Details

analyze474.0ms (8.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
25%	74.9%	0.1%	8
31.2%	64%	4.8%	9
31.2%	42.1%	26.7%	10
35.9%	37.1%	27.1%	11
38.2%	32.2%	29.6%	12
47.8%	21.6%	30.6%	13
50.2%	19%	30.8%	14

Compiler

Compiled 19 to 9 computations (52.6% saved)

sample28.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	17×	body	128	invalid

Compiler

Compiled 40 to 20 computations (50% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

32×	`fma-def_binary64`
5×	`*-commutative_binary64`
4×	`associate-+l+_binary64`
4×	`associate-r_binary64`
3×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	17	15
2	34	11
3	54	11
4	68	11
5	72	11
6	70	11

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
▶	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))

Compiler

Compiled 84 to 41 computations (51.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (.f64 x y) (.f64 z z)) (*.f64 z z))
✓	0.0b	(+.f64 (.f64 x y) (.f64 z z))
✓	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))

series42.0ms (0.8%)

Counts

3 → 108

Calls

3 calls:

21.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 z z)) (*.f64 z z))
13.0ms	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))
8.0ms	(+.f64 (.f64 x y) (.f64 z z))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-log-exp_binary64`
10×	`sum-log_binary64`
7×	`fma-def_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

3 → 51

Calls

3 calls:

14.0ms	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))
10.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 z z)) (*.f64 z z))
6.0ms	(+.f64 (.f64 x y) (.f64 z z))

simplify156.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

700×	`fma-neg_binary64`
652×	`fma-def_binary64`
387×	`distribute-rgt-in_binary64`
335×	`distribute-lft-in_binary64`
267×	`associate-l_binary64`

Counts

159 → 93

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	1788
1	246	1682
2	775	1595
3	3142	1591
4	4640	1591
5	5115	1591

prune122.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	89	6	95

Error

Counts

95 → 6

Alt Table

Status	Error	Program
	38.1b	(+.f64 (cbrt.f64 (.f64 (.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z))) (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)))) (.f64 z z))
	17.1b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z))) (sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z))) (*.f64 z z))
▶	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
✓	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))
	11.5b	(+.f64 (+.f64 (expm1.f64 (log1p.f64 (fma.f64 z z (.f64 y x)))) (.f64 z z)) (*.f64 z z))
	17.2b	(.f64 (sqrt.f64 (fma.f64 3 (.f64 z z) (.f64 y x))) (sqrt.f64 (fma.f64 3 (.f64 z z) (*.f64 y x))))

Compiler

Compiled 2229 to 506 computations (77.3% saved)

localize10.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))

series228.0ms (4.3%)

Counts

1 → 36

Calls

1 calls:

228.0ms

(fma.f64 z (*.f64 z 3) (*.f64 x y))

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:

1.0ms

(fma.f64 z (*.f64 z 3) (*.f64 x y))

simplify111.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-def_binary64`
483×	`distribute-rgt-out_binary64`
466×	`distribute-rgt-in_binary64`
458×	`distribute-lft-in_binary64`
301×	`*-commutative_binary64`

Counts

46 → 23

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	508
1	34	485
2	65	485
3	184	485
4	750	485
5	2905	485
6	3790	485
7	4921	485

prune36.0ms (0.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	23	6	29

Error

Counts

29 → 6

Alt Table

Status	Error	Program
	38.1b	(+.f64 (cbrt.f64 (.f64 (.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z))) (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)))) (.f64 z z))
	17.1b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z))) (sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z))) (*.f64 z z))
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
✓	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))
▶	11.5b	(+.f64 (+.f64 (expm1.f64 (log1p.f64 (fma.f64 z z (.f64 y x)))) (.f64 z z)) (*.f64 z z))
	17.2b	(.f64 (sqrt.f64 (fma.f64 3 (.f64 z z) (.f64 y x))) (sqrt.f64 (fma.f64 3 (.f64 z z) (*.f64 y x))))

Compiler

Compiled 544 to 240 computations (55.9% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (fma.f64 z z (*.f64 y x)))
✓	0.0b	(fma.f64 z z (*.f64 y x))
✓	0.1b	(+.f64 (+.f64 (expm1.f64 (log1p.f64 (fma.f64 z z (.f64 y x)))) (.f64 z z)) (*.f64 z z))
✓	2.6b	(expm1.f64 (log1p.f64 (fma.f64 z z (*.f64 y x))))

series164.0ms (3.1%)

Counts

4 → 144

Calls

4 calls:

100.0ms	(log1p.f64 (fma.f64 z z (*.f64 y x)))
28.0ms	(+.f64 (+.f64 (expm1.f64 (log1p.f64 (fma.f64 z z (.f64 y x)))) (.f64 z z)) (*.f64 z z))
22.0ms	(fma.f64 z z (*.f64 y x))
14.0ms	(expm1.f64 (log1p.f64 (fma.f64 z z (*.f64 y x))))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
5×	`expm1-log1p-u_binary64`

Counts

4 → 51

Calls

4 calls:

9.0ms	(+.f64 (+.f64 (expm1.f64 (log1p.f64 (fma.f64 z z (.f64 y x)))) (.f64 z z)) (*.f64 z z))
1.0ms	(fma.f64 z z (*.f64 y x))
1.0ms	(expm1.f64 (log1p.f64 (fma.f64 z z (*.f64 y x))))
1.0ms	(log1p.f64 (fma.f64 z z (*.f64 y x)))

simplify195.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

385×	`sub-neg_binary64`
382×	`distribute-rgt-in_binary64`
347×	`cancel-sign-sub-inv_binary64`
289×	`fma-neg_binary64`
208×	`+-commutative_binary64`

Counts

195 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	248	3676
1	737	3504
2	2952	3359
3	4716	3355
4	5047	3355

prune183.0ms (3.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	146	6	152

Error

Counts

152 → 6

Alt Table

Status	Error	Program
	38.1b	(+.f64 (cbrt.f64 (.f64 (.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z))) (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)))) (.f64 z z))
▶	17.1b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z))) (sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z))) (*.f64 z z))
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
✓	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))
✓	11.5b	(+.f64 (+.f64 (expm1.f64 (log1p.f64 (fma.f64 z z (.f64 y x)))) (.f64 z z)) (*.f64 z z))
	17.2b	(.f64 (sqrt.f64 (fma.f64 3 (.f64 z z) (.f64 y x))) (sqrt.f64 (fma.f64 3 (.f64 z z) (*.f64 y x))))

Compiler

Compiled 5083 to 2100 computations (58.7% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (+.f64 (.f64 x y) (.f64 z z)) (*.f64 z z))
	0.0b	(+.f64 (.f64 x y) (.f64 z z))
✓	0.2b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z))) (sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z))) (*.f64 z z))
✓	2.2b	(sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (*.f64 z z)))

series773.0ms (14.6%)

Counts

2 → 40

Calls

2 calls:

668.0ms

(fma.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z z)) (*.f64 z z))) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z z)) (*.f64 z z))) (*.f64 z z))

104.0ms

(sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z z)) (*.f64 z z)))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
3×	`*-un-lft-identity_binary64`
3×	`sqrt-prod_binary64`
3×	`add-cube-cbrt_binary64`
3×	`pow1_binary64`

Counts

2 → 28

Calls

2 calls:

9.0ms

(sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z z)) (*.f64 z z)))

1.0ms

(fma.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z z)) (*.f64 z z))) (sqrt.f64 (+.f64 (+.f64 (*.f64 x y) (*.f64 z z)) (*.f64 z z))) (*.f64 z z))

simplify127.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

467×	`associate-l_binary64`
447×	`associate-/l*_binary64`
431×	`fma-def_binary64`
386×	`associate-/r*_binary64`
316×	`fma-neg_binary64`

Counts

68 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	1775
1	327	1404
2	1146	1370
3	4894	1370
4	5055	1370

prune287.0ms (5.4%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	243	0	243
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	243	6	249

Error

Counts

249 → 6

Alt Table

Status	Error	Program
	38.1b	(+.f64 (cbrt.f64 (.f64 (.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z))) (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)))) (.f64 z z))
✓	17.1b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z))) (sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z))) (*.f64 z z))
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
✓	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))
✓	11.5b	(+.f64 (+.f64 (expm1.f64 (log1p.f64 (fma.f64 z z (.f64 y x)))) (.f64 z z)) (*.f64 z z))
	17.2b	(.f64 (sqrt.f64 (fma.f64 3 (.f64 z z) (.f64 y x))) (sqrt.f64 (fma.f64 3 (.f64 z z) (*.f64 y x))))

Compiler

Compiled 8725 to 1857 computations (78.7% saved)

regimes1.5s (27.5%)

Accuracy

Total 0.1b remaining (85.2%)

Threshold costs 0.1b (85.2%)

Counts

100 → 1

Compiler

Compiled 15582 to 7502 computations (51.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	9	11
2	9	11

end6.0ms (0.1%)

Remove: (sort x y)
Compiler: Compiled 33 to 21 computations (36.4% saved)

sample791.0ms (14.9%)

Algorithm

1×

intervals

Results

380.0ms	8000×	body	128	valid
17.0ms	459×	body	128	invalid

Compiler

Compiled 177 to 76 computations (57.1% saved)

Details

analyze474.0ms (8.9%)

sample28.0ms (0.5%)

simplify8.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series42.0ms (0.8%)

rewrite34.0ms (0.6%)

simplify156.0ms (2.9%)

prune122.0ms (2.3%)

localize10.0ms (0.2%)

series228.0ms (4.3%)

rewrite1.0ms (0%)

simplify111.0ms (2.1%)

prune36.0ms (0.7%)

localize21.0ms (0.4%)

series164.0ms (3.1%)

rewrite15.0ms (0.3%)

simplify195.0ms (3.7%)

prune183.0ms (3.4%)

localize16.0ms (0.3%)

series773.0ms (14.6%)

rewrite12.0ms (0.2%)

simplify127.0ms (2.4%)

prune287.0ms (5.4%)

regimes1.5s (27.5%)

simplify2.0ms (0%)

end6.0ms (0.1%)

sample791.0ms (14.9%)

Profiling