Details

analyze44.0ms (1%)

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
25%	74.9%	0.1%	3
62.4%	37.5%	0.1%	4
68.7%	31.2%	0.1%	5
68.7%	18.7%	12.6%	6
68.7%	17.2%	14.1%	7
68.7%	10.1%	21.2%	8
68.7%	9%	22.3%	9
68.7%	5.3%	26%	10
68.7%	4.6%	26.7%	11
68.7%	2.7%	28.6%	12
68.7%	2.3%	29%	13
68.7%	1.4%	30%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample820.0ms (18.6%)

Results

787.0ms	8256×	body	128	valid
3.0ms	32×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	8	13
2	8	13

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

1.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	1.0b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	1.0b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series30.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

25.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
5.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite51.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

793×	`log1p-expm1-u_binary64`
793×	`expm1-log1p-u_binary64`
485×	`prod-diff_binary64`
77×	`add-sqr-sqrt_binary64`
73×	`add-log-exp_binary64`

Counts

2 → 72

Calls

2 calls:

50.0ms	(+.f64 (exp.f64 a) (exp.f64 b))
50.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	21
1	147	21
2	1998	21
3	5794	21
0	0	0
1	0	0

simplify82.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

475×	`times-frac_binary64`
464×	`associate-+l+_binary64`
426×	`fma-def_binary64`
303×	`associate-/l*_binary64`
240×	`associate--l+_binary64`

Counts

120 → 100

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	103	1020
1	302	981
2	1070	965
3	5042	965

prune96.0ms (2.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	3	101

Error

Counts

101 → 3

Alt Table

Status	Error	Program
	22.5b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))
▶	0.3b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	13.6b	(/.f64 1 (+.f64 1 (exp.f64 b)))

Compiler

Compiled 2038 to 929 computations (54.4% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	1.6b	(-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
✓	3.0b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series741.0ms (16.8%)

Counts

3 → 72

Calls

3 calls:

358.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
204.0ms	(-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
179.0ms	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))

rewrite150.0ms (3.4%)

Algorithm

2×	batch-egg-rewrite

Rules

814×	`prod-diff_binary64`
400×	`fma-def_binary64`
204×	`fma-neg_binary64`
174×	`expm1-udef_binary64`
174×	`log1p-udef_binary64`

Counts

3 → 139

Calls

3 calls:

146.0ms	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
146.0ms	(-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
146.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	185	36
2	2454	36
3	4739	36
4	4995	36
5	4995	36
6	4973	36
0	0	0
1	0	0

simplify89.0ms (2%)

Algorithm

1×	egg-herbie

Rules

602×	`fma-def_binary64`
521×	`fma-neg_binary64`
485×	`times-frac_binary64`
415×	`associate-/l*_binary64`
217×	`sub-neg_binary64`

Counts

211 → 192

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	138	1993
1	442	1932
2	1737	1690
3	4741	1688
4	5125	1688

prune170.0ms (3.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	240	2	242
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	242	3	245

Error

Counts

245 → 3

Alt Table

Status	Error	Program
▶	1.0b	(exp.f64 (log.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
✓	0.3b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	1.0b	(exp.f64 (-.f64 a (+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))))

Compiler

Compiled 5503 to 2256 computations (59% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (log.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	0.8b	(log.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))
	1.0b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series494.0ms (11.2%)

Counts

2 → 48

Calls

2 calls:

467.0ms	(log.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))
26.0ms	(exp.f64 (log.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))

rewrite64.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

862×	`log1p-expm1-u_binary64`
862×	`expm1-log1p-u_binary64`
490×	`prod-diff_binary64`
90×	`egg-rr`
85×	`add-sqr-sqrt_binary64`

Counts

2 → 90

Calls

2 calls:

62.0ms	(exp.f64 (log.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
62.0ms	(log.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	164	26
2	2182	26
3	6232	26
0	0	0
1	0	0

simplify86.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

410×	`associate-+r+_binary64`
292×	`times-frac_binary64`
265×	`+-commutative_binary64`
263×	`cancel-sign-sub-inv_binary64`
246×	`associate-+l+_binary64`

Counts

138 → 122

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	279	2998
1	924	2709
2	4130	2653
3	5110	2653

prune204.0ms (4.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	222	3	225

Error

Counts

225 → 3

Alt Table

Status	Error	Program
✓	1.0b	(exp.f64 (log.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
✓	0.3b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
▶	1.0b	(exp.f64 (-.f64 a (+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))))

Compiler

Compiled 7262 to 3497 computations (51.8% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (+.f64 1 (exp.f64 b)))
✓	0.0b	(exp.f64 (-.f64 a (+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))))
✓	0.1b	(-.f64 a (+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b)))))
✓	0.7b	(log1p.f64 (exp.f64 b))

series528.0ms (11.9%)

Counts

4 → 64

Calls

4 calls:

203.0ms	(-.f64 a (+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b)))))
165.0ms	(exp.f64 (-.f64 a (+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))))
144.0ms	(log1p.f64 (exp.f64 b))
16.0ms	(/.f64 a (+.f64 1 (exp.f64 b)))

rewrite95.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

566×	`fma-def_binary64`
260×	`fma-neg_binary64`
218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
196×	`egg-rr`

Counts

4 → 196

Calls

4 calls:

89.0ms	(/.f64 a (+.f64 1 (exp.f64 b)))
89.0ms	(exp.f64 (-.f64 a (+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))))
89.0ms	(-.f64 a (+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b)))))
89.0ms	(log1p.f64 (exp.f64 b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	54
1	237	54
2	3296	54
3	5005	54
0	0	0
1	0	0

simplify79.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

700×	`fma-neg_binary64`
637×	`associate-l_binary64`
398×	`cancel-sign-sub-inv_binary64`
267×	`times-frac_binary64`
219×	`associate-/l*_binary64`

Counts

260 → 245

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	141	1696
1	441	1614
2	1649	1417
3	4883	1411
4	5365	1411

prune182.0ms (4.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	245	0	245
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	245	3	248

Error

Counts

248 → 3

Alt Table

Status	Error	Program
✓	1.0b	(exp.f64 (log.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))))
✓	0.3b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
✓	1.0b	(exp.f64 (-.f64 a (+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))))

Compiler

Compiled 6468 to 3518 computations (45.6% saved)

regimes322.0ms (7.3%)

Accuracy

Total 0.2b remaining (39.5%)

Threshold costs 0.2b (39.5%)

Counts

81 → 1

Compiler

Compiled 6272 to 4308 computations (31.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	12	15
2	17	15
3	19	15
4	20	15
5	20	15

end54.0ms (1.2%)

Compiler: Compiled 60 to 42 computations (30% saved)

Details

analyze44.0ms (1%)

sample820.0ms (18.6%)

simplify8.0ms (0.2%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series30.0ms (0.7%)

rewrite51.0ms (1.2%)

simplify82.0ms (1.9%)

prune96.0ms (2.2%)

localize7.0ms (0.2%)

series741.0ms (16.8%)

rewrite150.0ms (3.4%)

simplify89.0ms (2%)

prune170.0ms (3.9%)

localize7.0ms (0.2%)

series494.0ms (11.2%)

rewrite64.0ms (1.5%)

simplify86.0ms (1.9%)

prune204.0ms (4.6%)

localize8.0ms (0.2%)

series528.0ms (11.9%)

rewrite95.0ms (2.1%)

simplify79.0ms (1.8%)

prune182.0ms (4.1%)

regimes322.0ms (7.3%)

simplify3.0ms (0.1%)

end54.0ms (1.2%)

Profiling