Details

analyze39.0ms (1.2%)

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)

sample756.0ms (22.1%)

Results

725.0ms	8256×	body	128	valid
3.0ms	32×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify6.0ms (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

0.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.8b	(/.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))
✓	0.7b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series34.0ms (1%)

Counts

2 → 48

Calls

2 calls:

30.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite51.0ms (1.5%)

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 → 70

Calls

2 calls:

49.0ms	(+.f64 (exp.f64 a) (exp.f64 b))
49.0ms	(/.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

simplify41.0ms (1.2%)

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

118 → 98

Iterations

Useful iterations: 2 (0.0ms)

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

prune86.0ms (2.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	95	4	99

Error

0.2b

Counts

99 → 4

Alt Table

Status	Error	Program
	1.0b	(/.f64 (exp.f64 a) (fma.f64 1/2 (*.f64 a a) (+.f64 1 (+.f64 (exp.f64 b) a))))
✓	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
▶	0.8b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	12.4b	(/.f64 1 (+.f64 1 (exp.f64 b)))

Compiler

Compiled 2022 to 931 computations (54% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	0.0b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
✓	1.1b	(-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
✓	3.6b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series917.0ms (26.8%)

Counts

3 → 72

Calls

3 calls:

428.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
260.0ms	(-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
229.0ms	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))

rewrite146.0ms (4.3%)

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 → 137

Calls

3 calls:

142.0ms	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
141.0ms	(-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
141.0ms	(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

simplify80.0ms (2.4%)

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

209 → 190

Iterations

Useful iterations: 3 (0.0ms)

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

prune171.0ms (5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	238	1	239
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	239	4	243

Error

0.2b

Counts

243 → 4

Alt Table

Status	Error	Program
▶	1.0b	(/.f64 (exp.f64 a) (fma.f64 1/2 (*.f64 a a) (+.f64 1 (+.f64 (exp.f64 b) a))))
	12.4b	(exp.f64 (neg.f64 (log1p.f64 (exp.f64 b))))
✓	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
✓	0.8b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 5478 to 2259 computations (58.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series69.0ms (2%)

Counts

3 → 55

Calls

3 calls:

57.0ms	(/.f64 (exp.f64 a) (fma.f64 1/2 (*.f64 a a) (+.f64 1 (+.f64 (exp.f64 b) a))))
8.0ms	(fma.f64 1/2 (*.f64 a a) (+.f64 1 (+.f64 (exp.f64 b) a)))
3.0ms	(+.f64 1 (+.f64 (exp.f64 b) a))

rewrite63.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

871×	`prod-diff_binary64`
221×	`log1p-udef_binary64`
125×	`add-sqr-sqrt_binary64`
120×	`log1p-expm1-u_binary64`
120×	`expm1-log1p-u_binary64`

Counts

3 → 93

Calls

3 calls:

60.0ms	(+.f64 1 (+.f64 (exp.f64 b) a))
60.0ms	(/.f64 (exp.f64 a) (fma.f64 1/2 (*.f64 a a) (+.f64 1 (+.f64 (exp.f64 b) a))))
60.0ms	(fma.f64 1/2 (*.f64 a a) (+.f64 1 (+.f64 (exp.f64 b) a)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	253	46
2	3165	46
3	5133	46
0	0	0
1	0	0

simplify71.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

533×	`fma-def_binary64`
454×	`times-frac_binary64`
382×	`fma-neg_binary64`
331×	`associate-/l*_binary64`
236×	`associate-/r*_binary64`

Counts

148 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	1528
1	379	1481
2	1336	1429
3	4709	1419
4	4987	1419

prune119.0ms (3.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	146	4	150

Error

0.2b

Counts

150 → 4

Alt Table

Status	Error	Program
✓	1.0b	(/.f64 (exp.f64 a) (fma.f64 1/2 (*.f64 a a) (+.f64 1 (+.f64 (exp.f64 b) a))))
▶	12.4b	(exp.f64 (neg.f64 (log1p.f64 (exp.f64 b))))
✓	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
✓	0.8b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 3502 to 1830 computations (47.7% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.7b	(log1p.f64 (exp.f64 b))

series189.0ms (5.5%)

Counts

1 → 12

Calls

1 calls:

189.0ms

(log1p.f64 (exp.f64 b))

rewrite73.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

291×	`expm1-log1p-u_binary64`
290×	`log1p-expm1-u_binary64`
269×	`add-cbrt-cube_binary64`
261×	`add-log-exp_binary64`
259×	`add-exp-log_binary64`

Counts

1 → 33

Calls

1 calls:

72.0ms

(log1p.f64 (exp.f64 b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	5
1	73	5
2	786	5
3	4890	5
4	4923	5
0	0	0
1	0	0

simplify146.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

749×	`fma-def_binary64`
668×	`fma-neg_binary64`
607×	`distribute-rgt-neg-in_binary64`
528×	`cancel-sign-sub-inv_binary64`
420×	`sub-neg_binary64`

Counts

45 → 42

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	93
1	47	91
2	96	85
3	264	79
4	812	79
5	1766	79
6	2961	79
7	4131	79
8	4494	79
9	4811	79
10	4956	79
11	4824	79
12	4955	79
13	4812	79

prune33.0ms (1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	42	4	46

Error

0.2b

Counts

46 → 4

Alt Table

Status	Error	Program
	13.2b	(exp.f64 (neg.f64 (*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (log1p.f64 (exp.f64 b)))) 2) 3) (cbrt.f64 (log1p.f64 (exp.f64 b))))))
✓	1.0b	(/.f64 (exp.f64 a) (fma.f64 1/2 (*.f64 a a) (+.f64 1 (+.f64 (exp.f64 b) a))))
✓	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
✓	0.8b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 520 to 328 computations (36.9% saved)

regimes237.0ms (6.9%)

Accuracy

Total 0.4b remaining (72.1%)

Threshold costs 0.4b (72.1%)

Counts

61 → 1

Compiler

Compiled 4819 to 3413 computations (29.2% saved)

simplify2.0ms (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	12	20
1	15	20
2	20	20
3	22	20
4	23	20
5	23	20

end67.0ms (2%)

Compiler: Compiled 83 to 60 computations (27.7% saved)

Details

analyze39.0ms (1.2%)

sample756.0ms (22.1%)

simplify6.0ms (0.2%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series34.0ms (1%)

rewrite51.0ms (1.5%)

simplify41.0ms (1.2%)

prune86.0ms (2.5%)

localize7.0ms (0.2%)

series917.0ms (26.8%)

rewrite146.0ms (4.3%)

simplify80.0ms (2.4%)

prune171.0ms (5%)

localize8.0ms (0.2%)

series69.0ms (2%)

rewrite63.0ms (1.8%)

simplify71.0ms (2.1%)

prune119.0ms (3.5%)

localize4.0ms (0.1%)

series189.0ms (5.5%)

rewrite73.0ms (2.1%)

simplify146.0ms (4.3%)

prune33.0ms (1%)

regimes237.0ms (6.9%)

simplify2.0ms (0.1%)

end67.0ms (2%)

Profiling