Details

analyze852.0ms (5%)

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
25%	74.9%	0.1%	4
50%	50%	0.1%	5
50%	50%	0.1%	6
50%	50%	0.1%	7
50%	50%	0.1%	8
50%	50%	0.1%	9
50%	50%	0.1%	10
50%	50%	0.1%	11
50%	50%	0.1%	12
50%	50%	0.1%	13
50%	50%	0.1%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample12.9s (75.2%)

Symmetry

(sort a b)

Results

9.8s	7823×	body	8192	exit
1.6s	1970×	body	1024	valid
617.0ms	4595×	body	128	valid
437.0ms	984×	body	512	valid
189.0ms	200×	body	2048	valid
138.0ms	507×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

prune2.0ms (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

26.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	26.3b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	2.8b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series332.0ms (1.9%)

Counts

2 → 48

Calls

2 calls:

328.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite44.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

666×	`log1p-expm1-u_binary64`
666×	`expm1-log1p-u_binary64`
455×	`prod-diff_binary64`
71×	`add-sqr-sqrt_binary64`
68×	`add-log-exp_binary64`

Counts

2 → 58

Calls

2 calls:

42.0ms	(+.f64 (exp.f64 a) (exp.f64 b))
42.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	137	18
2	1701	18
3	4952	18

prune65.0ms (0.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	102	4	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	4	107

Error

1.1b

Counts

107 → 4

Alt Table

Status	Error	Program
	27.5b	(pow.f64 (cbrt.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) 3)
▶	1.9b	(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a))))
	29.1b	(log.f64 (+.f64 1 (exp.f64 b)))
	26.3b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 1370 to 584 computations (57.4% saved)

localize6.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 a))
✓	0.0b	(/.f64 b (+.f64 1 (exp.f64 a)))
✓	0.0b	(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a))))
✓	0.5b	(log.f64 (+.f64 1 (exp.f64 a)))

series358.0ms (2.1%)

Counts

4 → 19

Calls

4 calls:

194.0ms	(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a))))
145.0ms	(log.f64 (+.f64 1 (exp.f64 a)))
17.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
1.0ms	(+.f64 1 (exp.f64 a))

rewrite96.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

816×	`prod-diff_binary64`
366×	`fma-def_binary64`
205×	`fma-neg_binary64`
170×	`expm1-udef_binary64`
169×	`log1p-udef_binary64`

Counts

4 → 144

Calls

4 calls:

92.0ms	(+.f64 1 (exp.f64 a))
92.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
92.0ms	(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a))))
92.0ms	(log.f64 (+.f64 1 (exp.f64 a)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	187	36
2	2486	36
3	4739	36
4	5016	36

prune171.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	198	5	203
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	199	8	207

Error

0.8b

Counts

207 → 8

Alt Table

Status	Error	Program
▶	1.7b	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
	29.6b	(+.f64 (log.f64 2) (*.f64 1/2 b))
	27.5b	(pow.f64 (cbrt.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) 3)
	1.9b	(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (/.f64 b (exp.f64 (log1p.f64 (exp.f64 a)))))
	29.1b	(log.f64 (+.f64 1 (exp.f64 b)))
	27.2b	(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
	26.3b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	3.5b	(pow.f64 (cbrt.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))) 3)

Compiler

Compiled 3720 to 2190 computations (41.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 b (+.f64 1 (exp.f64 a)))
✓	0.0b	(log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))
✓	0.1b	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
✓	0.2b	(log1p.f64 (exp.f64 a))

series853.0ms (5%)

Counts

4 → 64

Calls

4 calls:

478.0ms	(log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))
210.0ms	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
144.0ms	(log1p.f64 (exp.f64 a))
20.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))

rewrite123.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

865×	`prod-diff_binary64`
702×	`fma-udef_binary64`
185×	`expm1-udef_binary64`
185×	`log1p-udef_binary64`
130×	`fma-neg_binary64`

Counts

4 → 114

Calls

4 calls:

119.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
119.0ms	(log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))
119.0ms	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
119.0ms	(log1p.f64 (exp.f64 a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	48
1	206	48
2	2678	48
3	4991	48
4	4602	48
5	4996	48

prune143.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	174	4	178
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	179	7	186

Error

0.8b

Counts

186 → 7

Alt Table

Status	Error	Program
	27.5b	(pow.f64 (cbrt.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) 3)
	63.4b	(expm1.f64 (-.f64 (+.f64 (/.f64 (exp.f64 a) b) (+.f64 (log.f64 (/.f64 1 (+.f64 1 (exp.f64 a)))) (+.f64 (/.f64 1 b) (+.f64 (/.f64 (log.f64 (+.f64 1 (exp.f64 a))) b) (/.f64 (*.f64 (log.f64 (+.f64 1 (exp.f64 a))) (exp.f64 a)) b))))) (log.f64 (/.f64 1 b))))
	30.1b	(expm1.f64 (log.f64 (+.f64 1 (+.f64 (log.f64 2) (*.f64 1/2 b)))))
	29.1b	(log.f64 (+.f64 1 (exp.f64 b)))
	26.3b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	2.5b	(expm1.f64 (*.f64 (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 (exp.f64 a) 1))))) (pow.f64 (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 (exp.f64 a) 1))))) 2)))
▶	1.7b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 (exp.f64 a) 1)))

Compiler

Compiled 4825 to 3097 computations (35.8% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) 1)
✓	0.0b	(/.f64 b (+.f64 (exp.f64 a) 1))
✓	0.0b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 (exp.f64 a) 1)))
✓	0.2b	(log1p.f64 (exp.f64 a))

series362.0ms (2.1%)

Counts

4 → 72

Calls

4 calls:

197.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 (exp.f64 a) 1)))
146.0ms	(log1p.f64 (exp.f64 a))
17.0ms	(/.f64 b (+.f64 (exp.f64 a) 1))
2.0ms	(+.f64 (exp.f64 a) 1)

rewrite95.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

810×	`prod-diff_binary64`
327×	`fma-def_binary64`
222×	`fma-neg_binary64`
168×	`expm1-udef_binary64`
168×	`log1p-udef_binary64`

Counts

4 → 146

Calls

4 calls:

91.0ms	(+.f64 (exp.f64 a) 1)
91.0ms	(/.f64 b (+.f64 (exp.f64 a) 1))
91.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 (exp.f64 a) 1)))
91.0ms	(log1p.f64 (exp.f64 a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	188	36
2	2458	36
3	4743	36
4	4968	36

prune132.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	218	7	225

Error

0.8b

Counts

225 → 7

Alt Table

Status	Error	Program
	27.5b	(pow.f64 (cbrt.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) 3)
	63.4b	(expm1.f64 (-.f64 (+.f64 (/.f64 (exp.f64 a) b) (+.f64 (log.f64 (/.f64 1 (+.f64 1 (exp.f64 a)))) (+.f64 (/.f64 1 b) (+.f64 (/.f64 (log.f64 (+.f64 1 (exp.f64 a))) b) (/.f64 (*.f64 (log.f64 (+.f64 1 (exp.f64 a))) (exp.f64 a)) b))))) (log.f64 (/.f64 1 b))))
	30.1b	(expm1.f64 (log.f64 (+.f64 1 (+.f64 (log.f64 2) (*.f64 1/2 b)))))
	29.1b	(log.f64 (+.f64 1 (exp.f64 b)))
	26.3b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	2.5b	(expm1.f64 (*.f64 (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 (exp.f64 a) 1))))) (pow.f64 (cbrt.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 (exp.f64 a) 1))))) 2)))
✓	1.7b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 (exp.f64 a) 1)))

Compiler

Compiled 3424 to 1763 computations (48.5% saved)

regimes334.0ms (2%)

Accuracy

Total 0.5b remaining (43.4%)

Threshold costs 0.5b (43.4%)

Counts

65 → 1

Compiler

Compiled 6188 to 4618 computations (25.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	13	16
2	12	16

end258.0ms (1.5%)

Compiler: Compiled 173 to 123 computations (28.9% saved)

Details

analyze852.0ms (5%)

sample12.9s (75.2%)

prune2.0ms (0%)

localize5.0ms (0%)

series332.0ms (1.9%)

rewrite44.0ms (0.3%)

prune65.0ms (0.4%)

localize6.0ms (0%)

series358.0ms (2.1%)

rewrite96.0ms (0.6%)

prune171.0ms (1%)

localize9.0ms (0.1%)

series853.0ms (5%)

rewrite123.0ms (0.7%)

prune143.0ms (0.8%)

localize8.0ms (0%)

series362.0ms (2.1%)

rewrite95.0ms (0.6%)

prune132.0ms (0.8%)

regimes334.0ms (2%)

simplify2.0ms (0%)

end258.0ms (1.5%)

Profiling