Details

analyze340.0ms (8.8%)

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
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample988.0ms (25.6%)

Results

923.0ms	8256×	body	128	valid
52.0ms	478×	body	128	invalid

Compiler

Compiled 30 to 22 computations (26.7% saved)

preprocess29.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

131×	`fma-def_binary64`
98×	`associate-l_binary64`
68×	`associate-r_binary64`
58×	`distribute-lft-in_binary64`
58×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	64
1	69	56
2	146	56
3	322	56
4	491	56
5	616	56
6	624	56
0	3	3
1	3	3

Stop Event

1×	unsound
1×	saturated

Symmetry

(sort x y)

Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

44×	`fma-def_binary64`
31×	`associate-l_binary64`
30×	`associate-r_binary64`
19×	`distribute-lft-in_binary64`
19×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	24	14
2	46	14
3	107	14
4	173	14
5	234	14
6	238	14

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

5.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	5.9b	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
	6.2b	(/.f64 1 (.f64 x (.f64 y (fma.f64 z z 1))))

Compiler

Compiled 78 to 54 computations (30.8% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.1b	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
✓	5.2b	(.f64 y (+.f64 1 (.f64 z z)))

series89.0ms (2.3%)

Counts

2 → 60

Calls

15 calls:

18.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))	x	0
15.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))	x	-inf
12.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))	y	-inf
11.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))	y	0
10.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))	x	inf

rewrite54.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

289×	`prod-diff_binary64`
220×	`fma-def_binary64`
187×	`expm1-udef_binary64`
187×	`log1p-udef_binary64`
170×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	222	22
2	3134	22

Stop Event

1×	node limit

Counts

2 → 98

simplify49.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

671×	`times-frac_binary64`
428×	`distribute-neg-frac_binary64`
318×	`associate-/l*_binary64`
199×	`sub-neg_binary64`
189×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	993
1	151	903
2	366	901
3	1295	897
4	4292	897

Stop Event

1×	node limit

Counts

158 → 124

prune108.0ms (2.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	114	10	124
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	115	11	126

Error

0.0b

Counts

126 → 11

Alt Table

Status	Error	Program
	6.4b	(pow.f64 (.f64 (fma.f64 z z 1) (.f64 y x)) -1)
	30.1b	(/.f64 (/.f64 (/.f64 1 y) z) (*.f64 z x))
	49.2b	(.f64 (/.f64 (pow.f64 x -1/2) (pow.f64 (cbrt.f64 (.f64 y (fma.f64 z z 1))) 2)) (/.f64 (pow.f64 x -1/2) (cbrt.f64 (*.f64 y (fma.f64 z z 1)))))
	6.3b	(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
▶	5.7b	(*.f64 1 (/.f64 (/.f64 (/.f64 1 y) (fma.f64 z z 1)) x))
	5.9b	(/.f64 (/.f64 1 x) (fma.f64 y (*.f64 z z) y))
	16.1b	(.f64 (/.f64 1 (.f64 (sqrt.f64 y) (hypot.f64 1 z))) (/.f64 (/.f64 1 x) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	32.1b	(/.f64 (/.f64 1 x) (.f64 z (.f64 y z)))
	6.4b	(*.f64 (cbrt.f64 (/.f64 (/.f64 (/.f64 1 y) (fma.f64 z z 1)) x)) (pow.f64 (cbrt.f64 (/.f64 (/.f64 (/.f64 1 y) (fma.f64 z z 1)) x)) 2))
	9.7b	(/.f64 (/.f64 1 x) (fma.f64 (*.f64 y (cbrt.f64 (pow.f64 z 4))) (pow.f64 (cbrt.f64 z) 2) y))
	6.2b	(/.f64 1 (.f64 x (.f64 y (fma.f64 z z 1))))

Compiler

Compiled 2310 to 1364 computations (41% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	2.6b	(/.f64 (/.f64 (/.f64 1 y) (fma.f64 z z 1)) x)
✓	5.4b	(/.f64 (/.f64 1 y) (fma.f64 z z 1))

series118.0ms (3.1%)

Counts

2 → 60

Calls

15 calls:

22.0ms	(/.f64 (/.f64 (/.f64 1 y) (fma.f64 z z 1)) x)	y	0
16.0ms	(/.f64 (/.f64 (/.f64 1 y) (fma.f64 z z 1)) x)	x	0
16.0ms	(/.f64 (/.f64 (/.f64 1 y) (fma.f64 z z 1)) x)	x	-inf
11.0ms	(/.f64 (/.f64 (/.f64 1 y) (fma.f64 z z 1)) x)	y	-inf
10.0ms	(/.f64 (/.f64 (/.f64 1 y) (fma.f64 z z 1)) x)	y	inf

rewrite51.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

499×	`log-prod_binary64`
176×	`pow1/3_binary64`
171×	`expm1-udef_binary64`
171×	`log1p-udef_binary64`
162×	`pow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	192	25
2	2688	25

Stop Event

1×	node limit

Counts

2 → 86

simplify38.0ms (1%)

Algorithm

1×	egg-herbie

Rules

710×	`times-frac_binary64`
342×	`associate-/l*_binary64`
281×	`fma-def_binary64`
265×	`associate-/l/_binary64`
185×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	1170
1	199	1146
2	474	1144
3	1628	1134

Stop Event

1×	node limit

Counts

146 → 123

prune128.0ms (3.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	126	8	134

Error

0.0b

Counts

134 → 8

Alt Table

Status	Error	Program
	20.8b	(.f64 1 (.f64 (/.f64 (pow.f64 y -1/2) x) (/.f64 (pow.f64 y -1/2) (fma.f64 z z 1))))
	9.7b	(/.f64 (/.f64 1 x) (fma.f64 (*.f64 y (cbrt.f64 (pow.f64 z 4))) (pow.f64 (cbrt.f64 z) 2) y))
	30.1b	(/.f64 (/.f64 (/.f64 1 y) z) (*.f64 z x))
	16.1b	(.f64 (/.f64 1 (.f64 (sqrt.f64 y) (hypot.f64 1 z))) (/.f64 (/.f64 1 x) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	6.3b	(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
	32.1b	(/.f64 (/.f64 1 x) (.f64 z (.f64 y z)))
✓	5.7b	(*.f64 1 (/.f64 (/.f64 (/.f64 1 y) (fma.f64 z z 1)) x))
▶	6.2b	(/.f64 1 (.f64 x (.f64 y (fma.f64 z z 1))))

Compiler

Compiled 2522 to 1743 computations (30.9% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.8b	(/.f64 1 (.f64 x (.f64 y (fma.f64 z z 1))))
✓	2.6b	(.f64 x (.f64 y (fma.f64 z z 1)))
✓	5.2b	(*.f64 y (fma.f64 z z 1))

series103.0ms (2.7%)

Counts

3 → 96

Calls

24 calls:

13.0ms	(/.f64 1 (.f64 x (.f64 y (fma.f64 z z 1))))	x	-inf
11.0ms	(/.f64 1 (.f64 x (.f64 y (fma.f64 z z 1))))	x	0
10.0ms	(/.f64 1 (.f64 x (.f64 y (fma.f64 z z 1))))	y	0
10.0ms	(/.f64 1 (.f64 x (.f64 y (fma.f64 z z 1))))	y	-inf
10.0ms	(/.f64 1 (.f64 x (.f64 y (fma.f64 z z 1))))	x	inf

rewrite45.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

797×	`log1p-expm1-u_binary64`
797×	`expm1-log1p-u_binary64`
89×	`add-sqr-sqrt_binary64`
81×	`add-cbrt-cube_binary64`
81×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	180	33
2	2226	33

Stop Event

1×	node limit

Counts

3 → 69

simplify54.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

671×	`times-frac_binary64`
429×	`distribute-neg-frac_binary64`
327×	`associate-/l*_binary64`
199×	`sub-neg_binary64`
189×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	57	1446
1	154	1290
2	369	1288
3	1294	1284
4	4293	1284

Stop Event

1×	node limit

Counts

165 → 104

prune96.0ms (2.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	104	8	112

Error

0.0b

Counts

112 → 8

Alt Table

Status	Error	Program
	20.8b	(.f64 1 (.f64 (/.f64 (pow.f64 y -1/2) x) (/.f64 (pow.f64 y -1/2) (fma.f64 z z 1))))
	9.7b	(/.f64 (/.f64 1 x) (fma.f64 (*.f64 y (cbrt.f64 (pow.f64 z 4))) (pow.f64 (cbrt.f64 z) 2) y))
▶	3.6b	(/.f64 1 (.f64 y (fma.f64 z (.f64 z x) x)))
	30.1b	(/.f64 (/.f64 (/.f64 1 y) z) (*.f64 z x))
	16.1b	(.f64 (/.f64 1 (.f64 (sqrt.f64 y) (hypot.f64 1 z))) (/.f64 (/.f64 1 x) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	6.3b	(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
	32.1b	(/.f64 (/.f64 1 x) (.f64 z (.f64 y z)))
✓	5.7b	(*.f64 1 (/.f64 (/.f64 (/.f64 1 y) (fma.f64 z z 1)) x))

Compiler

Compiled 1709 to 1071 computations (37.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (*.f64 z x) x)
✓	0.8b	(/.f64 1 (.f64 y (fma.f64 z (.f64 z x) x)))
✓	2.8b	(.f64 y (fma.f64 z (.f64 z x) x))

series111.0ms (2.9%)

Counts

3 → 96

Calls

24 calls:

17.0ms	(/.f64 1 (.f64 y (fma.f64 z (.f64 z x) x)))	x	-inf
15.0ms	(/.f64 1 (.f64 y (fma.f64 z (.f64 z x) x)))	y	0
11.0ms	(/.f64 1 (.f64 y (fma.f64 z (.f64 z x) x)))	y	-inf
10.0ms	(/.f64 1 (.f64 y (fma.f64 z (.f64 z x) x)))	y	inf
10.0ms	(/.f64 1 (.f64 y (fma.f64 z (.f64 z x) x)))	x	0

rewrite53.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

784×	`log1p-expm1-u_binary64`
784×	`expm1-log1p-u_binary64`
153×	`prod-diff_binary64`
89×	`add-sqr-sqrt_binary64`
81×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	179	33
2	2187	33

Stop Event

1×	node limit

Counts

3 → 73

simplify62.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

555×	`times-frac_binary64`
418×	`distribute-neg-frac_binary64`
299×	`associate-/l*_binary64`
199×	`sub-neg_binary64`
195×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	1290
1	146	1290
2	369	1288
3	1230	1284
4	3996	1284

Stop Event

1×	node limit

Counts

169 → 108

prune82.0ms (2.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	108	8	116

Error

0.0b

Counts

116 → 8

Alt Table

Status	Error	Program
	20.8b	(.f64 1 (.f64 (/.f64 (pow.f64 y -1/2) x) (/.f64 (pow.f64 y -1/2) (fma.f64 z z 1))))
	9.7b	(/.f64 (/.f64 1 x) (fma.f64 (*.f64 y (cbrt.f64 (pow.f64 z 4))) (pow.f64 (cbrt.f64 z) 2) y))
✓	3.6b	(/.f64 1 (.f64 y (fma.f64 z (.f64 z x) x)))
	30.1b	(/.f64 (/.f64 (/.f64 1 y) z) (*.f64 z x))
	16.1b	(.f64 (/.f64 1 (.f64 (sqrt.f64 y) (hypot.f64 1 z))) (/.f64 (/.f64 1 x) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	6.3b	(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
	32.1b	(/.f64 (/.f64 1 x) (.f64 z (.f64 y z)))
✓	5.7b	(*.f64 1 (/.f64 (/.f64 (/.f64 1 y) (fma.f64 z z 1)) x))

Compiler

Compiled 1693 to 753 computations (55.5% saved)

regimes962.0ms (24.9%)

Accuracy

Total 0.4b remaining (95.5%)

Threshold costs 0.4b (95.5%)

Counts

86 → 2

Compiler

Compiled 11596 to 8375 computations (27.8% saved)

bsearch2.0ms (0.1%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

(*.f64 y (+.f64 1 (*.f64 z z)))

Steps

Iters	Point		Range
5.786246149407601e+285	∈ [	5.786246149407601e+285	,	1.8947436636436216e+290	]

Compiler

Compiled 10 to 7 computations (30% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	66
1	34	66

Stop Event

1×

saturated

end256.0ms (6.6%)

Stop Event

1×

fuel

Compiler

Compiled 313 to 224 computations (28.4% saved)

Details

analyze340.0ms (8.8%)

sample988.0ms (25.6%)

preprocess29.0ms (0.8%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series89.0ms (2.3%)

rewrite54.0ms (1.4%)

simplify49.0ms (1.3%)

prune108.0ms (2.8%)

localize8.0ms (0.2%)

series118.0ms (3.1%)

rewrite51.0ms (1.3%)

simplify38.0ms (1%)

prune128.0ms (3.3%)

localize6.0ms (0.2%)

series103.0ms (2.7%)

rewrite45.0ms (1.2%)

simplify54.0ms (1.4%)

prune96.0ms (2.5%)

localize6.0ms (0.2%)

series111.0ms (2.9%)

rewrite53.0ms (1.4%)

simplify62.0ms (1.6%)

prune82.0ms (2.1%)

regimes962.0ms (24.9%)

bsearch2.0ms (0.1%)

simplify3.0ms (0.1%)

end256.0ms (6.6%)

Profiling