Details

analyze3.0ms (0.1%)

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)

sample909.0ms (40.9%)

Results

856.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 47 to 38 computations (19.1% saved)

simplify32.0ms (1.4%)

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

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(/.f64 (.f64 6 (-.f64 x 1)) (+.f64 (+.f64 x 1) (.f64 4 (sqrt.f64 x))))
▶	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (-.f64 x -1)))

Compiler

Compiled 83 to 64 computations (22.9% 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))
✓	0.1b	(fma.f64 6 x -6)
✓	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (-.f64 x -1)))

series17.0ms (0.8%)

Counts

3 → 18

Calls

3 calls:

12.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (-.f64 x -1)))
4.0ms	(fma.f64 4 (sqrt.f64 x) (-.f64 x -1))
1.0ms	(fma.f64 6 x -6)

rewrite50.0ms (2.2%)

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

Calls

3 calls:

48.0ms	(fma.f64 4 (sqrt.f64 x) (-.f64 x -1))
48.0ms	(fma.f64 6 x -6)
48.0ms	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (-.f64 x -1)))

simplify10.0ms (0.5%)

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

prune84.0ms (3.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	97	5	102

Error

Counts

102 → 5

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (fma.f64 6 x -6) (/.f64 1 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1)))
✓	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (-.f64 x -1)))
	1.4b	(/.f64 (*.f64 (cbrt.f64 (fma.f64 6 x -6)) (pow.f64 (cbrt.f64 (fma.f64 6 x -6)) 2)) (fma.f64 4 (sqrt.f64 x) (-.f64 x -1)))
	36.3b	(exp.f64 (log.f64 (/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))))
	0.3b	(*.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 1934 to 1425 computations (26.3% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series26.0ms (1.2%)

Counts

3 → 8

Calls

3 calls:

12.0ms	(/.f64 1 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))
9.0ms	(*.f64 (fma.f64 6 x -6) (/.f64 1 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1)))
4.0ms	(fma.f64 4 (sqrt.f64 x) x)

rewrite53.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

488×	`log-prod_binary64`
201×	`log1p-udef_binary64`
200×	`expm1-udef_binary64`
174×	`fma-def_binary64`
172×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	37
1	257	37
2	2992	37

Stop Event

1×	node limit

Counts

3 → 94

Calls

3 calls:

51.0ms	(fma.f64 4 (sqrt.f64 x) x)
51.0ms	(/.f64 1 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))
51.0ms	(*.f64 (fma.f64 6 x -6) (/.f64 1 (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1)))

simplify9.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	14
1	8	14

Stop Event

1×

saturated

Counts

102 → 99

prune117.0ms (5.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	129	4	133

Error

Counts

133 → 4

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (/.f64 (fma.f64 6 x -6) (sqrt.f64 (+.f64 1 (fma.f64 4 (sqrt.f64 x) x)))) (sqrt.f64 (+.f64 1 (fma.f64 4 (sqrt.f64 x) x))))
	36.3b	(exp.f64 (log.f64 (/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))))
	2.6b	(*.f64 (fma.f64 6 x -6) (pow.f64 (cbrt.f64 (exp.f64 (neg.f64 (log1p.f64 (fma.f64 4 (sqrt.f64 x) x))))) 3))
✓	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (-.f64 x -1)))

Compiler

Compiled 2480 to 1839 computations (25.8% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series49.0ms (2.2%)

Counts

3 → 5

Calls

3 calls:

22.0ms

(/.f64 (fma.f64 6 x -6) (sqrt.f64 (+.f64 1 (fma.f64 4 (sqrt.f64 x) x))))

15.0ms

(sqrt.f64 (+.f64 1 (fma.f64 4 (sqrt.f64 x) x)))

11.0ms

(/.f64 (/.f64 (fma.f64 6 x -6) (sqrt.f64 (+.f64 1 (fma.f64 4 (sqrt.f64 x) x)))) (sqrt.f64 (+.f64 1 (fma.f64 4 (sqrt.f64 x) x))))

rewrite73.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

272×	`prod-diff_binary64`
223×	`expm1-udef_binary64`
223×	`log1p-udef_binary64`
211×	`fma-def_binary64`
130×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	48
1	278	48
2	3422	48

Stop Event

1×	node limit

Counts

3 → 106

Calls

3 calls:

67.0ms

(sqrt.f64 (+.f64 1 (fma.f64 4 (sqrt.f64 x) x)))

67.0ms

(/.f64 (/.f64 (fma.f64 6 x -6) (sqrt.f64 (+.f64 1 (fma.f64 4 (sqrt.f64 x) x)))) (sqrt.f64 (+.f64 1 (fma.f64 4 (sqrt.f64 x) x))))

67.0ms

(/.f64 (fma.f64 6 x -6) (sqrt.f64 (+.f64 1 (fma.f64 4 (sqrt.f64 x) x))))

simplify8.0ms (0.4%)

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

111 → 109

prune143.0ms (6.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	165	4	169

Error

Counts

169 → 4

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 (/.f64 (fma.f64 6 x -6) (sqrt.f64 (+.f64 1 (fma.f64 4 (sqrt.f64 x) x)))) (sqrt.f64 (+.f64 1 (fma.f64 4 (sqrt.f64 x) x))))
	36.3b	(exp.f64 (log.f64 (/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))))
▶	2.6b	(*.f64 (fma.f64 6 x -6) (pow.f64 (cbrt.f64 (exp.f64 (neg.f64 (log1p.f64 (fma.f64 4 (sqrt.f64 x) x))))) 3))
✓	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (-.f64 x -1)))

Compiler

Compiled 4432 to 3184 computations (28.2% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (fma.f64 6 x -6) (pow.f64 (cbrt.f64 (exp.f64 (neg.f64 (log1p.f64 (fma.f64 4 (sqrt.f64 x) x))))) 3))
✓	0.3b	(cbrt.f64 (exp.f64 (neg.f64 (log1p.f64 (fma.f64 4 (sqrt.f64 x) x)))))
✓	0.3b	(pow.f64 (cbrt.f64 (exp.f64 (neg.f64 (log1p.f64 (fma.f64 4 (sqrt.f64 x) x))))) 3)
✓	2.5b	(exp.f64 (neg.f64 (log1p.f64 (fma.f64 4 (sqrt.f64 x) x))))

series167.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(pow.f64 (cbrt.f64 (exp.f64 (neg.f64 (log1p.f64 (fma.f64 4 (sqrt.f64 x) x))))) 3)
56.0ms	(cbrt.f64 (exp.f64 (neg.f64 (log1p.f64 (fma.f64 4 (sqrt.f64 x) x)))))
24.0ms	(*.f64 (fma.f64 6 x -6) (pow.f64 (cbrt.f64 (exp.f64 (neg.f64 (log1p.f64 (fma.f64 4 (sqrt.f64 x) x))))) 3))
17.0ms	(exp.f64 (neg.f64 (log1p.f64 (fma.f64 4 (sqrt.f64 x) x))))

rewrite66.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

504×	`log-prod_binary64`
209×	`expm1-udef_binary64`
209×	`log1p-udef_binary64`
184×	`log-pow_binary64`
132×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	61
1	303	49
2	3184	49

Stop Event

1×	node limit

Counts

4 → 132

Calls

4 calls:

63.0ms	(*.f64 (fma.f64 6 x -6) (pow.f64 (cbrt.f64 (exp.f64 (neg.f64 (log1p.f64 (fma.f64 4 (sqrt.f64 x) x))))) 3))
63.0ms	(cbrt.f64 (exp.f64 (neg.f64 (log1p.f64 (fma.f64 4 (sqrt.f64 x) x)))))
63.0ms	(pow.f64 (cbrt.f64 (exp.f64 (neg.f64 (log1p.f64 (fma.f64 4 (sqrt.f64 x) x))))) 3)
63.0ms	(exp.f64 (neg.f64 (log1p.f64 (fma.f64 4 (sqrt.f64 x) x))))

simplify31.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

613×	`fma-neg_binary64`
579×	`fma-def_binary64`
362×	`unswap-sqr_binary64`
200×	`exp-sum_binary64`
185×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	34
1	39	34
2	75	34
3	177	34
4	383	34
5	809	34
6	1584	34
7	3636	34

Stop Event

1×	node limit

Counts

144 → 105

prune82.0ms (3.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	105	4	109

Error

Counts

109 → 4

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 (/.f64 (fma.f64 6 x -6) (sqrt.f64 (+.f64 1 (fma.f64 4 (sqrt.f64 x) x)))) (sqrt.f64 (+.f64 1 (fma.f64 4 (sqrt.f64 x) x))))
	36.3b	(exp.f64 (log.f64 (/.f64 (fma.f64 6 x -6) (+.f64 (fma.f64 4 (sqrt.f64 x) x) 1))))
✓	2.6b	(*.f64 (fma.f64 6 x -6) (pow.f64 (cbrt.f64 (exp.f64 (neg.f64 (log1p.f64 (fma.f64 4 (sqrt.f64 x) x))))) 3))
✓	0.1b	(/.f64 (fma.f64 6 x -6) (fma.f64 4 (sqrt.f64 x) (-.f64 x -1)))

Compiler

Compiled 2156 to 1618 computations (25% saved)

regimes170.0ms (7.7%)

Accuracy

Total 0.1b remaining (40.6%)

Threshold costs 0.1b (40.6%)

Counts

96 → 1

Compiler

Compiled 3299 to 2670 computations (19.1% saved)

simplify3.0ms (0.1%)

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

end82.0ms (3.7%)

Compiler: Compiled 94 to 73 computations (22.3% saved)

Details

analyze3.0ms (0.1%)

sample909.0ms (40.9%)

simplify32.0ms (1.4%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

series17.0ms (0.8%)

rewrite50.0ms (2.2%)

simplify10.0ms (0.5%)

prune84.0ms (3.8%)

localize9.0ms (0.4%)

series26.0ms (1.2%)

rewrite53.0ms (2.4%)

simplify9.0ms (0.4%)

prune117.0ms (5.3%)

localize9.0ms (0.4%)

series49.0ms (2.2%)

rewrite73.0ms (3.3%)

simplify8.0ms (0.4%)

prune143.0ms (6.4%)

localize11.0ms (0.5%)

series167.0ms (7.5%)

rewrite66.0ms (3%)

simplify31.0ms (1.4%)

prune82.0ms (3.7%)

regimes170.0ms (7.7%)

simplify3.0ms (0.1%)

end82.0ms (3.7%)

Profiling