Details

analyze1.4s (23.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample2.8s (46.9%)

Results

1.5s	2644×	body	1024	valid
518.0ms	1366×	body	512	valid
397.0ms	3191×	body	128	valid
220.0ms	339×	body	2048	valid
182.0ms	716×	body	256	valid
1.0ms	2×	body	2048	invalid

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`expm1-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8
3	11	8

prune10.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))
	41.2b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))

Compiler

Compiled 41 to 25 computations (39% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 x)
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

series21.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

17.0ms	(/.f64 (exp.f64 x) (expm1.f64 x))
3.0ms	(expm1.f64 x)

rewrite113.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

477×	`log1p-expm1-u_binary64`
477×	`expm1-log1p-u_binary64`
334×	`unpow-prod-down_binary64`
258×	`log-prod_binary64`
241×	`prod-diff_binary64`

Counts

2 → 103

Calls

2 calls:

110.0ms	(expm1.f64 x)
110.0ms	(/.f64 (exp.f64 x) (expm1.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	98	11
2	1250	11
3	4894	11
4	5321	11
0	0	0
1	0	0

simplify81.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

804×	`unswap-sqr_binary64`
534×	`fma-def_binary64`
487×	`distribute-lft-out_binary64`
366×	`fma-neg_binary64`
361×	`*-commutative_binary64`

Counts

127 → 120

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	31	180
1	78	176
2	182	174
3	494	168
4	1472	168
5	2433	168
6	4835	168
7	4933	168

prune115.0ms (1.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	120	2	122

Error

0.4b

Counts

122 → 2

Alt Table

Status	Error	Program
	27.4b	(cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (expm1.f64 x) 3)))
▶	21.7b	(+.f64 1/2 (/.f64 1 x))

Compiler

Compiled 1496 to 669 computations (55.3% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/2 (/.f64 1 x))

series2.0ms (0%)

Counts

1 → 3

Calls

1 calls:

2.0ms

(+.f64 1/2 (/.f64 1 x))

rewrite98.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

588×	`log1p-expm1-u_binary64`
588×	`expm1-log1p-u_binary64`
241×	`log-prod_binary64`
158×	`prod-diff_binary64`
109×	`expm1-udef_binary64`

Counts

1 → 38

Calls

1 calls:

97.0ms

(+.f64 1/2 (/.f64 1 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	130	7
2	1492	7
3	4897	7
4	5058	7
0	0	0
1	0	0

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Counts

41 → 40

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	7	6
2	6	6

prune52.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	38	4	42

Error

0.4b

Counts

42 → 4

Alt Table

Status	Error	Program
	27.4b	(cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (expm1.f64 x) 3)))
▶	22.5b	(pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 3)
	41.6b	(pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 1 x))) 2)
✓	21.7b	(+.f64 1/2 (/.f64 1 x))

Compiler

Compiled 477 to 399 computations (16.4% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1/2 (/.f64 1 x))
✓	0.3b	(cbrt.f64 (+.f64 1/2 (/.f64 1 x)))
✓	0.8b	(pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 3)

series145.0ms (2.4%)

Counts

2 → 24

Calls

2 calls:

136.0ms	(pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 3)
9.0ms	(cbrt.f64 (+.f64 1/2 (/.f64 1 x)))

rewrite79.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

743×	`log1p-expm1-u_binary64`
743×	`expm1-log1p-u_binary64`
138×	`expm1-udef_binary64`
138×	`log1p-udef_binary64`
81×	`add-sqr-sqrt_binary64`

Counts

2 → 61

Calls

2 calls:

76.0ms	(cbrt.f64 (+.f64 1/2 (/.f64 1 x)))
76.0ms	(pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 1 x))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	177	16
2	1909	16
3	4871	16
0	0	0
1	0	0

simplify154.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

720×	`times-frac_binary64`
577×	`fma-neg_binary64`
366×	`associate-*l/_binary64`
322×	`associate-/l*_binary64`
290×	`associate-/r*_binary64`

Counts

85 → 82

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	419
1	151	343
2	385	319
3	1344	311
4	4119	311
5	4808	311
6	4984	311
7	4996	311
8	4928	311

prune113.0ms (1.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	123	3	126

Error

0.4b

Counts

126 → 3

Alt Table

Status	Error	Program
▶	27.4b	(cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (expm1.f64 x) 3)))
✓	21.7b	(+.f64 1/2 (/.f64 1 x))
	62.3b	(pow.f64 (fma.f64 2/3 (/.f64 (cbrt.f64 1/2) x) (cbrt.f64 1/2)) 3)

Compiler

Compiled 1664 to 1438 computations (13.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (expm1.f64 x) 3)
✓	0.0b	(pow.f64 (exp.f64 x) 3)
✓	0.6b	(/.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (expm1.f64 x) 3))
✓	25.1b	(cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (expm1.f64 x) 3)))

series108.0ms (1.8%)

Counts

4 → 40

Calls

4 calls:

66.0ms	(/.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (expm1.f64 x) 3))
18.0ms	(cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (expm1.f64 x) 3)))
14.0ms	(pow.f64 (expm1.f64 x) 3)
10.0ms	(pow.f64 (exp.f64 x) 3)

rewrite99.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

795×	`log1p-expm1-u_binary64`
795×	`expm1-log1p-u_binary64`
125×	`egg-rr`
85×	`add-sqr-sqrt_binary64`
85×	`prod-diff_binary64`

Counts

4 → 125

Calls

4 calls:

95.0ms	(pow.f64 (expm1.f64 x) 3)
95.0ms	(pow.f64 (exp.f64 x) 3)
95.0ms	(/.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (expm1.f64 x) 3))
95.0ms	(cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (expm1.f64 x) 3)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	34
1	182	31
2	2100	31
3	4998	31
0	0	0
1	0	0

simplify85.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

911×	`fma-def_binary64`
557×	`unswap-sqr_binary64`
503×	`associate-l_binary64`
383×	`associate-r_binary64`
230×	`fma-neg_binary64`

Counts

165 → 157

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	58	441
1	151	435
2	391	430
3	1074	399
4	3175	399
5	4788	399
6	5068	399

prune146.0ms (2.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

0.4b

Counts

160 → 3

Alt Table

Status	Error	Program
✓	27.4b	(cbrt.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (expm1.f64 x) 3)))
✓	21.7b	(+.f64 1/2 (/.f64 1 x))
	48.5b	(cbrt.f64 (+.f64 (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 3/2 (*.f64 x x)))) 3/8))

Compiler

Compiled 2079 to 1174 computations (43.5% saved)

regimes199.0ms (3.3%)

Accuracy

Total 0.0b remaining (8.5%)

Threshold costs 0.0b (8.5%)

Counts

53 → 1

Compiler

Compiled 1545 to 1197 computations (22.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	13	20
2	12	20

end106.0ms (1.8%)

Compiler: Compiled 62 to 45 computations (27.4% saved)

Details

analyze1.4s (23.3%)

sample2.8s (46.9%)

simplify12.0ms (0.2%)

prune10.0ms (0.2%)

localize6.0ms (0.1%)

series21.0ms (0.3%)

rewrite113.0ms (1.9%)

simplify81.0ms (1.4%)

prune115.0ms (1.9%)

localize5.0ms (0.1%)

series2.0ms (0%)

rewrite98.0ms (1.6%)

simplify12.0ms (0.2%)

prune52.0ms (0.9%)

localize10.0ms (0.2%)

series145.0ms (2.4%)

rewrite79.0ms (1.3%)

simplify154.0ms (2.6%)

prune113.0ms (1.9%)

localize13.0ms (0.2%)

series108.0ms (1.8%)

rewrite99.0ms (1.7%)

simplify85.0ms (1.4%)

prune146.0ms (2.4%)

regimes199.0ms (3.3%)

simplify4.0ms (0.1%)

end106.0ms (1.8%)

Profiling