Details

analyze100.0ms (1.1%)

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)

sample27.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	63×	body	1024	valid
5.0ms	139×	body	128	valid
3.0ms	30×	body	512	valid
1.0ms	20×	body	256	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify104.0ms (1.1%)

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

28.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.9b	(-.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))
✓	3.1b	(-.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))

rewrite233.0ms (2.6%)

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:

50.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
6.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
4.0ms	(/.f64 x (+.f64 x 1))

simplify997.0ms (11%)

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

prune1.4s (15%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	614	5	619
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	615	5	620

Error

0.0b

Counts

620 → 5

Alt Table

Status	Error	Program
	31.8b	(+.f64 1 (*.f64 x (+.f64 3 x)))
	29.9b	(/.f64 (fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x))) (fma.f64 x x -1))
	32.3b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
▶	29.4b	(+.f64 (fma.f64 (/.f64 x (-.f64 (.f64 x x) (.f64 1 1))) (-.f64 x 1) (neg.f64 (.f64 (/.f64 (+.f64 x 1) (cbrt.f64 (-.f64 x 1))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1))))))) (fma.f64 (neg.f64 (/.f64 (+.f64 x 1) (cbrt.f64 (-.f64 x 1)))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (.f64 (/.f64 (+.f64 x 1) (cbrt.f64 (-.f64 x 1))) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))))))
	47.5b	(+.f64 (fma.f64 (+.f64 x -1) (/.f64 x (fma.f64 x x -1)) (/.f64 (/.f64 (-.f64 -1 x) (+.f64 1 (sqrt.f64 x))) (+.f64 -1 (sqrt.f64 x)))) 0)

Compiler

Compiled 30580 to 22537 computations (26.3% saved)

localize39.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(cbrt.f64 (-.f64 x 1))
✓	13.4b	(/.f64 x (-.f64 (.f64 x x) (.f64 1 1)))
✓	29.0b	(fma.f64 (/.f64 x (-.f64 (.f64 x x) (.f64 1 1))) (-.f64 x 1) (neg.f64 (.f64 (/.f64 (+.f64 x 1) (cbrt.f64 (-.f64 x 1))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))))))
✓	33.0b	(fma.f64 (neg.f64 (/.f64 (+.f64 x 1) (cbrt.f64 (-.f64 x 1)))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (.f64 (/.f64 (+.f64 x 1) (cbrt.f64 (-.f64 x 1))) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1))))))

series137.0ms (1.5%)

Counts

4 → 48

Calls

4 calls:

87.0ms	(fma.f64 (neg.f64 (/.f64 (+.f64 x 1) (cbrt.f64 (-.f64 x 1)))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (.f64 (/.f64 (+.f64 x 1) (cbrt.f64 (-.f64 x 1))) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1))))))
23.0ms	(cbrt.f64 (-.f64 x 1))
20.0ms	(fma.f64 (/.f64 x (-.f64 (.f64 x x) (.f64 1 1))) (-.f64 x 1) (neg.f64 (.f64 (/.f64 (+.f64 x 1) (cbrt.f64 (-.f64 x 1))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))))))
6.0ms	(/.f64 x (-.f64 (.f64 x x) (.f64 1 1)))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
7×	`cbrt-prod_binary64`

Counts

4 → 74

Calls

4 calls:

9.0ms	(/.f64 x (-.f64 (.f64 x x) (.f64 1 1)))
6.0ms	(cbrt.f64 (-.f64 x 1))
1.0ms	(fma.f64 (neg.f64 (/.f64 (+.f64 x 1) (cbrt.f64 (-.f64 x 1)))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (.f64 (/.f64 (+.f64 x 1) (cbrt.f64 (-.f64 x 1))) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1))))))
1.0ms	(fma.f64 (/.f64 x (-.f64 (.f64 x x) (.f64 1 1))) (-.f64 x 1) (neg.f64 (.f64 (/.f64 (+.f64 x 1) (cbrt.f64 (-.f64 x 1))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))))))

simplify194.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

679×	`times-frac_binary64`
502×	`fma-neg_binary64`
262×	`cancel-sign-sub-inv_binary64`
204×	`distribute-neg-in_binary64`
193×	`distribute-rgt-neg-in_binary64`

Counts

122 → 197

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	253	3001
1	658	2329
2	2279	1940
3	4631	1936
4	4881	1936

prune2.7s (30.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	628	1	629
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	629	5	634

Error

0.0b

Counts

634 → 5

Alt Table

Status	Error	Program
	30.9b	(+.f64 (exp.f64 (log.f64 (fma.f64 (/.f64 x (-.f64 (.f64 x x) (.f64 1 1))) (-.f64 x 1) (neg.f64 (.f64 (/.f64 (+.f64 x 1) (cbrt.f64 (-.f64 x 1))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1))))))))) (fma.f64 (neg.f64 (/.f64 (+.f64 x 1) (cbrt.f64 (-.f64 x 1)))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (.f64 (/.f64 (+.f64 x 1) (cbrt.f64 (-.f64 x 1))) (/.f64 1 (*.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))))))
	47.5b	(+.f64 (fma.f64 (+.f64 x -1) (/.f64 x (fma.f64 x x -1)) (/.f64 (/.f64 (-.f64 -1 x) (+.f64 1 (sqrt.f64 x))) (+.f64 -1 (sqrt.f64 x)))) 0)
	31.8b	(+.f64 1 (*.f64 x (+.f64 3 x)))
▶	29.9b	(/.f64 (fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x))) (fma.f64 x x -1))
	32.3b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))

Compiler

Compiled 52726 to 41146 computations (22% saved)

localize19.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 1 x) (-.f64 -1 x))
✓	0.0b	(/.f64 (fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x))) (fma.f64 x x -1))
✓	29.8b	(fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x)))

series17.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

7.0ms	(/.f64 (fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x))) (fma.f64 x x -1))
6.0ms	(fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x)))
4.0ms	(*.f64 (+.f64 1 x) (-.f64 -1 x))

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
27×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 96

Calls

3 calls:

17.0ms	(*.f64 (+.f64 1 x) (-.f64 -1 x))
4.0ms	(/.f64 (fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x))) (fma.f64 x x -1))
1.0ms	(fma.f64 x (+.f64 x -1) (*.f64 (+.f64 1 x) (-.f64 -1 x)))

simplify163.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

795×	`distribute-rgt-in_binary64`
696×	`distribute-lft-in_binary64`
603×	`fma-neg_binary64`
160×	`associate-l_binary64`
149×	`associate-r_binary64`

Counts

132 → 165

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	224	2768
1	465	2474
2	1647	2284
3	4716	2272
4	4988	2272

prune199.0ms (2.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	168	2	170

Error

0.0b

Counts

170 → 2

Alt Table

Status	Error	Program
▶	13.5b	(/.f64 (fma.f64 x -3 -1) (fma.f64 x x -1))
	32.3b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))

Compiler

Compiled 4571 to 2981 computations (34.8% saved)

localize16.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x -3 -1)
✓	13.5b	(/.f64 (fma.f64 x -3 -1) (fma.f64 x x -1))

series7.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(/.f64 (fma.f64 x -3 -1) (fma.f64 x x -1))
3.0ms	(fma.f64 x -3 -1)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

4.0ms	(/.f64 (fma.f64 x -3 -1) (fma.f64 x x -1))
1.0ms	(fma.f64 x -3 -1)

simplify95.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

661×	`fma-def_binary64`
370×	`distribute-rgt-in_binary64`
362×	`div-sub_binary64`
336×	`neg-mul-1_binary64`
289×	`distribute-lft-in_binary64`

Counts

63 → 63

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	89	997
1	188	875
2	506	871
3	1616	868
4	4434	860
5	4943	860

prune92.0ms (1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	60	3	63
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	62	3	65

Error

Counts

65 → 3

Alt Table

Status	Error	Program
	13.5b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 x -3 -1) (fma.f64 x x -1))))
	19.2b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x -3 -1) (fma.f64 x x -1)) 3))
	32.3b	(+.f64 (fma.f64 (/.f64 1 (*.f64 x x)) (-.f64 -1 (/.f64 3 x)) (/.f64 -3 x)) (/.f64 -1 (pow.f64 x 4)))

Compiler

Compiled 981 to 722 computations (26.4% saved)

regimes548.0ms (6.1%)

Accuracy

Total 0.0b remaining (28.2%)

Threshold costs 0.0b (28.2%)

Counts

80 → 3

Compiler

Compiled 4374 to 3300 computations (24.6% saved)

bsearch12.0ms (0.1%)

Steps

Iters	Range		Point
2	7.006997086362317	31673153790710.03	22131881926.828556
0	-13980.750242557919	-13484.244541746411	-13732.497392152165

Compiler

Compiled 2 to 1 computations (50% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
7×	`sub-neg_binary64`
5×	`*-commutative_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	70
1	40	70
2	55	70
3	67	70
4	72	70
5	73	70
6	70	70

end2.0ms (0%)

Compiler: Compiled 49 to 35 computations (28.6% saved)

sample1.8s (20.5%)

Algorithm

1×

intervals

Results

644.0ms	2054×	body	1024	valid
347.0ms	4249×	body	128	valid
228.0ms	974×	body	512	valid
84.0ms	514×	body	256	valid
84.0ms	209×	body	2048	valid

Compiler

Compiled 111 to 82 computations (26.1% saved)

Details

analyze100.0ms (1.1%)

sample27.0ms (0.3%)

simplify104.0ms (1.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series8.0ms (0.1%)

rewrite233.0ms (2.6%)

simplify997.0ms (11%)

prune1.4s (15%)

localize39.0ms (0.4%)

series137.0ms (1.5%)

rewrite24.0ms (0.3%)

simplify194.0ms (2.1%)

prune2.7s (30.3%)

localize19.0ms (0.2%)

series17.0ms (0.2%)

rewrite36.0ms (0.4%)

simplify163.0ms (1.8%)

prune199.0ms (2.2%)

localize16.0ms (0.2%)

series7.0ms (0.1%)

rewrite7.0ms (0.1%)

simplify95.0ms (1.1%)

prune92.0ms (1%)

regimes548.0ms (6.1%)

bsearch12.0ms (0.1%)

simplify9.0ms (0.1%)

end2.0ms (0%)

sample1.8s (20.5%)

Profiling