Details

analyze1.0ms (0%)

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)

sample1.9s (43.4%)

Results

811.0ms	2008×	body	1024	valid
465.0ms	4484×	body	128	valid
280.0ms	1009×	body	512	valid
103.0ms	552×	body	256	valid
98.0ms	203×	body	2048	valid

Compiler

Compiled 38 to 35 computations (7.9% saved)

simplify65.0ms (1.5%)

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

29.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.0b	(-.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))))
✓	3.1b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

series18.0ms (0.4%)

Counts

3 → 20

Calls

3 calls:

9.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
7.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
1.0ms	(+.f64 1 (exp.f64 (*.f64 -2 x)))

rewrite31.0ms (0.7%)

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)))

simplify120.0ms (2.8%)

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

prune180.0ms (4.2%)

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

0.0b

Counts

221 → 3

Alt Table

Status	Error	Program
	32.2b	(fma.f64 (pow.f64 x 3) -1/3 x)
▶	29.0b	(log.f64 (/.f64 (exp.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))) (exp.f64 1)))
	44.8b	(+.f64 (fma.f64 (/.f64 2 (neg.f64 (expm1.f64 (.f64 x -4)))) (neg.f64 (expm1.f64 (.f64 x -2))) -1) 0)

Compiler

Compiled 5056 to 4605 computations (8.9% saved)

localize10.0ms (0.2%)

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))))
✓	0.3b	(/.f64 (exp.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))) (exp.f64 1))
✓	3.1b	(log.f64 (/.f64 (exp.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))) (exp.f64 1)))

series228.0ms (5.3%)

Counts

2 → 16

Calls

2 calls:

215.0ms	(log.f64 (/.f64 (exp.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))) (exp.f64 1)))
13.0ms	(/.f64 (exp.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))) (exp.f64 1))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
17×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64`
13×	`log-prod_binary64`

Counts

2 → 59

Calls

2 calls:

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

simplify87.0ms (2%)

Algorithm

1×	egg-herbie

Rules

609×	`fma-def_binary64`
342×	`times-frac_binary64`
310×	`associate-/l*_binary64`
284×	`fma-neg_binary64`
265×	`div-exp_binary64`

Counts

75 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	122	1941
1	252	1739
2	540	1662
3	1369	1654
4	4296	1654
5	5001	1654

prune140.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	215	3	218

Error

0.0b

Counts

218 → 3

Alt Table

Status	Error	Program
▶	32.2b	(fma.f64 (pow.f64 x 3) -1/3 x)
✓	29.0b	(log.f64 (/.f64 (exp.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))) (exp.f64 1)))
	44.8b	(+.f64 (fma.f64 (/.f64 2 (neg.f64 (expm1.f64 (.f64 x -4)))) (neg.f64 (expm1.f64 (.f64 x -2))) -1) 0)

Compiler

Compiled 4503 to 4032 computations (10.5% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (pow.f64 x 3) -1/3 x)

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(fma.f64 (pow.f64 x 3) -1/3 x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (pow.f64 x 3) -1/3 x)

simplify57.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

435×	`neg-mul-1_binary64`
394×	`associate-l_binary64`
372×	`associate-r_binary64`
317×	`distribute-rgt-out_binary64`
261×	`exp-prod_binary64`

Counts

22 → 16

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	232
1	35	197
2	87	197
3	323	197
4	1660	197
5	4537	197
6	5209	197

prune8.0ms (0.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	16	3	19

Error

0.0b

Counts

19 → 3

Alt Table

Status	Error	Program
✓	32.2b	(fma.f64 (pow.f64 x 3) -1/3 x)
✓	29.0b	(log.f64 (/.f64 (exp.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))) (exp.f64 1)))
▶	44.8b	(+.f64 (fma.f64 (/.f64 2 (neg.f64 (expm1.f64 (.f64 x -4)))) (neg.f64 (expm1.f64 (.f64 x -2))) -1) 0)

Compiler

Compiled 208 to 162 computations (22.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (*.f64 x -2))
✓	0.0b	(expm1.f64 (*.f64 x -4))
✓	0.0b	(/.f64 2 (neg.f64 (expm1.f64 (*.f64 x -4))))
✓	29.6b	(fma.f64 (/.f64 2 (neg.f64 (expm1.f64 (.f64 x -4)))) (neg.f64 (expm1.f64 (.f64 x -2))) -1)

series23.0ms (0.5%)

Counts

4 → 48

Calls

4 calls:

12.0ms	(fma.f64 (/.f64 2 (neg.f64 (expm1.f64 (.f64 x -4)))) (neg.f64 (expm1.f64 (.f64 x -2))) -1)
7.0ms	(/.f64 2 (neg.f64 (expm1.f64 (*.f64 x -4))))
2.0ms	(expm1.f64 (*.f64 x -4))
2.0ms	(expm1.f64 (*.f64 x -2))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`times-frac_binary64`
27×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
27×	`add-cube-cbrt_binary64`
12×	`distribute-lft-neg-in_binary64`

Counts

4 → 89

Calls

4 calls:

3.0ms	(/.f64 2 (neg.f64 (expm1.f64 (*.f64 x -4))))
0.0ms	(expm1.f64 (*.f64 x -2))
0.0ms	(fma.f64 (/.f64 2 (neg.f64 (expm1.f64 (.f64 x -4)))) (neg.f64 (expm1.f64 (.f64 x -2))) -1)
0.0ms	(expm1.f64 (*.f64 x -4))

simplify103.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

869×	`fma-neg_binary64`
239×	`fma-def_binary64`
217×	`sub-neg_binary64`
210×	`cancel-sign-sub-inv_binary64`
188×	`associate-/r*_binary64`

Counts

137 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	193	2336
1	393	2135
2	1022	2094
3	3003	1992
4	4616	1992
5	4867	1992

prune95.0ms (2.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	153	3	156

Error

0.0b

Counts

156 → 3

Alt Table

Status	Error	Program
✓	32.2b	(fma.f64 (pow.f64 x 3) -1/3 x)
✓	29.0b	(log.f64 (/.f64 (exp.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))) (exp.f64 1)))
✓	44.8b	(+.f64 (fma.f64 (/.f64 2 (neg.f64 (expm1.f64 (.f64 x -4)))) (neg.f64 (expm1.f64 (.f64 x -2))) -1) 0)

Compiler

Compiled 3472 to 3039 computations (12.5% saved)

regimes1.1s (26.3%)

Accuracy

Total 0.1b remaining (75.3%)

Threshold costs 0.1b (75.3%)

Counts

81 → 3

Compiler

Compiled 11625 to 10773 computations (7.3% saved)

bsearch2.0ms (0.1%)

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

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
1×	`+-rgt-identity_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	66
1	42	66
2	44	66
3	45	66
4	44	66

end79.0ms (1.8%)

Compiler: Compiled 131 to 112 computations (14.5% saved)

Details

analyze1.0ms (0%)

sample1.9s (43.4%)

simplify65.0ms (1.5%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series18.0ms (0.4%)

rewrite31.0ms (0.7%)

simplify120.0ms (2.8%)

prune180.0ms (4.2%)

localize10.0ms (0.2%)

series228.0ms (5.3%)

rewrite19.0ms (0.4%)

simplify87.0ms (2%)

prune140.0ms (3.3%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite1.0ms (0%)

simplify57.0ms (1.3%)

prune8.0ms (0.2%)

localize10.0ms (0.2%)

series23.0ms (0.5%)

rewrite8.0ms (0.2%)

simplify103.0ms (2.4%)

prune95.0ms (2.2%)

regimes1.1s (26.3%)

bsearch2.0ms (0.1%)

simplify3.0ms (0.1%)

end79.0ms (1.8%)

Profiling