Details

analyze589.0ms (17.4%)

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
18.7%	81.1%	0.1%	8
31.2%	68.6%	0.1%	9
35.9%	55.4%	8.7%	10
42.9%	47.6%	9.5%	11
51.5%	38.2%	10.3%	12
55%	30%	15%	13
59.5%	25.3%	15.3%	14

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample1.2s (35.4%)

Results

862.0ms	7596×	body	128	valid
82.0ms	242×	body	1024	valid
72.0ms	257×	body	512	valid
72.0ms	618×	body	128	invalid
29.0ms	161×	body	256	valid

Compiler

Compiled 50 to 38 computations (24% saved)

simplify218.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

5304×	`fma-neg_binary64`
679×	`unsub-neg_binary64`
400×	`sub-neg_binary64`
376×	`fma-def_binary64`
289×	`associate--r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	16
1	23	14
2	59	14
3	157	12
4	438	12
5	1253	12
6	2078	12
7	2563	12
8	2777	12
9	2907	12
10	2949	12
11	2964	12
12	2967	12
13	2967	12
14	2967	12
15	3141	12
16	3015	12
17	3015	12
18	8062	12

prune4.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
▶	0.2b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)

Compiler

Compiled 81 to 56 computations (30.9% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z -6 4)
✓	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)

series12.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
1.0ms	(fma.f64 z -6 4)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
0.0ms	(fma.f64 z -6 4)

simplify90.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

747×	`fma-def_binary64`
445×	`associate-l_binary64`
416×	`exp-prod_binary64`
398×	`distribute-rgt-in_binary64`
387×	`associate-r_binary64`

Counts

68 → 49

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	1086
1	149	928
2	343	874
3	949	793
4	4177	793
5	4989	793
6	4976	793

prune47.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	44	5	49
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	45	6	51

Error

0.0b

Counts

51 → 6

Alt Table

Status	Error	Program
	0.2b	(fma.f64 (-.f64 y x) (-.f64 4 (*.f64 6 z)) x)
	11.9b	(fma.f64 (-.f64 y x) (expm1.f64 (log1p.f64 (fma.f64 z -6 4))) x)
	30.8b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
▶	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))

Compiler

Compiled 809 to 491 computations (39.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 z -6 4)
✓	0.0b	(fma.f64 6 z -3)
✓	0.1b	(*.f64 y (fma.f64 z -6 4))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))

series21.0ms (0.6%)

Counts

3 → 72

Calls

3 calls:

13.0ms	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
5.0ms	(*.f64 y (fma.f64 z -6 4))
2.0ms	(fma.f64 6 z -3)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

3.0ms	(*.f64 y (fma.f64 z -6 4))
0.0ms	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
0.0ms	(fma.f64 6 z -3)

simplify78.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

798×	`neg-mul-1_binary64`
520×	`distribute-rgt-neg-out_binary64`
469×	`distribute-lft-neg-out_binary64`
296×	`fma-neg_binary64`
289×	`associate-l_binary64`

Counts

114 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	1678
1	209	1387
2	553	1252
3	1824	1252
4	4279	1252
5	5516	1252

prune82.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	92	7	99

Error

0.0b

Counts

99 → 7

Alt Table

Status	Error	Program
	11.9b	(fma.f64 (-.f64 y x) (expm1.f64 (log1p.f64 (fma.f64 z -6 4))) x)
	22.7b	(fma.f64 x (fma.f64 6 z -3) (.f64 -6 (.f64 y z)))
▶	0.1b	(fma.f64 x (fma.f64 6 z -3) (.f64 y (+.f64 (.f64 z -6) 4)))
	0.8b	(fma.f64 x (fma.f64 6 z -3) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (fma.f64 z -6 4))))
	30.8b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))

Compiler

Compiled 1699 to 1181 computations (30.5% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 z -6) 4)
	0.0b	(fma.f64 6 z -3)
✓	0.1b	(.f64 y (+.f64 (.f64 z -6) 4))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (.f64 y (+.f64 (.f64 z -6) 4)))

series21.0ms (0.6%)

Counts

3 → 72

Calls

3 calls:

12.0ms	(fma.f64 x (fma.f64 6 z -3) (.f64 y (+.f64 (.f64 z -6) 4)))
7.0ms	(.f64 y (+.f64 (.f64 z -6) 4))
1.0ms	(+.f64 (*.f64 z -6) 4)

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 48

Calls

3 calls:

5.0ms	(.f64 y (+.f64 (.f64 z -6) 4))
3.0ms	(+.f64 (*.f64 z -6) 4)
0.0ms	(fma.f64 x (fma.f64 6 z -3) (.f64 y (+.f64 (.f64 z -6) 4)))

simplify80.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

649×	`distribute-rgt-neg-out_binary64`
523×	`fma-neg_binary64`
336×	`fma-def_binary64`
286×	`distribute-rgt-in_binary64`
269×	`distribute-lft-in_binary64`

Counts

120 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	109	1748
1	292	1447
2	833	1310
3	2360	1310
4	4830	1310
5	5000	1310

prune96.0ms (2.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	117	7	124

Error

0.0b

Counts

124 → 7

Alt Table

Status	Error	Program
	11.9b	(fma.f64 (-.f64 y x) (expm1.f64 (log1p.f64 (fma.f64 z -6 4))) x)
	22.7b	(fma.f64 x (fma.f64 6 z -3) (.f64 -6 (.f64 y z)))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (.f64 y (+.f64 (.f64 z -6) 4)))
	0.8b	(fma.f64 x (fma.f64 6 z -3) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (fma.f64 z -6 4))))
	30.8b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
▶	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))

Compiler

Compiled 2255 to 1613 computations (28.5% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
✓	0.0b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
✓	0.3b	(.f64 6 (.f64 z x))
✓	0.3b	(.f64 6 (.f64 y z))

series31.0ms (0.9%)

Counts

4 → 18

Calls

4 calls:

15.0ms	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
7.0ms	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
4.0ms	(.f64 6 (.f64 y z))
4.0ms	(.f64 6 (.f64 z x))

rewrite26.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-log-exp_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
14×	`add-cbrt-cube_binary64`

Counts

4 → 93

Calls

4 calls:

10.0ms	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
4.0ms	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
4.0ms	(.f64 6 (.f64 y z))
3.0ms	(.f64 6 (.f64 z x))

simplify97.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

443×	`times-frac_binary64`
372×	`cancel-sign-sub-inv_binary64`
279×	`associate-l_binary64`
278×	`distribute-rgt-neg-in_binary64`
271×	`associate-r_binary64`

Counts

111 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	2856
1	619	2159
2	2427	1906
3	4509	1906
4	5450	1906

prune137.0ms (4.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	148	7	155

Error

Counts

155 → 7

Alt Table

Status	Error	Program
	0.2b	(+.f64 (.f64 4 y) (fma.f64 6 (.f64 z (-.f64 x y)) (*.f64 x -3)))
	0.2b	(+.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (fma.f64 x -3 (.f64 z (*.f64 y -6))))
	11.9b	(fma.f64 (-.f64 y x) (expm1.f64 (log1p.f64 (fma.f64 z -6 4))) x)
	30.8b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
	45.3b	(/.f64 (.f64 (fma.f64 6 (.f64 z y) (.f64 x -3)) (-.f64 (fma.f64 216 (pow.f64 (.f64 z x) 3) (pow.f64 (.f64 y 4) 3)) (.f64 (fma.f64 16 (.f64 y y) (.f64 (.f64 z x) (fma.f64 (.f64 z x) 36 (.f64 y -24)))) (fma.f64 6 (.f64 z y) (.f64 x 3))))) (.f64 (fma.f64 16 (.f64 y y) (.f64 (.f64 z x) (fma.f64 (.f64 z x) 36 (.f64 y -24)))) (fma.f64 6 (.f64 z y) (*.f64 x -3))))
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (.f64 y (+.f64 (.f64 z -6) 4)))

Compiler

Compiled 4959 to 3027 computations (39% saved)

regimes386.0ms (11.4%)

Accuracy

Total 0.1b remaining (89.6%)

Threshold costs 0.1b (89.6%)

Counts

81 → 1

Compiler

Compiled 6460 to 4687 computations (27.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`distribute-lft-neg-in_binary64`
4×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	21
1	27	21
2	34	21
3	44	21
4	51	21
5	56	21
6	58	21
7	56	21

end125.0ms (3.7%)

Compiler: Compiled 222 to 147 computations (33.8% saved)

Details

analyze589.0ms (17.4%)

sample1.2s (35.4%)

simplify218.0ms (6.4%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series12.0ms (0.3%)

rewrite1.0ms (0%)

simplify90.0ms (2.6%)

prune47.0ms (1.4%)

localize8.0ms (0.2%)

series21.0ms (0.6%)

rewrite5.0ms (0.1%)

simplify78.0ms (2.3%)

prune82.0ms (2.4%)

localize9.0ms (0.3%)

series21.0ms (0.6%)

rewrite9.0ms (0.3%)

simplify80.0ms (2.4%)

prune96.0ms (2.8%)

localize11.0ms (0.3%)

series31.0ms (0.9%)

rewrite26.0ms (0.8%)

simplify97.0ms (2.9%)

prune137.0ms (4.1%)

regimes386.0ms (11.4%)

simplify3.0ms (0.1%)

end125.0ms (3.7%)

Profiling