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)

sample138.0ms (3.8%)

Algorithm

1×

intervals

Results

15.0ms	61×	body	1024	valid
7.0ms	41×	body	512	valid
6.0ms	139×	body	128	valid
1.0ms	11×	body	256	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify67.0ms (1.8%)

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 (0.1%)

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

29.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.5b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

Compiler

Compiled 36 to 33 computations (8.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series20.0ms (0.6%)

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 (0.8%)

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:

10.0ms	(-.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)))

simplify196.0ms (5.4%)

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

prune241.0ms (6.6%)

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
▶	29.5b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) 1) 3))
	29.7b	(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)
	30.6b	x

Compiler

Compiled 5054 to 4605 computations (8.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) 1) 3)
✓	0.0b	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))
✓	0.0b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) 1) 3))
✓	2.8b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) 1)

series48.0ms (1.3%)

Counts

4 → 48

Calls

4 calls:

19.0ms	(pow.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) 1) 3)
11.0ms	(cbrt.f64 (pow.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) 1) 3))
9.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) 1)
8.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))

rewrite54.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

125×	`add-sqr-sqrt_binary64`
122×	`*-un-lft-identity_binary64`
75×	`times-frac_binary64`
70×	`add-cube-cbrt_binary64`
54×	`prod-diff_binary64`

Counts

4 → 212

Calls

4 calls:

11.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) 1)
10.0ms	(pow.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) 1) 3)
10.0ms	(cbrt.f64 (pow.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) 1) 3))
5.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2))))

simplify170.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

756×	`times-frac_binary64`
336×	`distribute-rgt-in_binary64`
333×	`fma-def_binary64`
318×	`distribute-lft-in_binary64`
245×	`fma-neg_binary64`

Counts

260 → 237

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	208	5877
1	450	5640
2	1235	5097
3	3451	5042
4	5109	5042

prune245.0ms (6.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	237	0	237
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	237	3	240

Error

Counts

240 → 3

Alt Table

Status	Error	Program
✓	29.5b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) 1) 3))
▶	29.7b	(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)
	30.6b	x

Compiler

Compiled 6436 to 5937 computations (7.8% saved)

localize10.0ms (0.3%)

Local error

Found 4 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))))
✓	0.2b	(sqrt.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))))
✓	3.2b	(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)

series55.0ms (1.5%)

Counts

2 → 24

Calls

2 calls:

40.0ms	(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)
15.0ms	(sqrt.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`sqrt-prod_binary64`
16×	`*-un-lft-identity_binary64`
13×	`times-frac_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`

Counts

2 → 42

Calls

2 calls:

4.0ms	(sqrt.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))))
0.0ms	(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)

simplify79.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

548×	`fma-neg_binary64`
323×	`distribute-rgt-neg-in_binary64`
312×	`distribute-lft-neg-in_binary64`
223×	`associate-r_binary64`
203×	`unswap-sqr_binary64`

Counts

66 → 84

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	144	1566
1	304	1333
2	820	1315
3	2993	1286
4	4983	1286

prune273.0ms (7.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	332	0	332
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	332	3	335

Error

Counts

335 → 3

Alt Table

Status	Error	Program
✓	29.5b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) 1) 3))
✓	29.7b	(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)
▶	30.6b	x

Compiler

Compiled 9230 to 8277 computations (10.3% saved)

localize1.0ms (0%)

prune3.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Error

Counts

3 → 3

Alt Table

Status	Error	Program
✓	29.5b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) 1) 3))
✓	29.7b	(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)
✓	30.6b	x

Compiler

Compiled 40 to 36 computations (10% saved)

regimes717.0ms (19.8%)

Accuracy

Total 0.2b remaining (74.9%)

Threshold costs 0.2b (74.9%)

Counts

52 → 3

Compiler

Compiled 7717 to 7149 computations (7.4% saved)

bsearch2.0ms (0%)

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

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	70
1	29	70
2	30	70
3	28	70

end1.0ms (0%)

Compiler: Compiled 48 to 42 computations (12.5% saved)

sample1.2s (34.2%)

Algorithm

1×

intervals

Results

485.0ms	2008×	body	1024	valid
187.0ms	4240×	body	128	valid
160.0ms	1079×	body	512	valid
54.0ms	197×	body	2048	valid
45.0ms	476×	body	256	valid

Compiler

Compiled 103 to 92 computations (10.7% saved)

Details

analyze2.0ms (0.1%)

sample138.0ms (3.8%)

simplify67.0ms (1.8%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series20.0ms (0.6%)

rewrite30.0ms (0.8%)

simplify196.0ms (5.4%)

prune241.0ms (6.6%)

localize10.0ms (0.3%)

series48.0ms (1.3%)

rewrite54.0ms (1.5%)

simplify170.0ms (4.7%)

prune245.0ms (6.8%)

localize10.0ms (0.3%)

series55.0ms (1.5%)

rewrite7.0ms (0.2%)

simplify79.0ms (2.2%)

prune273.0ms (7.5%)

localize1.0ms (0%)

prune3.0ms (0.1%)

regimes717.0ms (19.8%)

bsearch2.0ms (0%)

simplify7.0ms (0.2%)

end1.0ms (0%)

sample1.2s (34.2%)

Profiling