Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample118.0ms (2.5%)

Algorithm

1×

intervals

Results

11.0ms	71×	body	1024	valid
5.0ms	131×	body	128	valid
3.0ms	28×	body	512	valid
2.0ms	10×	body	2048	valid
1.0ms	16×	body	256	valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify78.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

859×	`fma-neg_binary64`
770×	`fma-def_binary64`
322×	`div-sub_binary64`
178×	`associate-/l*_binary64`
150×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	34	19
4	57	19
5	91	19
6	178	19
7	277	19
8	643	19
9	788	19
10	1024	19
11	1265	19
12	1242	19
13	1248	19
14	1246	19
15	1248	19
16	1250	19
17	1260	19
18	1260	19
19	1171	19

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

30.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.3b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	0.0b	(/.f64 x (+.f64 x 1))
✓	2.7b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series8.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
2.0ms	(/.f64 x (+.f64 x 1))

rewrite211.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Rules

1322×	`*-un-lft-identity_binary64`
1012×	`times-frac_binary64`
869×	`add-sqr-sqrt_binary64`
612×	`prod-diff_binary64`
533×	`add-cube-cbrt_binary64`

Counts

3 → 783

Calls

3 calls:

43.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
6.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
3.0ms	(/.f64 x (+.f64 x 1))

simplify918.0ms (19.5%)

Algorithm

1×	egg-herbie

Rules

654×	`fma-neg_binary64`
367×	`unsub-neg_binary64`
299×	`fma-udef_binary64`
213×	`sub-neg_binary64`
202×	`associate-+r-_binary64`

Counts

819 → 619

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	545	54602
1	1290	31108
2	3043	22839
3	4323	22837
4	4983	22837
5	4991	22837
6	4742	22837

prune693.0ms (14.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	615	4	619
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	616	4	620

Error

0.0b

Counts

620 → 4

Alt Table

Status	Error	Program
	62.6b	(+.f64 (fma.f64 (/.f64 x (+.f64 (pow.f64 x 3) (pow.f64 1 3))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))) (neg.f64 (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (*.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))))
▶	30.2b	(expm1.f64 (log1p.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
	31.3b	(-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x)))
	31.5b	(neg.f64 (+.f64 (*.f64 3 (/.f64 1 x)) (/.f64 1 (pow.f64 x 2))))

Compiler

Compiled 30508 to 22487 computations (26.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (+.f64 x 1))
✓	0.0b	(expm1.f64 (log1p.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
✓	0.0b	(log1p.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
	2.7b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(log1p.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
3.0ms	(expm1.f64 (log1p.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

1.0ms	(log1p.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
0.0ms	(expm1.f64 (log1p.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))

simplify79.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

437×	`sub-neg_binary64`
369×	`distribute-neg-frac_binary64`
327×	`neg-mul-1_binary64`
305×	`fma-neg_binary64`
265×	`div-sub_binary64`

Counts

46 → 57

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	968
1	202	851
2	557	841
3	1525	839
4	3794	839
5	4581	839
6	5031	839

prune632.0ms (13.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	589	1	590
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	590	4	594

Error

0.0b

Counts

594 → 4

Alt Table

Status	Error	Program
▶	31.0b	(expm1.f64 (-.f64 (/.f64 -3 x) (/.f64 11/2 (*.f64 x x))))
	62.6b	(+.f64 (fma.f64 (/.f64 x (+.f64 (pow.f64 x 3) (pow.f64 1 3))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))) (neg.f64 (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (*.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))))
✓	30.2b	(expm1.f64 (log1p.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
	31.3b	(-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x)))

Compiler

Compiled 30782 to 23005 computations (25.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (-.f64 (/.f64 -3 x) (/.f64 11/2 (*.f64 x x))))
✓	0.0b	(-.f64 (/.f64 -3 x) (/.f64 11/2 (*.f64 x x)))
✓	0.5b	(/.f64 11/2 (*.f64 x x))

series9.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(expm1.f64 (-.f64 (/.f64 -3 x) (/.f64 11/2 (*.f64 x x))))
3.0ms	(-.f64 (/.f64 -3 x) (/.f64 11/2 (*.f64 x x)))
2.0ms	(/.f64 11/2 (*.f64 x x))

rewrite29.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

121×	`times-frac_binary64`
99×	`add-sqr-sqrt_binary64`
91×	`prod-diff_binary64`
91×	`*-un-lft-identity_binary64`
89×	`add-cube-cbrt_binary64`

Counts

3 → 164

Calls

3 calls:

11.0ms	(-.f64 (/.f64 -3 x) (/.f64 11/2 (*.f64 x x)))
3.0ms	(/.f64 11/2 (*.f64 x x))
0.0ms	(expm1.f64 (-.f64 (/.f64 -3 x) (/.f64 11/2 (*.f64 x x))))

simplify147.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

626×	`fma-def_binary64`
596×	`fma-neg_binary64`
275×	`associate-*l/_binary64`
263×	`times-frac_binary64`
227×	`associate-/l*_binary64`

Counts

200 → 221

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	265	4722
1	513	3917
2	1329	2772
3	3803	2724
4	4909	2724
5	4833	2724

prune147.0ms (3.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	221	4	225

Error

0.0b

Counts

225 → 4

Alt Table

Status	Error	Program
✓	31.0b	(expm1.f64 (-.f64 (/.f64 -3 x) (/.f64 11/2 (*.f64 x x))))
	62.6b	(+.f64 (fma.f64 (/.f64 x (+.f64 (pow.f64 x 3) (pow.f64 1 3))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))) (neg.f64 (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (*.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))))
✓	30.2b	(expm1.f64 (log1p.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
▶	31.3b	(-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x)))

Compiler

Compiled 6604 to 4505 computations (31.8% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x)))
✓	0.4b	(/.f64 1 (*.f64 x x))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(/.f64 1 (*.f64 x x))
2.0ms	(-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x)))

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

125×	`times-frac_binary64`
101×	`add-sqr-sqrt_binary64`
94×	`*-un-lft-identity_binary64`
91×	`prod-diff_binary64`
88×	`add-cube-cbrt_binary64`

Counts

2 → 168

Calls

2 calls:

10.0ms	(-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x)))
3.0ms	(/.f64 1 (*.f64 x x))

simplify153.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

600×	`times-frac_binary64`
599×	`div-sub_binary64`
452×	`associate-l_binary64`
405×	`fma-def_binary64`
396×	`fma-neg_binary64`

Counts

192 → 193

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	179	4012
1	329	3196
2	829	2309
3	3614	1970
4	4477	1920
5	4474	1920
6	4986	1920

prune122.0ms (2.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	193	4	197

Error

0.0b

Counts

197 → 4

Alt Table

Status	Error	Program
✓	31.0b	(expm1.f64 (-.f64 (/.f64 -3 x) (/.f64 11/2 (*.f64 x x))))
	62.6b	(+.f64 (fma.f64 (/.f64 x (+.f64 (pow.f64 x 3) (pow.f64 1 3))) (+.f64 (.f64 x x) (-.f64 (.f64 1 1) (.f64 x 1))) (neg.f64 (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))))) (fma.f64 (neg.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (*.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))) (sqrt.f64 (/.f64 (+.f64 x 1) (-.f64 x 1))))))
✓	30.2b	(expm1.f64 (log1p.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))))
✓	31.3b	(-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x)))

Compiler

Compiled 5497 to 3697 computations (32.7% saved)

regimes340.0ms (7.2%)

Accuracy

Total 0.2b remaining (65.3%)

Threshold costs 0.2b (65.3%)

Counts

115 → 2

Compiler

Compiled 6352 to 4838 computations (23.8% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`*-commutative_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	91
1	47	91
2	64	91
3	73	91
4	77	91
5	78	91
6	75	91

end1.0ms (0%)

Compiler: Compiled 63 to 47 computations (25.4% saved)

sample944.0ms (20%)

Algorithm

1×

intervals

Results

306.0ms	2006×	body	1024	valid
182.0ms	4355×	body	128	valid
112.0ms	946×	body	512	valid
41.0ms	221×	body	2048	valid
35.0ms	472×	body	256	valid

Compiler

Compiled 192 to 145 computations (24.5% saved)

Details

analyze5.0ms (0.1%)

sample118.0ms (2.5%)

simplify78.0ms (1.7%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series8.0ms (0.2%)

rewrite211.0ms (4.5%)

simplify918.0ms (19.5%)

prune693.0ms (14.7%)

localize8.0ms (0.2%)

series6.0ms (0.1%)

rewrite2.0ms (0%)

simplify79.0ms (1.7%)

prune632.0ms (13.4%)

localize6.0ms (0.1%)

series9.0ms (0.2%)

rewrite29.0ms (0.6%)

simplify147.0ms (3.1%)

prune147.0ms (3.1%)

localize5.0ms (0.1%)

series6.0ms (0.1%)

rewrite30.0ms (0.6%)

simplify153.0ms (3.3%)

prune122.0ms (2.6%)

regimes340.0ms (7.2%)

bsearch5.0ms (0.1%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample944.0ms (20%)

Profiling