Details

analyze101.0ms (1.7%)

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)

sample28.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms	60×	body	1024	valid
5.0ms	137×	body	128	valid
4.0ms	32×	body	512	valid
2.0ms	8×	body	2048	valid
1.0ms	19×	body	256	valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify89.0ms (1.5%)

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

30.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.1b	(-.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 x (+.f64 x 1))
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	4.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series8.0ms (0.1%)

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))

rewrite225.0ms (3.7%)

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:

39.0ms	(-.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))

simplify948.0ms (15.5%)

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

prune834.0ms (13.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	613	6	619
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	614	6	620

Error

0.0b

Counts

620 → 6

Alt Table

Status	Error	Program
	31.7b	(neg.f64 (+.f64 (*.f64 3 (/.f64 1 x)) (/.f64 1 (pow.f64 x 2))))
	32.8b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))
	47.8b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 x (+.f64 x 1))) (sqrt.f64 (/.f64 x (+.f64 x 1))) (neg.f64 (.f64 (/.f64 1 (-.f64 x 1)) (+.f64 x 1)))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 x 1))) (+.f64 x 1) (.f64 (/.f64 1 (-.f64 x 1)) (+.f64 x 1))))
▶	30.1b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))) 3))
	30.4b	(fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))
	31.5b	(-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x)))

Compiler

Compiled 30502 to 22479 computations (26.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 1 x) (+.f64 x -1))
✓	0.1b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))) 3))
✓	0.1b	(pow.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))) 3)
✓	4.0b	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))

series13.0ms (0.2%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(pow.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))) 3)
3.0ms	(cbrt.f64 (pow.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))) 3))
3.0ms	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
2.0ms	(/.f64 (+.f64 1 x) (+.f64 x -1))

rewrite234.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Rules

1183×	`*-un-lft-identity_binary64`
824×	`times-frac_binary64`
568×	`add-sqr-sqrt_binary64`
468×	`prod-diff_binary64`
427×	`add-cube-cbrt_binary64`

Counts

4 → 692

Calls

4 calls:

33.0ms	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
26.0ms	(cbrt.f64 (pow.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))) 3))
25.0ms	(pow.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))) 3)
6.0ms	(/.f64 (+.f64 1 x) (+.f64 x -1))

simplify661.0ms (10.8%)

Algorithm

1×	egg-herbie

Rules

854×	`times-frac_binary64`
273×	`fma-neg_binary64`
255×	`fma-udef_binary64`
223×	`unsub-neg_binary64`
205×	`associate-+r-_binary64`

Counts

740 → 533

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	631	58875
1	1517	26092
2	3673	25776
3	5313	25776

prune737.0ms (12%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	533	0	533
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	533	6	539

Error

0.0b

Counts

539 → 6

Alt Table

Status	Error	Program
	31.7b	(neg.f64 (+.f64 (*.f64 3 (/.f64 1 x)) (/.f64 1 (pow.f64 x 2))))
	32.8b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))
	47.8b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 x (+.f64 x 1))) (sqrt.f64 (/.f64 x (+.f64 x 1))) (neg.f64 (.f64 (/.f64 1 (-.f64 x 1)) (+.f64 x 1)))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 x 1))) (+.f64 x 1) (.f64 (/.f64 1 (-.f64 x 1)) (+.f64 x 1))))
✓	30.1b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))) 3))
▶	30.4b	(fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))
	31.5b	(-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x)))

Compiler

Compiled 28095 to 21313 computations (24.1% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.0b	(/.f64 (-.f64 -1 x) (+.f64 x -1))
✓	30.4b	(fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))

series8.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

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

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
42×	`add-sqr-sqrt_binary64`
37×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
10×	`distribute-lft-out_binary64`

Counts

3 → 103

Calls

3 calls:

7.0ms	(/.f64 1 (+.f64 x 1))
7.0ms	(/.f64 (-.f64 -1 x) (+.f64 x -1))
0.0ms	(fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))

simplify86.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

593×	`div-sub_binary64`
585×	`fma-neg_binary64`
396×	`fma-def_binary64`
220×	`distribute-rgt-in_binary64`
164×	`times-frac_binary64`

Counts

139 → 168

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	197	2228
1	476	2034
2	1162	2028
3	3488	2028
4	5150	2028

prune139.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	168	6	174

Error

0.0b

Counts

174 → 6

Alt Table

Status	Error	Program
	31.7b	(neg.f64 (+.f64 (*.f64 3 (/.f64 1 x)) (/.f64 1 (pow.f64 x 2))))
	32.8b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))
	47.8b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 x (+.f64 x 1))) (sqrt.f64 (/.f64 x (+.f64 x 1))) (neg.f64 (.f64 (/.f64 1 (-.f64 x 1)) (+.f64 x 1)))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 x 1))) (+.f64 x 1) (.f64 (/.f64 1 (-.f64 x 1)) (+.f64 x 1))))
✓	30.1b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))) 3))
	31.8b	(*.f64 (sqrt.f64 (fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))) (sqrt.f64 (fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))))
▶	31.5b	(-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x)))

Compiler

Compiled 3682 to 2731 computations (25.8% 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)))
✓	0.3b	(/.f64 1 (*.f64 x x))

series5.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

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

rewrite33.0ms (0.5%)

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:

12.0ms	(-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x)))
4.0ms	(/.f64 1 (*.f64 x x))

simplify163.0ms (2.7%)

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

prune132.0ms (2.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	193	6	199

Error

0.0b

Counts

199 → 6

Alt Table

Status	Error	Program
	32.8b	(+.f64 1 (fma.f64 3 (+.f64 x (pow.f64 x 3)) (*.f64 x x)))
	31.7b	(*.f64 (/.f64 1 x) (-.f64 -3 (/.f64 1 x)))
	47.8b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 x (+.f64 x 1))) (sqrt.f64 (/.f64 x (+.f64 x 1))) (neg.f64 (.f64 (/.f64 1 (-.f64 x 1)) (+.f64 x 1)))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 x 1))) (+.f64 x 1) (.f64 (/.f64 1 (-.f64 x 1)) (+.f64 x 1))))
✓	30.1b	(cbrt.f64 (pow.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))) 3))
	31.8b	(*.f64 (sqrt.f64 (fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))) (sqrt.f64 (fma.f64 x (/.f64 1 (+.f64 x 1)) (/.f64 (-.f64 -1 x) (+.f64 x -1)))))
✓	31.5b	(-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x)))

Compiler

Compiled 5510 to 3706 computations (32.7% saved)

regimes588.0ms (9.6%)

Accuracy

Total 0.0b remaining (19.3%)

Threshold costs 0.0b (19.3%)

Counts

179 → 3

Compiler

Compiled 9722 to 7384 computations (24% saved)

bsearch38.0ms (0.6%)

Steps

Iters	Range		Point
9	250.24651870344834	695821765.7249262	387887.6914731773
10	-1686909009204.5947	-53.32475148437579	-452149.06294381135

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	44
1	26	44
2	30	44
3	32	44
4	33	44
5	33	44

end1.0ms (0%)

Compiler: Compiled 31 to 23 computations (25.8% saved)

sample1.0s (16.3%)

Algorithm

1×

intervals

Results

322.0ms	2024×	body	1024	valid
189.0ms	4314×	body	128	valid
118.0ms	985×	body	512	valid
41.0ms	198×	body	2048	valid
38.0ms	479×	body	256	valid

Compiler

Compiled 173 to 130 computations (24.9% saved)

Details

analyze101.0ms (1.7%)

sample28.0ms (0.4%)

simplify89.0ms (1.5%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series8.0ms (0.1%)

rewrite225.0ms (3.7%)

simplify948.0ms (15.5%)

prune834.0ms (13.6%)

localize9.0ms (0.2%)

series13.0ms (0.2%)

rewrite234.0ms (3.8%)

simplify661.0ms (10.8%)

prune737.0ms (12%)

localize10.0ms (0.2%)

series8.0ms (0.1%)

rewrite19.0ms (0.3%)

simplify86.0ms (1.4%)

prune139.0ms (2.3%)

localize5.0ms (0.1%)

series5.0ms (0.1%)

rewrite33.0ms (0.5%)

simplify163.0ms (2.7%)

prune132.0ms (2.2%)

regimes588.0ms (9.6%)

bsearch38.0ms (0.6%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.0s (16.3%)

Profiling