Details

analyze2.7s (12%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.9%	50.1%	0
0%	49.9%	50.1%	1
0%	49.9%	50.1%	2
0%	49.9%	50.1%	3
0%	49.9%	50.1%	4
0%	49.9%	50.1%	5
0%	49.9%	50.1%	6
0%	49.9%	50.1%	7
0%	49.9%	50.1%	8
0.4%	49.5%	50.1%	9
0.4%	49.3%	50.3%	10
0.6%	48.9%	50.5%	11
1.1%	48.1%	50.9%	12
1.5%	47.3%	51.2%	13
1.7%	46.9%	51.5%	14

Compiler

Compiled 34 to 24 computations (29.4% saved)

sample8.6s (38.1%)

Symmetry

(sort a b)

Results

5.0s	4196×	body	2048	valid
1.9s	2510×	body	1024	valid
467.0ms	401×	body	2048	invalid
370.0ms	578×	body	1024	invalid
358.0ms	724×	body	512	valid
135.0ms	297×	body	512	invalid
100.0ms	580×	body	128	valid
75.0ms	237×	body	256	valid
59.0ms	301×	body	128	invalid
44.0ms	132×	body	256	invalid
17.0ms	9×	body	4096	valid

Compiler

Compiled 95 to 67 computations (29.5% saved)

simplify23.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

986×	`times-frac_binary64`
580×	`associate-/l*_binary64`
372×	`fma-def_binary64`
126×	`distribute-rgt-in_binary64`
122×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	47	28
2	108	28
3	254	28
4	897	28
5	5292	28

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

37.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	37.9b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

Compiler

Compiled 87 to 54 computations (37.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(expm1.f64 (*.f64 eps (+.f64 a b)))
✓	0.1b	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
✓	0.1b	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
✓	36.4b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series282.0ms (1.2%)

Counts

4 → 144

Calls

4 calls:

223.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
24.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
22.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
13.0ms	(expm1.f64 (*.f64 eps (+.f64 a b)))

rewrite89.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

916×	`prod-diff_binary64`
149×	`add-sqr-sqrt_binary64`
141×	`associate-r_binary64`
141×	`log1p-expm1-u_binary64`
141×	`expm1-log1p-u_binary64`

Counts

4 → 108

Calls

4 calls:

85.0ms	(expm1.f64 (*.f64 eps (+.f64 a b)))
85.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
85.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
85.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	63
1	293	63
2	4113	63
3	5908	63

simplify149.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-def_binary64`
410×	`times-frac_binary64`
350×	`associate-/l*_binary64`
238×	`associate-/r*_binary64`
221×	`*-commutative_binary64`

Counts

252 → 212

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	556	7020
1	1978	6629
2	4932	6625
3	5215	6625

prune171.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	209	3	212
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	210	3	213

Error

0.0b

Counts

213 → 3

Alt Table

Status	Error	Program
▶	6.2b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
	37.9b	(pow.f64 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))) -1)
	36.5b	(.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (pow.f64 (cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))) 2)) (/.f64 eps (cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))))

Compiler

Compiled 10787 to 3843 computations (64.4% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
✓	0.0b	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
✓	5.9b	(.f64 a (.f64 eps eps))
✓	7.5b	(.f64 b (.f64 eps eps))

series57.0ms (0.3%)

Counts

4 → 120

Calls

4 calls:

24.0ms	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
16.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
9.0ms	(.f64 b (.f64 eps eps))
7.0ms	(.f64 a (.f64 eps eps))

rewrite65.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

743×	`prod-diff_binary64`
148×	`add-sqr-sqrt_binary64`
139×	`log1p-expm1-u_binary64`
139×	`expm1-log1p-u_binary64`
137×	`add-cbrt-cube_binary64`

Counts

4 → 82

Calls

4 calls:

63.0ms	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
63.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
63.0ms	(.f64 a (.f64 eps eps))
63.0ms	(.f64 b (.f64 eps eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	58
1	298	58
2	3557	58
3	4925	58

simplify133.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

731×	`distribute-rgt-out_binary64`
626×	`associate-l_binary64`
552×	`fma-def_binary64`
484×	`*-commutative_binary64`
362×	`distribute-rgt-in_binary64`

Counts

202 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	1742
1	65	1511
2	140	1461
3	295	1461
4	616	1461
5	1529	1461
6	2768	1461
7	3790	1461
8	4997	1461
9	4996	1461
10	4947	1461

prune83.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	106	4	110

Error

0.0b

Counts

110 → 4

Alt Table

Status	Error	Program
✓	6.2b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
	37.9b	(pow.f64 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))) -1)
	36.5b	(.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (pow.f64 (cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))) 2)) (/.f64 eps (cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))))
▶	7.4b	(pow.f64 (cbrt.f64 (fma.f64 1/12 (.f64 (.f64 eps eps) a) (+.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)) (/.f64 1 b)))) 3)

Compiler

Compiled 2745 to 1408 computations (48.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (fma.f64 1/12 (.f64 (.f64 eps eps) a) (+.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)) (/.f64 1 b))))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 1/12 (.f64 (.f64 eps eps) a) (+.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)) (/.f64 1 b)))) 3)
✓	5.9b	(.f64 (.f64 eps eps) a)
	7.5b	(.f64 b (.f64 eps eps))

series2.4s (10.6%)

Counts

3 → 96

Calls

3 calls:

2.3s

(pow.f64 (cbrt.f64 (fma.f64 1/12 (*.f64 (*.f64 eps eps) a) (+.f64 (fma.f64 1/12 (*.f64 b (*.f64 eps eps)) (/.f64 1 a)) (/.f64 1 b)))) 3)

98.0ms

(cbrt.f64 (fma.f64 1/12 (*.f64 (*.f64 eps eps) a) (+.f64 (fma.f64 1/12 (*.f64 b (*.f64 eps eps)) (/.f64 1 a)) (/.f64 1 b))))

7.0ms

(*.f64 (*.f64 eps eps) a)

rewrite68.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

725×	`prod-diff_binary64`
165×	`add-sqr-sqrt_binary64`
158×	`log1p-expm1-u_binary64`
158×	`expm1-log1p-u_binary64`
155×	`add-cbrt-cube_binary64`

Counts

3 → 68

Calls

3 calls:

65.0ms

(cbrt.f64 (fma.f64 1/12 (*.f64 (*.f64 eps eps) a) (+.f64 (fma.f64 1/12 (*.f64 b (*.f64 eps eps)) (/.f64 1 a)) (/.f64 1 b))))

65.0ms

(pow.f64 (cbrt.f64 (fma.f64 1/12 (*.f64 (*.f64 eps eps) a) (+.f64 (fma.f64 1/12 (*.f64 b (*.f64 eps eps)) (/.f64 1 a)) (/.f64 1 b)))) 3)

65.0ms

(*.f64 (*.f64 eps eps) a)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	69
1	344	69
2	3952	69
3	5170	69

simplify138.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

679×	`fma-def_binary64`
597×	`associate-/r*_binary64`
486×	`times-frac_binary64`
337×	`associate-/l*_binary64`
213×	`*-commutative_binary64`

Counts

164 → 188

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	615	9404
1	2125	8992
2	5599	8992

prune292.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	206	4	210

Error

0.0b

Counts

210 → 4

Alt Table

Status	Error	Program
✓	6.2b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
	37.9b	(pow.f64 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))) -1)
▶	36.5b	(.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (pow.f64 (cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))) 2)) (/.f64 eps (cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))))
✓	7.4b	(pow.f64 (cbrt.f64 (fma.f64 1/12 (.f64 (.f64 eps eps) a) (+.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)) (/.f64 1 b)))) 3)

Compiler

Compiled 13933 to 9513 computations (31.7% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.1b	(/.f64 eps (cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))))
✓	2.1b	(.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (pow.f64 (cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))) 2)) (/.f64 eps (cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))))
✓	20.1b	(/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (pow.f64 (cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))) 2))
✓	33.1b	(cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series4.8s (21.1%)

Counts

4 → 144

Calls

4 calls:

2.8s	(/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (pow.f64 (cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))) 2))
1.1s	(/.f64 eps (cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))))
734.0ms	(cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
178.0ms	(.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (pow.f64 (cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))) 2)) (/.f64 eps (cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))))

rewrite105.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

941×	`prod-diff_binary64`
187×	`add-sqr-sqrt_binary64`
178×	`log1p-expm1-u_binary64`
178×	`expm1-log1p-u_binary64`
172×	`associate-r_binary64`

Counts

4 → 160

Calls

4 calls:

101.0ms	(/.f64 eps (cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))))
101.0ms	(.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (pow.f64 (cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))) 2)) (/.f64 eps (cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))))
101.0ms	(/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (pow.f64 (cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))) 2))
101.0ms	(cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	93
1	379	93
2	5000	93
3	6863	93

simplify398.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

638×	`fma-def_binary64`
457×	`associate-*r/_binary64`
425×	`associate-/l*_binary64`
66×	`sqr-pow_binary64`
43×	`sub-neg_binary64`

Counts

304 → 260

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2503	44933
1	5263	44933

prune1.0s (4.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	306	1	307
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	307	4	311

Error

0.0b

Counts

311 → 4

Alt Table

Status	Error	Program
	36.1b	(/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) eps))
✓	6.2b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
✓	36.5b	(.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (pow.f64 (cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b)))) 2)) (/.f64 eps (cbrt.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))))))
✓	7.4b	(pow.f64 (cbrt.f64 (fma.f64 1/12 (.f64 (.f64 eps eps) a) (+.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)) (/.f64 1 b)))) 3)

Compiler

Compiled 70411 to 33559 computations (52.3% saved)

regimes664.0ms (2.9%)

Accuracy

Total 0.2b remaining (87.5%)

Threshold costs 0.2b (87.5%)

Counts

123 → 3

Compiler

Compiled 10922 to 7064 computations (35.3% saved)

bsearch5.0ms (0%)

Compiler: Compiled 27 to 19 computations (29.6% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
6×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	156
1	61	156
2	64	156
3	62	156

end303.0ms (1.3%)

Compiler: Compiled 527 to 299 computations (43.3% saved)

Details

analyze2.7s (12%)

sample8.6s (38.1%)

simplify23.0ms (0.1%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series282.0ms (1.2%)

rewrite89.0ms (0.4%)

simplify149.0ms (0.7%)

prune171.0ms (0.8%)

localize11.0ms (0%)

series57.0ms (0.3%)

rewrite65.0ms (0.3%)

simplify133.0ms (0.6%)

prune83.0ms (0.4%)

localize14.0ms (0.1%)

series2.4s (10.6%)

rewrite68.0ms (0.3%)

simplify138.0ms (0.6%)

prune292.0ms (1.3%)

localize19.0ms (0.1%)

series4.8s (21.1%)

rewrite105.0ms (0.5%)

simplify398.0ms (1.8%)

prune1.0s (4.5%)

regimes664.0ms (2.9%)

bsearch5.0ms (0%)

simplify5.0ms (0%)

end303.0ms (1.3%)

Profiling