Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample2.0s (41.3%)

Results

864.0ms	2092×	body	1024	valid
470.0ms	4392×	body	128	valid
288.0ms	1035×	body	512	valid
112.0ms	232×	body	2048	valid
104.0ms	505×	body	256	valid

Compiler

Compiled 38 to 35 computations (7.9% saved)

simplify64.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

978×	`times-frac_binary64`
434×	`unswap-sqr_binary64`
378×	`associate-*l/_binary64`
368×	`fma-neg_binary64`
358×	`fma-def_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	19	15
2	25	15
3	34	15
4	59	15
5	113	15
6	235	15
7	600	15
8	1504	15
9	2557	15
10	4582	15
11	4956	15
12	4701	15

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

25.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	25.3b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

Compiler

Compiled 36 to 33 computations (8.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 (*.f64 -2 x)))
✓	0.0b	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
✓	2.8b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

series20.0ms (0.4%)

Counts

3 → 20

Calls

3 calls:

9.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
8.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
3.0ms	(+.f64 1 (exp.f64 (*.f64 -2 x)))

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`*-un-lft-identity_binary64`
75×	`add-sqr-sqrt_binary64`
64×	`add-cube-cbrt_binary64`
63×	`times-frac_binary64`
54×	`prod-diff_binary64`

Counts

3 → 149

Calls

3 calls:

11.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
4.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
3.0ms	(+.f64 1 (exp.f64 (*.f64 -2 x)))

simplify124.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

745×	`fma-neg_binary64`
409×	`cancel-sign-sub-inv_binary64`
312×	`distribute-rgt-in_binary64`
288×	`fma-def_binary64`
267×	`distribute-lft-in_binary64`

Counts

169 → 220

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	151	3241
1	339	3128
2	809	2722
3	2297	2604
4	4742	2603
5	4949	2603

prune181.0ms (3.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	217	3	220
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	218	3	221

Error

Counts

221 → 3

Alt Table

Status	Error	Program
	25.6b	(fma.f64 (sqrt.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x))))) (sqrt.f64 (/.f64 2 (+.f64 1 (exp.f64 (.f64 -2 x))))) -1)
▶	25.3b	(expm1.f64 (-.f64 (log.f64 2) (log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))))
	36.1b	(-.f64 (fma.f64 2/15 (pow.f64 x 5) x) (fma.f64 1/3 (pow.f64 x 3) (*.f64 17/315 (pow.f64 x 7))))

Compiler

Compiled 5082 to 4627 computations (9% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (exp.f64 (*.f64 -2 x)))
✓	0.0b	(log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))
✓	2.8b	(-.f64 (log.f64 2) (log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x)))))

series415.0ms (8.8%)

Counts

2 → 8

Calls

2 calls:

216.0ms	(-.f64 (log.f64 2) (log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x)))))
199.0ms	(log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
17×	`pow1_binary64`
16×	`prod-diff_binary64`
15×	`add-cube-cbrt_binary64`

Counts

2 → 69

Calls

2 calls:

8.0ms	(-.f64 (log.f64 2) (log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x)))))
3.0ms	(log.f64 (+.f64 1 (exp.f64 (*.f64 -2 x))))

simplify111.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

757×	`fma-neg_binary64`
512×	`cancel-sign-sub-inv_binary64`
388×	`fma-def_binary64`
292×	`associate-l_binary64`
287×	`neg-mul-1_binary64`

Counts

77 → 103

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	125	1570
1	259	1267
2	729	1077
3	2446	1071
4	3814	1059
5	4638	1059
6	4829	1059

prune95.0ms (2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	137	2	139

Error

Counts

139 → 2

Alt Table

Status	Error	Program
	36.1b	(-.f64 (fma.f64 2/15 (pow.f64 x 5) x) (fma.f64 1/3 (pow.f64 x 3) (*.f64 17/315 (pow.f64 x 7))))
▶	25.2b	(expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2)))))

Compiler

Compiled 2814 to 2510 computations (10.8% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (exp.f64 (*.f64 x -2)))
✓	2.8b	(-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))

series409.0ms (8.7%)

Counts

2 → 24

Calls

2 calls:

210.0ms	(-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))
198.0ms	(log1p.f64 (exp.f64 (*.f64 x -2)))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`prod-diff_binary64`
12×	`add-cube-cbrt_binary64`
7×	`pow1_binary64`

Counts

2 → 50

Calls

2 calls:

5.0ms	(-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))
0.0ms	(log1p.f64 (exp.f64 (*.f64 x -2)))

simplify113.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

458×	`unsub-neg_binary64`
359×	`cancel-sign-sub-inv_binary64`
352×	`sub-neg_binary64`
345×	`*-commutative_binary64`
332×	`fma-neg_binary64`

Counts

74 → 67

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	104	1244
1	200	1100
2	540	976
3	1862	976
4	3891	967
5	4351	967
6	4785	967
7	4768	967

prune46.0ms (1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	67	2	69

Error

Counts

69 → 2

Alt Table

Status	Error	Program
▶	36.1b	(-.f64 (fma.f64 2/15 (pow.f64 x 5) x) (fma.f64 1/3 (pow.f64 x 3) (*.f64 17/315 (pow.f64 x 7))))
✓	25.2b	(expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2)))))

Compiler

Compiled 1390 to 1219 computations (12.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2/15 (pow.f64 x 5) x)
✓	0.0b	(*.f64 17/315 (pow.f64 x 7))
✓	0.1b	(fma.f64 1/3 (pow.f64 x 3) (*.f64 17/315 (pow.f64 x 7)))
✓	25.8b	(-.f64 (fma.f64 2/15 (pow.f64 x 5) x) (fma.f64 1/3 (pow.f64 x 3) (*.f64 17/315 (pow.f64 x 7))))

series17.0ms (0.3%)

Counts

4 → 36

Calls

4 calls:

5.0ms	(fma.f64 1/3 (pow.f64 x 3) (*.f64 17/315 (pow.f64 x 7)))
4.0ms	(-.f64 (fma.f64 2/15 (pow.f64 x 5) x) (fma.f64 1/3 (pow.f64 x 3) (*.f64 17/315 (pow.f64 x 7))))
4.0ms	(*.f64 17/315 (pow.f64 x 7))
3.0ms	(fma.f64 2/15 (pow.f64 x 5) x)

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
9×	`add-exp-log_binary64`
9×	`prod-diff_binary64`

Counts

4 → 79

Calls

4 calls:

5.0ms	(*.f64 17/315 (pow.f64 x 7))
3.0ms	(-.f64 (fma.f64 2/15 (pow.f64 x 5) x) (fma.f64 1/3 (pow.f64 x 3) (*.f64 17/315 (pow.f64 x 7))))
0.0ms	(fma.f64 2/15 (pow.f64 x 5) x)
0.0ms	(fma.f64 1/3 (pow.f64 x 3) (*.f64 17/315 (pow.f64 x 7)))

simplify102.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

874×	`fma-neg_binary64`
633×	`times-frac_binary64`
600×	`associate-r_binary64`
389×	`fma-def_binary64`
339×	`distribute-lft-in_binary64`

Counts

115 → 122

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	142	2229
1	264	2018
2	793	1831
3	3426	1774
4	4427	1759
5	5637	1759

prune105.0ms (2.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	122	2	124

Error

Counts

124 → 2

Alt Table

Status	Error	Program
✓	36.1b	(-.f64 (fma.f64 2/15 (pow.f64 x 5) x) (fma.f64 1/3 (pow.f64 x 3) (*.f64 17/315 (pow.f64 x 7))))
✓	25.2b	(expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2)))))

Compiler

Compiled 3465 to 2751 computations (20.6% saved)

regimes797.0ms (16.9%)

Accuracy

Total 0.1b remaining (96.8%)

Threshold costs 0.1b (96.8%)

Counts

66 → 2

Compiler

Compiled 11699 to 10665 computations (8.8% saved)

bsearch2.0ms (0%)

Compiler: Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	34
1	22	34
2	27	34
3	29	34
4	30	34
5	30	34

end63.0ms (1.3%)

Compiler: Compiled 78 to 63 computations (19.2% saved)

Details

analyze2.0ms (0.1%)

sample2.0s (41.3%)

simplify64.0ms (1.4%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series20.0ms (0.4%)

rewrite30.0ms (0.6%)

simplify124.0ms (2.6%)

prune181.0ms (3.8%)

localize9.0ms (0.2%)

series415.0ms (8.8%)

rewrite15.0ms (0.3%)

simplify111.0ms (2.3%)

prune95.0ms (2%)

localize9.0ms (0.2%)

series409.0ms (8.7%)

rewrite8.0ms (0.2%)

simplify113.0ms (2.4%)

prune46.0ms (1%)

localize12.0ms (0.2%)

series17.0ms (0.3%)

rewrite13.0ms (0.3%)

simplify102.0ms (2.2%)

prune105.0ms (2.2%)

regimes797.0ms (16.9%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end63.0ms (1.3%)

Profiling