series102.0ms (2%)

rewrite69.0ms (1.4%)

simplify84.0ms (1.7%)

prune171.0ms (3.4%)

regimes1.0s (20.9%)

simplify2.0ms (0%)

end56.0ms (1.1%)

Profiling