Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample932.0ms (36.3%)

Results

916.0ms	8256×	body	128	valid
2.0ms	5×	body	128	invalid

Compiler

Compiled 32 to 26 computations (18.8% saved)

preprocess41.0ms (1.6%)

Algorithm

2×	egg-herbie

Rules

688×	`times-frac_binary64`
636×	`fma-def_binary64`
499×	`fma-neg_binary64`
324×	`div-sub_binary64`
319×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	25	19
2	46	17
3	70	17
4	87	17
5	106	17
6	149	17
7	246	17
8	402	17
9	680	17
10	1146	17
11	1625	17
12	2083	17
13	3268	17
0	1	1

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 15 to 12 computations (20% saved)

simplify34.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

688×	`times-frac_binary64`
636×	`fma-def_binary64`
499×	`fma-neg_binary64`
324×	`div-sub_binary64`
319×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	25	19
2	46	17
3	70	17
4	87	17
5	106	17
6	149	17
7	246	17
8	402	17
9	680	17
10	1146	17
11	1625	17
12	2083	17
13	3268	17

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.6b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (-.f64 x -1)))

Compiler

Compiled 53 to 40 computations (24.5% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (sqrt.f64 x) (-.f64 x -1))
✓	0.0b	(fma.f64 6 x -6)
✓	0.6b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (-.f64 x -1)))

series18.0ms (0.7%)

Counts

3 → 18

Calls

9 calls:

6.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (-.f64 x -1)))	x	-inf
3.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (-.f64 x -1)))	x	inf
3.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (-.f64 x -1)))	x	0
1.0ms	(fma.f64 4 (sqrt.f64 x) (-.f64 x -1))	x	0
1.0ms	(fma.f64 4 (sqrt.f64 x) (-.f64 x -1))	x	-inf

rewrite61.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

451×	`log-prod_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
160×	`log-pow_binary64`
131×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	32
1	237	32
2	2786	32

Stop Event

1×	node limit

Counts

3 → 93

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-neg_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	60
1	13	60
2	15	60

Stop Event

1×

saturated

Counts

111 → 100

prune102.0ms (4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	93	7	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	7	101

Error

Counts

101 → 7

Alt Table

Status	Error	Program
	18.8b	(/.f64 (fma.f64 6 x -6) (cbrt.f64 (pow.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1) 3)))
	34.4b	6
	1.0b	(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1)))) (cbrt.f64 (exp.f64 (/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))))))
▶	0.6b	(/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))
	1.9b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))) 3)
	0.8b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))) (/.f64 (fma.f64 6 x -6) (sqrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))))
	0.7b	(*.f64 (fma.f64 6 x -6) (/.f64 1 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1)))

Compiler

Compiled 2035 to 1503 computations (26.1% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 4 (sqrt.f64 x) x) 1)
✓	0.0b	(fma.f64 4 (sqrt.f64 x) x)
	0.0b	(fma.f64 6 x -6)
✓	0.6b	(/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))

series20.0ms (0.8%)

Counts

3 → 8

Calls

9 calls:

3.0ms	(/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))	x	-inf
3.0ms	(/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))	x	inf
3.0ms	(/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))	x	0
3.0ms	(fma.f64 4 (sqrt.f64 x) x)	x	-inf
2.0ms	(fma.f64 4 (sqrt.f64 x) x)	x	0

rewrite58.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

447×	`log-prod_binary64`
188×	`log1p-udef_binary64`
187×	`expm1-udef_binary64`
174×	`prod-diff_binary64`
167×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	234	34
2	2761	34

Stop Event

1×	node limit

Counts

3 → 115

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
1	7	8

Stop Event

1×

saturated

Counts

123 → 119

prune135.0ms (5.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	150	5	155

Error

Counts

155 → 5

Alt Table

Status	Error	Program
	19.3b	(*.f64 (/.f64 (fma.f64 6 x -6) (+.f64 1 (pow.f64 (fma.f64 4 (sqrt.f64 x) x) 3))) (+.f64 (pow.f64 (fma.f64 4 (sqrt.f64 x) x) 2) (-.f64 1 (fma.f64 4 (sqrt.f64 x) x))))
	15.3b	(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1) 2))) (/.f64 (fma.f64 6 x -6) (cbrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))))
	34.4b	6
✓	0.6b	(/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))
▶	0.8b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))) (/.f64 (fma.f64 6 x -6) (sqrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))))

Compiler

Compiled 2885 to 2071 computations (28.2% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 6 x -6)
✓	0.1b	(/.f64 1 (sqrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1)))
✓	0.2b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))) (/.f64 (fma.f64 6 x -6) (sqrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))))
✓	0.6b	(/.f64 (fma.f64 6 x -6) (sqrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1)))

series47.0ms (1.8%)

Counts

3 → 5

Calls

9 calls:

7.0ms	(/.f64 (fma.f64 6 x -6) (sqrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1)))	x	-inf
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1)))	x	-inf
7.0ms	(/.f64 (fma.f64 6 x -6) (sqrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1)))	x	inf
5.0ms	(/.f64 1 (sqrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1)))	x	inf
5.0ms	(/.f64 (fma.f64 6 x -6) (sqrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1)))	x	0

rewrite69.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

235×	`log1p-udef_binary64`
234×	`expm1-udef_binary64`
201×	`prod-diff_binary64`
196×	`fma-def_binary64`
150×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	51
1	302	49
2	3691	49

Stop Event

1×	node limit

Counts

3 → 119

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	5
1	6	5

Stop Event

1×

saturated

Counts

124 → 122

prune165.0ms (6.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	151	5	156

Error

Counts

156 → 5

Alt Table

Status	Error	Program
	19.3b	(*.f64 (/.f64 (fma.f64 6 x -6) (+.f64 1 (pow.f64 (fma.f64 4 (sqrt.f64 x) x) 3))) (+.f64 (pow.f64 (fma.f64 4 (sqrt.f64 x) x) 2) (-.f64 1 (fma.f64 4 (sqrt.f64 x) x))))
▶	15.3b	(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1) 2))) (/.f64 (fma.f64 6 x -6) (cbrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))))
	34.4b	6
✓	0.6b	(/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))
✓	0.8b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))) (/.f64 (fma.f64 6 x -6) (sqrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))))

Compiler

Compiled 4215 to 3088 computations (26.7% saved)

localize16.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1) 2))) (/.f64 (fma.f64 6 x -6) (cbrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))))
✓	0.3b	(cbrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))
✓	0.7b	(/.f64 (fma.f64 6 x -6) (cbrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1)))
✓	14.9b	(cbrt.f64 (pow.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1) 2))

series246.0ms (9.6%)

Counts

4 → 6

Calls

12 calls:

87.0ms	(/.f64 (fma.f64 6 x -6) (cbrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1)))	x	-inf
71.0ms	(/.f64 (fma.f64 6 x -6) (cbrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1)))	x	inf
26.0ms	(cbrt.f64 (pow.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1) 2))	x	inf
26.0ms	(cbrt.f64 (pow.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1) 2))	x	-inf
7.0ms	(/.f64 (fma.f64 6 x -6) (cbrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1)))	x	0

rewrite78.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

269×	`log1p-udef_binary64`
201×	`prod-diff_binary64`
160×	`add-sqr-sqrt_binary64`
158×	`log1p-expm1-u_binary64`
158×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	82
1	361	63
2	4273	63

Stop Event

1×	node limit

Counts

4 → 140

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	6
1	6	6

Stop Event

1×

saturated

Counts

146 → 143

prune154.0ms (6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	143	5	148

Error

Counts

148 → 5

Alt Table

Status	Error	Program
	19.3b	(*.f64 (/.f64 (fma.f64 6 x -6) (+.f64 1 (pow.f64 (fma.f64 4 (sqrt.f64 x) x) 3))) (+.f64 (pow.f64 (fma.f64 4 (sqrt.f64 x) x) 2) (-.f64 1 (fma.f64 4 (sqrt.f64 x) x))))
✓	15.3b	(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1) 2))) (/.f64 (fma.f64 6 x -6) (cbrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))))
	34.4b	6
✓	0.6b	(/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))
✓	0.8b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))) (/.f64 (fma.f64 6 x -6) (sqrt.f64 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))))

Compiler

Compiled 4223 to 3148 computations (25.5% saved)

regimes231.0ms (9%)

Accuracy

Total 0.2b remaining (95.5%)

Threshold costs 0.2b (95.5%)

Counts

109 → 1

Compiler

Compiled 4861 to 3814 computations (21.5% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	14	17

Stop Event

1×

saturated

end96.0ms (3.7%)

Stop Event

1×

fuel

Compiler

Compiled 124 to 94 computations (24.2% saved)

Details

analyze4.0ms (0.2%)

sample932.0ms (36.3%)

preprocess41.0ms (1.6%)

simplify34.0ms (1.3%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

series18.0ms (0.7%)

rewrite61.0ms (2.4%)

simplify8.0ms (0.3%)

prune102.0ms (4%)

localize8.0ms (0.3%)

series20.0ms (0.8%)

rewrite58.0ms (2.2%)

simplify8.0ms (0.3%)

prune135.0ms (5.2%)

localize10.0ms (0.4%)

series47.0ms (1.8%)

rewrite69.0ms (2.7%)

simplify9.0ms (0.3%)

prune165.0ms (6.4%)

localize16.0ms (0.6%)

series246.0ms (9.6%)

rewrite78.0ms (3%)

simplify8.0ms (0.3%)

prune154.0ms (6%)

regimes231.0ms (9%)

simplify5.0ms (0.2%)

end96.0ms (3.7%)

Profiling