Details

analyze806.0ms (4.5%)

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)

sample13.0s (72.8%)

Alt Table

Status	Error	Program
▶	31.8b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Symmetry

(sort a b)

Results

10.1s	7838×	body	8192	exit
1.4s	1972×	body	1024	valid
623.0ms	4565×	body	128	valid
451.0ms	1032×	body	512	valid
202.0ms	216×	body	2048	valid
137.0ms	471×	body	256	valid

Compiler

Compiled 42 to 32 computations (23.8% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

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

series439.0ms (2.5%)

Counts

2 → 48

Calls

2 calls:

433.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
5.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite45.0ms (0.3%)

Algorithm

2×	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:

44.0ms	(+.f64 (exp.f64 a) (exp.f64 b))
44.0ms	(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
0	0	0
1	0	0

prune61.0ms (0.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	101	5	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	5	107

Error

0.7b

Counts

107 → 5

Alt Table

Status	Error	Program
	31.8b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))) 3))
	32.7b	(pow.f64 (cbrt.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) 3)
	31.9b	(log.f64 (cbrt.f64 (pow.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 3)))
▶	0.9b	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (+.f64 1 (exp.f64 a)))) (+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a))))) (.f64 1/2 (/.f64 (pow.f64 b 2) (pow.f64 (+.f64 1 (exp.f64 a)) 2))))
	1.1b	(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a))))

Compiler

Compiled 1456 to 648 computations (55.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 1 (exp.f64 a)) 2)
✓	0.0b	(log.f64 (+.f64 1 (exp.f64 a)))
✓	0.0b	(*.f64 1/2 (/.f64 (pow.f64 b 2) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))
✓	0.0b	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (+.f64 1 (exp.f64 a)))) (+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a))))) (.f64 1/2 (/.f64 (pow.f64 b 2) (pow.f64 (+.f64 1 (exp.f64 a)) 2))))

series548.0ms (3.1%)

Counts

4 → 26

Calls

4 calls:

279.0ms	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (+.f64 1 (exp.f64 a)))) (+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a))))) (.f64 1/2 (/.f64 (pow.f64 b 2) (pow.f64 (+.f64 1 (exp.f64 a)) 2))))
188.0ms	(log.f64 (+.f64 1 (exp.f64 a)))
78.0ms	(*.f64 1/2 (/.f64 (pow.f64 b 2) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))
3.0ms	(pow.f64 (+.f64 1 (exp.f64 a)) 2)

rewrite92.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

497×	`prod-diff_binary64`
210×	`add-sqr-sqrt_binary64`
207×	`log1p-expm1-u_binary64`
207×	`expm1-log1p-u_binary64`
199×	`add-log-exp_binary64`

Counts

4 → 104

Calls

4 calls:

88.0ms	(pow.f64 (+.f64 1 (exp.f64 a)) 2)
88.0ms	(log.f64 (+.f64 1 (exp.f64 a)))
88.0ms	(*.f64 1/2 (/.f64 (pow.f64 b 2) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))
88.0ms	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (+.f64 1 (exp.f64 a)))) (+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a))))) (.f64 1/2 (/.f64 (pow.f64 b 2) (pow.f64 (+.f64 1 (exp.f64 a)) 2))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	83
1	434	77
2	4760	77
3	5618	77
0	0	0
1	0	0

prune190.0ms (1.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	132	3	135

Error

0.4b

Counts

135 → 3

Alt Table

Status	Error	Program
	31.8b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))) 3))
	1.1b	(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a))))
▶	0.6b	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (+.f64 1 (exp.f64 a)))) (+.f64 (exp.f64 (log.f64 (log1p.f64 (exp.f64 a)))) (/.f64 b (+.f64 1 (exp.f64 a))))) (.f64 1/2 (/.f64 (pow.f64 b 2) (pow.f64 (+.f64 1 (exp.f64 a)) 2))))

Compiler

Compiled 6394 to 4128 computations (35.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 1 (exp.f64 a)) 2)
✓	0.0b	(*.f64 1/2 (/.f64 (pow.f64 b 2) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))
✓	0.0b	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (+.f64 1 (exp.f64 a)))) (+.f64 (exp.f64 (log.f64 (log1p.f64 (exp.f64 a)))) (/.f64 b (+.f64 1 (exp.f64 a))))) (.f64 1/2 (/.f64 (pow.f64 b 2) (pow.f64 (+.f64 1 (exp.f64 a)) 2))))
✓	0.3b	(log.f64 (log1p.f64 (exp.f64 a)))

series765.0ms (4.3%)

Counts

4 → 44

Calls

4 calls:

394.0ms	(log.f64 (log1p.f64 (exp.f64 a)))
281.0ms	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (+.f64 1 (exp.f64 a)))) (+.f64 (exp.f64 (log.f64 (log1p.f64 (exp.f64 a)))) (/.f64 b (+.f64 1 (exp.f64 a))))) (.f64 1/2 (/.f64 (pow.f64 b 2) (pow.f64 (+.f64 1 (exp.f64 a)) 2))))
87.0ms	(*.f64 1/2 (/.f64 (pow.f64 b 2) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))
4.0ms	(pow.f64 (+.f64 1 (exp.f64 a)) 2)

rewrite85.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

326×	`prod-diff_binary64`
218×	`add-sqr-sqrt_binary64`
215×	`expm1-log1p-u_binary64`
214×	`log1p-expm1-u_binary64`
206×	`add-log-exp_binary64`

Counts

4 → 99

Calls

4 calls:

80.0ms	(pow.f64 (+.f64 1 (exp.f64 a)) 2)
80.0ms	(*.f64 1/2 (/.f64 (pow.f64 b 2) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))
80.0ms	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (+.f64 1 (exp.f64 a)))) (+.f64 (exp.f64 (log.f64 (log1p.f64 (exp.f64 a)))) (/.f64 b (+.f64 1 (exp.f64 a))))) (.f64 1/2 (/.f64 (pow.f64 b 2) (pow.f64 (+.f64 1 (exp.f64 a)) 2))))
80.0ms	(log.f64 (log1p.f64 (exp.f64 a)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	85
1	450	79
2	4738	79
3	5232	79
0	0	0
1	0	0

prune178.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	143	3	146

Error

0.4b

Counts

146 → 3

Alt Table

Status	Error	Program
	31.8b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))) 3))
▶	1.1b	(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (/.f64 b (+.f64 1 (exp.f64 a))))
✓	0.6b	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (+.f64 1 (exp.f64 a)))) (+.f64 (exp.f64 (log.f64 (log1p.f64 (exp.f64 a)))) (/.f64 b (+.f64 1 (exp.f64 a))))) (.f64 1/2 (/.f64 (pow.f64 b 2) (pow.f64 (+.f64 1 (exp.f64 a)) 2))))

Compiler

Compiled 6666 to 4237 computations (36.4% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

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

series192.0ms (1.1%)

Counts

2 → 8

Calls

2 calls:

190.0ms	(log.f64 (+.f64 1 (exp.f64 a)))
2.0ms	(+.f64 1 (exp.f64 a))

rewrite82.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

505×	`prod-diff_binary64`
494×	`log1p-expm1-u_binary64`
494×	`expm1-log1p-u_binary64`
295×	`unpow-prod-down_binary64`
230×	`log-prod_binary64`

Counts

2 → 95

Calls

2 calls:

80.0ms	(+.f64 1 (exp.f64 a))
80.0ms	(log.f64 (+.f64 1 (exp.f64 a)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	112	11
2	1274	11
3	4868	11
4	5598	11
0	0	0
1	0	0

prune178.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	157	3	160

Error

0.4b

Counts

160 → 3

Alt Table

Status	Error	Program
	31.8b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))) 3))
	1.1b	(+.f64 (log.f64 (+.f64 1 (exp.f64 a))) (/.f64 b (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 a))) 2)) (cbrt.f64 (log1p.f64 (exp.f64 a))))))
✓	0.6b	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 b 2) (+.f64 1 (exp.f64 a)))) (+.f64 (exp.f64 (log.f64 (log1p.f64 (exp.f64 a)))) (/.f64 b (+.f64 1 (exp.f64 a))))) (.f64 1/2 (/.f64 (pow.f64 b 2) (pow.f64 (+.f64 1 (exp.f64 a)) 2))))

Compiler

Compiled 2976 to 1787 computations (40% saved)

regimes878.0ms (4.9%)

Accuracy

Total 0.5b remaining (59.2%)

Threshold costs 0.5b (59.2%)

Counts

163 → 1

Compiler

Compiled 21075 to 15100 computations (28.4% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
5×	`*-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	57
1	34	57
2	41	57
3	47	57
4	52	57
5	55	57
6	56	57
7	54	57

end255.0ms (1.4%)

Compiler: Compiled 223 to 163 computations (26.9% saved)

Details

analyze806.0ms (4.5%)

sample13.0s (72.8%)

localize5.0ms (0%)

series439.0ms (2.5%)

rewrite45.0ms (0.3%)

prune61.0ms (0.3%)

localize16.0ms (0.1%)

series548.0ms (3.1%)

rewrite92.0ms (0.5%)

prune190.0ms (1.1%)

localize18.0ms (0.1%)

series765.0ms (4.3%)

rewrite85.0ms (0.5%)

prune178.0ms (1%)

localize6.0ms (0%)

series192.0ms (1.1%)

rewrite82.0ms (0.5%)

prune178.0ms (1%)

regimes878.0ms (4.9%)

simplify4.0ms (0%)

end255.0ms (1.4%)

Profiling