Details

analyze418.0ms (12.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
31.2%	68.6%	0.1%	8
34.3%	62.4%	3.3%	9
42.1%	49.9%	7.9%	10
53.8%	37.8%	8.3%	11
56.2%	33%	10.9%	12
60.3%	25.6%	14.1%	13
66.4%	19.4%	14.2%	14

Compiler

Compiled 13 to 10 computations (23.1% saved)

sample877.0ms (25.7%)

Results

797.0ms	8256×	body	128	valid
66.0ms	679×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

preprocess111.0ms (3.3%)

Algorithm

2×	egg-herbie

Rules

2243×	`fma-neg_binary64`
413×	`unsub-neg_binary64`
262×	`associate--r+_binary64`
234×	`distribute-rgt-in_binary64`
215×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	52
1	55	52
2	144	44
3	494	44
4	1584	44
5	2961	44
6	3611	44
7	3718	44
8	3756	44
9	3772	44
10	3960	44
11	4041	44
12	4087	44
13	4154	44
14	4204	44
15	4204	44
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 12 to 9 computations (25% saved)

simplify31.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-def_binary64`
419×	`fma-neg_binary64`
208×	`distribute-rgt-in_binary64`
163×	`distribute-lft-in_binary64`
138×	`unsub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	20	13
2	49	11
3	153	11
4	470	11
5	1119	11
6	1863	11
7	2564	11
8	2672	11
9	2672	11

Stop Event

1×

saturated

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
	5.6b	(fma.f64 z (-.f64 (*.f64 x y) x) x)
▶	3.1b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))

Compiler

Compiled 66 to 42 computations (36.4% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (*.f64 (-.f64 1 y) z))
✓	0.0b	(*.f64 (-.f64 1 y) z)
✓	2.9b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))

series19.0ms (0.6%)

Counts

3 → 72

Calls

21 calls:

2.0ms	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))	x	-inf
1.0ms	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))	x	0
1.0ms	(*.f64 (-.f64 1 y) z)	y	inf
1.0ms	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))	x	inf
1.0ms	(*.f64 (-.f64 1 y) z)	z	-inf

rewrite62.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

555×	`prod-diff_binary64`
479×	`log-prod_binary64`
199×	`fma-def_binary64`
175×	`expm1-udef_binary64`
173×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	195	30
2	2550	30

Stop Event

1×	node limit

Counts

3 → 117

simplify58.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

608×	`fma-neg_binary64`
428×	`fma-def_binary64`
131×	`unsub-neg_binary64`
123×	`cancel-sign-sub-inv_binary64`
113×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	715
1	77	619
2	194	619
3	438	619
4	921	619
5	1752	619
6	2299	619
7	2459	619
8	2471	619
9	2471	619

Stop Event

1×

saturated

Counts

189 → 142

prune102.0ms (3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	139	3	142
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	139	5	144

Error

0.0b

Counts

144 → 5

Alt Table

Status	Error	Program
✓	3.1b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))
	25.9b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 (-.f64 1 y) z) 3)) x) (fma.f64 (*.f64 (-.f64 1 y) z) (fma.f64 (-.f64 1 y) z 1) 1))
	5.6b	(fma.f64 z (-.f64 (*.f64 x y) x) x)
▶	1.5b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
	23.6b	(.f64 x (-.f64 1 (cbrt.f64 (pow.f64 (.f64 (-.f64 1 y) z) 3))))

Compiler

Compiled 2090 to 1372 computations (34.4% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 y (.f64 z x)) x)
✓	0.0b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
✓	2.8b	(.f64 y (.f64 z x))

series26.0ms (0.8%)

Counts

3 → 60

Calls

27 calls:

2.0ms	(+.f64 (.f64 y (.f64 z x)) x)	x	-inf
1.0ms	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))	x	-inf
1.0ms	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))	x	inf
1.0ms	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))	x	0
1.0ms	(+.f64 (.f64 y (.f64 z x)) x)	x	inf

rewrite68.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

680×	`fma-def_binary64`
321×	`fma-neg_binary64`
248×	`egg-rr`
178×	`expm1-udef_binary64`
178×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	29
1	187	29
2	2873	29

Stop Event

1×	node limit

Counts

3 → 248

simplify53.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

850×	`fma-def_binary64`
459×	`fma-neg_binary64`
142×	`distribute-rgt-in_binary64`
135×	`unsub-neg_binary64`
109×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	696
1	71	528
2	187	528
3	500	528
4	1276	528
5	2190	528
6	2772	528
7	2792	528
8	2792	528

Stop Event

1×

saturated

Counts

308 → 263

prune223.0ms (6.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	259	4	263
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	259	9	268

Error

Counts

268 → 9

Alt Table

Status	Error	Program
	13.8b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 z x) 2)) (.f64 (cbrt.f64 (.f64 z x)) y) (-.f64 x (.f64 z x)))
	23.6b	(.f64 x (-.f64 1 (cbrt.f64 (pow.f64 (.f64 (-.f64 1 y) z) 3))))
✓	3.1b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))
	25.9b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 (-.f64 1 y) z) 3)) x) (fma.f64 (*.f64 (-.f64 1 y) z) (fma.f64 (-.f64 1 y) z 1) 1))
▶	5.6b	(fma.f64 z (-.f64 (*.f64 x y) x) x)
	36.6b	(-.f64 (/.f64 (+.f64 (pow.f64 (.f64 y (.f64 z x)) 3) (pow.f64 x 3)) (fma.f64 x (-.f64 x (.f64 y (.f64 z x))) (pow.f64 (.f64 y (.f64 z x)) 2))) (*.f64 z x))
✓	1.5b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
	35.8b	(fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (.f64 z x)) (-.f64 x (*.f64 z x)))
	25.3b	(-.f64 (+.f64 (pow.f64 (sqrt.f64 (.f64 y (.f64 z x))) 2) x) (*.f64 z x))

Compiler

Compiled 4997 to 1884 computations (62.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 x y) x)
✓	5.3b	(fma.f64 z (-.f64 (*.f64 x y) x) x)

series14.0ms (0.4%)

Counts

2 → 60

Calls

15 calls:

2.0ms	(fma.f64 z (-.f64 (*.f64 x y) x) x)	z	0
1.0ms	(fma.f64 z (-.f64 (*.f64 x y) x) x)	x	-inf
1.0ms	(fma.f64 z (-.f64 (*.f64 x y) x) x)	x	inf
1.0ms	(fma.f64 z (-.f64 (*.f64 x y) x) x)	z	inf
1.0ms	(fma.f64 z (-.f64 (*.f64 x y) x) x)	z	-inf

rewrite53.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

778×	`log1p-expm1-u_binary64`
778×	`expm1-log1p-u_binary64`
680×	`prod-diff_binary64`
115×	`egg-rr`
79×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	151	18
2	2051	18

Stop Event

1×	node limit

Counts

2 → 115

simplify66.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-def_binary64`
436×	`fma-neg_binary64`
144×	`distribute-rgt-in_binary64`
133×	`unsub-neg_binary64`
112×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	32	620
1	90	530
2	218	530
3	554	530
4	1345	530
5	2164	530
6	2657	530
7	2677	530
8	2677	530

Stop Event

1×

saturated

Counts

175 → 136

prune123.0ms (3.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	136	9	145

Error

Counts

145 → 9

Alt Table

Status	Error	Program
▶	13.8b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 z x) 2)) (.f64 (cbrt.f64 (.f64 z x)) y) (-.f64 x (.f64 z x)))
	23.6b	(.f64 x (-.f64 1 (cbrt.f64 (pow.f64 (.f64 (-.f64 1 y) z) 3))))
✓	3.1b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))
	25.9b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 (-.f64 1 y) z) 3)) x) (fma.f64 (*.f64 (-.f64 1 y) z) (fma.f64 (-.f64 1 y) z 1) 1))
	30.6b	(fma.f64 z (fma.f64 (sqrt.f64 (.f64 x y)) (sqrt.f64 (.f64 x y)) (neg.f64 x)) x)
✓	5.6b	(fma.f64 z (-.f64 (*.f64 x y) x) x)
✓	1.5b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
	35.8b	(fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (.f64 z x)) (-.f64 x (*.f64 z x)))
	25.3b	(-.f64 (+.f64 (pow.f64 (sqrt.f64 (.f64 y (.f64 z x))) 2) x) (*.f64 z x))

Compiler

Compiled 2410 to 815 computations (66.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cbrt.f64 (.f64 z x)) y)
✓	0.3b	(pow.f64 (*.f64 z x) 2)
✓	7.9b	(cbrt.f64 (*.f64 z x))
✓	26.2b	(cbrt.f64 (pow.f64 (*.f64 z x) 2))

series134.0ms (3.9%)

Counts

4 → 36

Calls

27 calls:

22.0ms	(.f64 (cbrt.f64 (.f64 z x)) y)	y	0
21.0ms	(.f64 (cbrt.f64 (.f64 z x)) y)	y	-inf
18.0ms	(.f64 (cbrt.f64 (.f64 z x)) y)	y	inf
12.0ms	(cbrt.f64 (*.f64 z x))	z	-inf
12.0ms	(.f64 (cbrt.f64 (.f64 z x)) y)	x	-inf

rewrite51.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

759×	`log1p-expm1-u_binary64`
759×	`expm1-log1p-u_binary64`
157×	`log1p-udef_binary64`
96×	`egg-rr`
91×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	199	31
2	2200	31

Stop Event

1×	node limit

Counts

4 → 96

simplify105.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

2318×	`associate-l_binary64`
791×	`sqr-pow_binary64`
265×	`pow-sqr_binary64`
263×	`unswap-sqr_binary64`
232×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	348
1	28	348
2	55	348
3	139	348
4	529	348
5	1055	348
6	1135	348
7	1256	348
8	1404	348
9	1561	348
10	1754	348
11	1976	348
12	2232	348
13	2527	348
14	2848	348
15	3188	348
16	3558	348
17	3948	348
18	4048	348
19	4126	348

Stop Event

1×	node limit

Counts

132 → 99

prune97.0ms (2.9%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	99	9	108

Error

Counts

108 → 9

Alt Table

Status	Error	Program
✓	13.8b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 z x) 2)) (.f64 (cbrt.f64 (.f64 z x)) y) (-.f64 x (.f64 z x)))
	23.6b	(.f64 x (-.f64 1 (cbrt.f64 (pow.f64 (.f64 (-.f64 1 y) z) 3))))
✓	3.1b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))
	25.9b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 (-.f64 1 y) z) 3)) x) (fma.f64 (*.f64 (-.f64 1 y) z) (fma.f64 (-.f64 1 y) z 1) 1))
	30.6b	(fma.f64 z (fma.f64 (sqrt.f64 (.f64 x y)) (sqrt.f64 (.f64 x y)) (neg.f64 x)) x)
✓	5.6b	(fma.f64 z (-.f64 (*.f64 x y) x) x)
✓	1.5b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
	35.8b	(fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (.f64 z x)) (-.f64 x (*.f64 z x)))
	25.3b	(-.f64 (+.f64 (pow.f64 (sqrt.f64 (.f64 y (.f64 z x))) 2) x) (*.f64 z x))

Compiler

Compiled 2326 to 756 computations (67.5% saved)

regimes539.0ms (15.8%)

Accuracy

Total 0.2b remaining (95.7%)

Threshold costs 0.2b (95.7%)

Counts

47 → 3

Compiler

Compiled 5046 to 3002 computations (40.5% saved)

bsearch28.0ms (0.8%)

Algorithm

2×	binary-search

Calls

2 calls:

19.0ms	z
8.0ms	z

Steps

Iters	Point		Range
4.6176097849876254e-54	∈ [	6.552312162094534e-56	,	8.610650488274598e-54	]
-2.8203134534163076e-14	∈ [	-1.9102760442637524e-12	,	-2.3356543987893667e-15	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	48
1	34	48
2	48	48
3	54	48
4	57	48

Stop Event

1×

saturated

end116.0ms (3.4%)

Stop Event

1×

fuel

Compiler

Compiled 226 to 130 computations (42.5% saved)

Details

analyze418.0ms (12.2%)

sample877.0ms (25.7%)

preprocess111.0ms (3.3%)

simplify31.0ms (0.9%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series19.0ms (0.6%)

rewrite62.0ms (1.8%)

simplify58.0ms (1.7%)

prune102.0ms (3%)

localize7.0ms (0.2%)

series26.0ms (0.8%)

rewrite68.0ms (2%)

simplify53.0ms (1.6%)

prune223.0ms (6.5%)

localize5.0ms (0.1%)

series14.0ms (0.4%)

rewrite53.0ms (1.5%)

simplify66.0ms (1.9%)

prune123.0ms (3.6%)

localize11.0ms (0.3%)

series134.0ms (3.9%)

rewrite51.0ms (1.5%)

simplify105.0ms (3.1%)

prune97.0ms (2.9%)

regimes539.0ms (15.8%)

bsearch28.0ms (0.8%)

simplify3.0ms (0.1%)

end116.0ms (3.4%)

Profiling