Details

analyze954.0ms (25.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
13.3%	86.5%	0.2%	9
19.9%	79.9%	0.2%	10
24%	75.2%	0.8%	11
25.4%	72.7%	1.9%	12
35.8%	59.6%	4.6%	13
42%	52.3%	5.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.5s (39.6%)

Results

1.1s	8256×	body	128	valid
235.0ms	2222×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify65.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

799×	`fma-def_binary64`
661×	`fma-neg_binary64`
203×	`cancel-sign-sub-inv_binary64`
145×	`distribute-rgt-in_binary64`
99×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	30	11
3	61	11
4	129	11
5	232	11
6	397	11
7	667	11
8	1062	11
9	1355	11
10	1480	11
11	1529	11
12	1535	11
13	1540	11
14	1540	11
15	1455	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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	5.6b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
	6.5b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z x) t)
✓	5.3b	(fma.f64 y (/.f64 (-.f64 z x) t) x)

series29.0ms (0.8%)

Counts

2 → 76

Calls

2 calls:

18.0ms	(fma.f64 y (/.f64 (-.f64 z x) t) x)
11.0ms	(/.f64 (-.f64 z x) t)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/l*_binary64`

Counts

2 → 50

Calls

2 calls:

4.0ms	(/.f64 (-.f64 z x) t)
0.0ms	(fma.f64 y (/.f64 (-.f64 z x) t) x)

simplify58.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

704×	`distribute-rgt-in_binary64`
694×	`distribute-lft-in_binary64`
580×	`times-frac_binary64`
456×	`fma-def_binary64`
219×	`div-sub_binary64`

Counts

126 → 76

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	112	1693
1	247	1350
2	554	1350
3	1352	1350
4	4976	1350

prune44.0ms (1.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	73	5	78

Error

0.0b

Counts

78 → 5

Alt Table

Status	Error	Program
	33.5b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (sqrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)))
▶	1.8b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
✓	5.6b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
	31.6b	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 (-.f64 z x) t)) (sqrt.f64 (/.f64 (-.f64 z x) t))) x)
	6.5b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

Compiler

Compiled 1180 to 338 computations (71.4% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.8b	(fma.f64 (/.f64 y t) (-.f64 z x) x)

series17.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

17.0ms

(fma.f64 (/.f64 y t) (-.f64 z x) x)

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:

0.0ms

(fma.f64 (/.f64 y t) (-.f64 z x) x)

simplify69.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

546×	`distribute-rgt-neg-out_binary64`
522×	`distribute-lft-neg-out_binary64`
389×	`distribute-rgt-in_binary64`
386×	`distribute-lft-in_binary64`
294×	`times-frac_binary64`

Counts

58 → 24

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	946
1	87	635
2	197	623
3	473	623
4	2335	623
5	4674	623
6	5331	623

prune11.0ms (0.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	24	5	29

Error

0.0b

Counts

29 → 5

Alt Table

Status	Error	Program
	33.5b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (sqrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)))
✓	1.8b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
✓	5.6b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
	31.6b	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 (-.f64 z x) t)) (sqrt.f64 (/.f64 (-.f64 z x) t))) x)
▶	6.5b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

Compiler

Compiled 397 to 129 computations (67.5% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
✓	0.0b	(*.f64 y (-.f64 z x))
✓	6.8b	(/.f64 (*.f64 y (-.f64 z x)) t)

series46.0ms (1.2%)

Counts

3 → 104

Calls

3 calls:

21.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
19.0ms	(/.f64 (*.f64 y (-.f64 z x)) t)
6.0ms	(*.f64 y (-.f64 z x))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 92

Calls

3 calls:

7.0ms	(/.f64 (*.f64 y (-.f64 z x)) t)
5.0ms	(*.f64 y (-.f64 z x))
3.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

simplify92.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

611×	`fma-def_binary64`
609×	`times-frac_binary64`
591×	`distribute-rgt-in_binary64`
370×	`fma-neg_binary64`
158×	`associate-l_binary64`

Counts

196 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	200	2470
1	431	2151
2	1681	2001
3	4818	2001
4	4992	2001

prune84.0ms (2.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	137	3	140
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	138	7	145

Error

Counts

145 → 7

Alt Table

Status	Error	Program
	33.5b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (sqrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)))
✓	1.8b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
✓	6.5b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
	29.2b	(+.f64 x (/.f64 (.f64 y (-.f64 (.f64 z z) (.f64 x x))) (.f64 t (+.f64 z x))))
	35.4b	(+.f64 x (/.f64 (/.f64 (*.f64 y (-.f64 z x)) (sqrt.f64 t)) (sqrt.f64 t)))
✓	5.6b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
▶	6.5b	(+.f64 x (/.f64 1 (/.f64 t (*.f64 y (-.f64 z x)))))

Compiler

Compiled 2531 to 727 computations (71.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (-.f64 z x))
✓	0.0b	(+.f64 x (/.f64 1 (/.f64 t (*.f64 y (-.f64 z x)))))
✓	0.3b	(/.f64 1 (/.f64 t (*.f64 y (-.f64 z x))))
✓	6.8b	(/.f64 t (*.f64 y (-.f64 z x)))

series75.0ms (2%)

Counts

3 → 128

Calls

3 calls:

34.0ms	(/.f64 t (*.f64 y (-.f64 z x)))
21.0ms	(+.f64 x (/.f64 1 (/.f64 t (*.f64 y (-.f64 z x)))))
19.0ms	(/.f64 1 (/.f64 t (*.f64 y (-.f64 z x))))

rewrite27.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`times-frac_binary64`
29×	`add-exp-log_binary64`
27×	`*-un-lft-identity_binary64`
24×	`add-sqr-sqrt_binary64`
24×	`add-cube-cbrt_binary64`

Counts

3 → 109

Calls

3 calls:

8.0ms	(+.f64 x (/.f64 1 (/.f64 t (*.f64 y (-.f64 z x)))))
7.0ms	(/.f64 1 (/.f64 t (*.f64 y (-.f64 z x))))
6.0ms	(/.f64 t (*.f64 y (-.f64 z x)))

simplify150.0ms (4%)

Algorithm

1×	egg-herbie

Rules

474×	`fma-def_binary64`
458×	`distribute-rgt-in_binary64`
423×	`distribute-lft-in_binary64`
269×	`associate-/l/_binary64`
178×	`fma-neg_binary64`

Counts

237 → 178

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	4017
1	500	3446
2	1832	3256
3	4772	3256
4	5027	3256

prune149.0ms (3.9%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	1	2	3
Picked	0	1	1
Done	0	3	3
Total	237	7	244

Error

Counts

244 → 7

Alt Table

Status	Error	Program
	33.5b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)) (sqrt.f64 (fma.f64 (/.f64 y t) (-.f64 z x) x)))
✓	1.8b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	6.8b	(+.f64 x (/.f64 1 (.f64 t (/.f64 1 (.f64 y (-.f64 z x))))))
	35.4b	(+.f64 x (/.f64 (/.f64 (*.f64 y (-.f64 z x)) (sqrt.f64 t)) (sqrt.f64 t)))
✓	5.6b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
✓	6.5b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
✓	6.5b	(+.f64 x (/.f64 1 (/.f64 t (*.f64 y (-.f64 z x)))))

Compiler

Compiled 4571 to 1649 computations (63.9% saved)

regimes250.0ms (6.6%)

Accuracy

Total 2.3b remaining (99.2%)

Threshold costs 0b (0%)

Counts

38 → 3

Compiler

Compiled 3036 to 1798 computations (40.8% saved)

bsearch31.0ms (0.8%)

Steps

Iters	Range		Point
7	3.2672198906603047e-150	2.2244600200509845e-148	3.325314396267599e-150
5	2.5919346033857505e-297	6.060096698110874e-297	5.875674242652246e-297

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	52
1	30	52
2	34	52
3	36	52
4	37	52
5	36	52

end82.0ms (2.2%)

Compiler: Compiled 189 to 105 computations (44.4% saved)

Details

analyze954.0ms (25.1%)

sample1.5s (39.6%)

simplify65.0ms (1.7%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series29.0ms (0.8%)

rewrite7.0ms (0.2%)

simplify58.0ms (1.5%)

prune44.0ms (1.2%)

localize6.0ms (0.2%)

series17.0ms (0.4%)

rewrite1.0ms (0%)

simplify69.0ms (1.8%)

prune11.0ms (0.3%)

localize7.0ms (0.2%)

series46.0ms (1.2%)

rewrite20.0ms (0.5%)

simplify92.0ms (2.4%)

prune84.0ms (2.2%)

localize9.0ms (0.2%)

series75.0ms (2%)

rewrite27.0ms (0.7%)

simplify150.0ms (4%)

prune149.0ms (3.9%)

regimes250.0ms (6.6%)

bsearch31.0ms (0.8%)

simplify4.0ms (0.1%)

end82.0ms (2.2%)

Profiling