Details

analyze377.0ms (12.7%)

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
37.4%	59.3%	3.3%	9
45.2%	48.4%	6.4%	10
56.9%	36.7%	6.4%	11
60.5%	30.8%	8.7%	12
64.2%	24.8%	11.1%	13
70.3%	18.6%	11.1%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample869.0ms (29.3%)

Results

807.0ms	8256×	body	128	valid
47.0ms	530×	body	128	invalid

Compiler

Compiled 22 to 16 computations (27.3% saved)

preprocess42.0ms (1.4%)

Algorithm

2×	egg-herbie

Rules

754×	`fma-def_binary64`
220×	`fma-neg_binary64`
86×	`distribute-rgt-in_binary64`
81×	`unsub-neg_binary64`
60×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	40
1	44	40
2	88	40
3	179	40
4	368	40
5	545	40
6	724	40
7	964	40
8	1709	40
9	1751	40
10	1828	40
11	1828	40
0	3	3
1	3	3

Stop Event

1×	unsound
1×	saturated

Symmetry

(sort y z)

Compiler

Compiled 10 to 7 computations (30% saved)

simplify19.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

419×	`fma-def_binary64`
121×	`fma-neg_binary64`
46×	`distribute-rgt-in_binary64`
44×	`associate-r_binary64`
43×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	17	10
2	34	10
3	80	10
4	227	10
5	306	10
6	418	10
7	551	10
8	883	10
9	1011	10
10	1091	10
11	1111	10

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

2.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	2.4b	(.f64 x (-.f64 1 (.f64 y z)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (*.f64 y z))
✓	2.2b	(.f64 x (-.f64 1 (.f64 y z)))

series12.0ms (0.4%)

Counts

2 → 42

Calls

15 calls:

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

rewrite42.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

760×	`log1p-expm1-u_binary64`
760×	`expm1-log1p-u_binary64`
423×	`prod-diff_binary64`
83×	`add-sqr-sqrt_binary64`
77×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	165	17
2	2057	17

Stop Event

1×	node limit

Counts

2 → 51

simplify33.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

428×	`fma-def_binary64`
125×	`fma-neg_binary64`
48×	`associate-l_binary64`
48×	`cancel-sign-sub-inv_binary64`
43×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	364
1	35	364
2	80	364
3	162	364
4	261	364
5	410	364
6	696	364
7	830	364
8	1045	364
9	1135	364

Stop Event

1×

saturated

Counts

93 → 60

prune43.0ms (1.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	52	8	60
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	52	9	61

Error

0.0b

Counts

61 → 9

Alt Table

Status	Error	Program
✓	2.4b	(.f64 x (-.f64 1 (.f64 y z)))
	4.9b	(fma.f64 y (*.f64 z (neg.f64 x)) x)
	34.2b	(exp.f64 (log.f64 (.f64 x (-.f64 1 (.f64 y z)))))
	38.4b	(cbrt.f64 (pow.f64 (.f64 x (-.f64 1 (.f64 y z))) 3))
	31.8b	(pow.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) 2)
	3.5b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) 3)
	16.1b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 y z) 2)) x) (+.f64 1 (*.f64 y z)))
	18.6b	(.f64 x (cbrt.f64 (pow.f64 (-.f64 1 (.f64 y z)) 3)))
▶	2.9b	(.f64 x (pow.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) 3))

Compiler

Compiled 927 to 537 computations (42.1% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 1 (*.f64 y z))
✓	0.3b	(pow.f64 (cbrt.f64 (-.f64 1 (*.f64 y z))) 3)
✓	2.2b	(.f64 x (pow.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) 3))
✓	2.4b	(cbrt.f64 (-.f64 1 (*.f64 y z)))

series128.0ms (4.3%)

Counts

3 → 52

Calls

21 calls:

51.0ms	(pow.f64 (cbrt.f64 (-.f64 1 (*.f64 y z))) 3)	y	0
49.0ms	(pow.f64 (cbrt.f64 (-.f64 1 (*.f64 y z))) 3)	z	0
3.0ms	(pow.f64 (cbrt.f64 (-.f64 1 (*.f64 y z))) 3)	y	-inf
3.0ms	(pow.f64 (cbrt.f64 (-.f64 1 (*.f64 y z))) 3)	y	inf
3.0ms	(pow.f64 (cbrt.f64 (-.f64 1 (*.f64 y z))) 3)	z	inf

rewrite52.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

476×	`log-prod_binary64`
423×	`prod-diff_binary64`
175×	`expm1-udef_binary64`
174×	`log1p-udef_binary64`
160×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	226	26
2	2542	26

Stop Event

1×	node limit

Counts

3 → 116

simplify29.0ms (1%)

Algorithm

1×	egg-herbie

Rules

699×	`fma-def_binary64`
602×	`cancel-sign-sub-inv_binary64`
340×	`distribute-rgt-neg-in_binary64`
329×	`distribute-lft-neg-in_binary64`
316×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	522
1	99	522
2	309	514
3	1399	498

Stop Event

1×	node limit

Counts

168 → 128

prune142.0ms (4.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	159	2	161
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	160	10	170

Error

0.0b

Counts

170 → 10

Alt Table

Status	Error	Program
✓	2.4b	(.f64 x (-.f64 1 (.f64 y z)))
	4.9b	(fma.f64 y (*.f64 z (neg.f64 x)) x)
	34.2b	(exp.f64 (log.f64 (.f64 x (-.f64 1 (.f64 y z)))))
	38.4b	(cbrt.f64 (pow.f64 (.f64 x (-.f64 1 (.f64 y z))) 3))
	31.8b	(pow.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) 2)
▶	3.5b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) 3)
	18.4b	(.f64 x (fma.f64 (.f64 (neg.f64 y) (sqrt.f64 z)) (sqrt.f64 z) 1))
	16.1b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 y z) 2)) x) (fma.f64 y z 1))
	18.6b	(.f64 x (cbrt.f64 (pow.f64 (-.f64 1 (.f64 y z)) 3)))
✓	2.9b	(.f64 x (pow.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) 3))

Compiler

Compiled 2571 to 1500 computations (41.7% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 1 (*.f64 y z))
✓	0.5b	(cbrt.f64 (.f64 x (-.f64 1 (.f64 y z))))
✓	0.7b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) 3)
	2.2b	(.f64 x (-.f64 1 (.f64 y z)))

series332.0ms (11.2%)

Counts

2 → 16

Calls

18 calls:

137.0ms	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) 3)	y	0
131.0ms	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) 3)	z	0
17.0ms	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) 3)	x	-inf
8.0ms	(cbrt.f64 (.f64 x (-.f64 1 (.f64 y z))))	x	-inf
6.0ms	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) 3)	x	0

rewrite47.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

482×	`log-prod_binary64`
423×	`prod-diff_binary64`
175×	`expm1-udef_binary64`
174×	`log1p-udef_binary64`
154×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	226	22
2	2550	22

Stop Event

1×	node limit

Counts

2 → 81

simplify37.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

612×	`unswap-sqr_binary64`
566×	`distribute-rgt-neg-in_binary64`
562×	`distribute-lft-neg-in_binary64`
405×	`fma-neg_binary64`
373×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	504
1	143	504
2	454	500
3	2390	500

Stop Event

1×	node limit

Counts

97 → 92

prune97.0ms (3.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	152	10	162

Error

0.0b

Counts

162 → 10

Alt Table

Status	Error	Program
✓	2.4b	(.f64 x (-.f64 1 (.f64 y z)))
▶	4.9b	(fma.f64 y (*.f64 z (neg.f64 x)) x)
	34.2b	(exp.f64 (log.f64 (.f64 x (-.f64 1 (.f64 y z)))))
	38.4b	(cbrt.f64 (pow.f64 (.f64 x (-.f64 1 (.f64 y z))) 3))
	31.8b	(pow.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) 2)
✓	3.5b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) 3)
	18.4b	(.f64 x (fma.f64 (.f64 (neg.f64 y) (sqrt.f64 z)) (sqrt.f64 z) 1))
	16.1b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 y z) 2)) x) (fma.f64 y z 1))
	18.6b	(.f64 x (cbrt.f64 (pow.f64 (-.f64 1 (.f64 y z)) 3)))
✓	2.9b	(.f64 x (pow.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) 3))

Compiler

Compiled 2596 to 1591 computations (38.7% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.7b	(fma.f64 y (*.f64 z (neg.f64 x)) x)

series9.0ms (0.3%)

Counts

1 → 36

Calls

9 calls:

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

rewrite47.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

557×	`log1p-expm1-u_binary64`
557×	`expm1-log1p-u_binary64`
314×	`log-prod_binary64`
172×	`prod-diff_binary64`
115×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	143	8
2	1832	8

Stop Event

1×	node limit

Counts

1 → 89

simplify29.0ms (1%)

Algorithm

1×	egg-herbie

Rules

412×	`fma-def_binary64`
110×	`fma-neg_binary64`
61×	`associate-l_binary64`
53×	`distribute-rgt-in_binary64`
45×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	338
1	43	338
2	102	338
3	222	338
4	385	338
5	606	338
6	1038	338
7	1087	338
8	1159	338

Stop Event

1×

saturated

Counts

125 → 96

prune57.0ms (1.9%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	96	10	106

Error

0.0b

Counts

106 → 10

Alt Table

Status	Error	Program
✓	2.4b	(.f64 x (-.f64 1 (.f64 y z)))
✓	4.9b	(fma.f64 y (*.f64 z (neg.f64 x)) x)
	34.2b	(exp.f64 (log.f64 (.f64 x (-.f64 1 (.f64 y z)))))
	38.4b	(cbrt.f64 (pow.f64 (.f64 x (-.f64 1 (.f64 y z))) 3))
	31.8b	(pow.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) 2)
✓	3.5b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) 3)
	18.4b	(.f64 x (fma.f64 (.f64 (neg.f64 y) (sqrt.f64 z)) (sqrt.f64 z) 1))
	16.1b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 y z) 2)) x) (fma.f64 y z 1))
	18.6b	(.f64 x (cbrt.f64 (pow.f64 (-.f64 1 (.f64 y z)) 3)))
✓	2.9b	(.f64 x (pow.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) 3))

Compiler

Compiled 2444 to 962 computations (60.6% saved)

regimes222.0ms (7.5%)

Accuracy

Total 1.6b remaining (98.1%)

Threshold costs 0b (0%)

Counts

25 → 2

Compiler

Compiled 2194 to 1626 computations (25.9% saved)

bsearch1.0ms (0%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

(*.f64 x (-.f64 1 (*.f64 y z)))

Steps

Iters	Point		Range
#hash((type . real) (value . -inf))	∈ [	#hash((type . real) (value . -inf))	,	-8.009673229782804e+307	]

Compiler

Compiled 10 to 7 computations (30% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
7×	`+-commutative_binary64`
7×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	34
1	31	34
2	52	34
3	68	34
4	75	34
5	77	34

Stop Event

1×

saturated

end263.0ms (8.9%)

Stop Event

1×

fuel

Compiler

Compiled 232 to 157 computations (32.3% saved)

Details

analyze377.0ms (12.7%)

sample869.0ms (29.3%)

preprocess42.0ms (1.4%)

simplify19.0ms (0.6%)

prune1.0ms (0%)

localize5.0ms (0.2%)

series12.0ms (0.4%)

rewrite42.0ms (1.4%)

simplify33.0ms (1.1%)

prune43.0ms (1.5%)

localize10.0ms (0.4%)

series128.0ms (4.3%)

rewrite52.0ms (1.8%)

simplify29.0ms (1%)

prune142.0ms (4.8%)

localize7.0ms (0.2%)

series332.0ms (11.2%)

rewrite47.0ms (1.6%)

simplify37.0ms (1.2%)

prune97.0ms (3.3%)

localize6.0ms (0.2%)

series9.0ms (0.3%)

rewrite47.0ms (1.6%)

simplify29.0ms (1%)

prune57.0ms (1.9%)

regimes222.0ms (7.5%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end263.0ms (8.9%)

Profiling