Details

analyze759.0ms (10.2%)

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
3.1%	96.7%	0.2%	8
17.2%	82.7%	0.2%	9
21.8%	78%	0.2%	10
30%	68.8%	1.2%	11
31.8%	65.3%	2.9%	12
40.1%	55.3%	4.6%	13
44.5%	50.1%	5.4%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample220.0ms (3%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
2.0ms	59×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify67.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

938×	`fma-def_binary64`
721×	`fma-neg_binary64`
220×	`cancel-sign-sub-inv_binary64`
144×	`distribute-rgt-in_binary64`
108×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	16	11
2	37	11
3	72	11
4	140	11
5	242	11
6	395	11
7	682	11
8	1049	11
9	1368	11
10	1492	11
11	1530	11
12	1536	11
13	1541	11
14	1541	11
15	1456	11

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

2.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.2b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

Compiler

Compiled 45 to 23 computations (48.9% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.1b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

series15.0ms (0.2%)

Counts

1 → 48

Calls

1 calls:

15.0ms

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

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

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

550×	`distribute-rgt-neg-out_binary64`
522×	`distribute-lft-neg-out_binary64`
356×	`distribute-rgt-in_binary64`
354×	`distribute-lft-in_binary64`
297×	`times-frac_binary64`

Counts

58 → 23

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	730
1	85	635
2	196	623
3	466	623
4	2285	623
5	4620	623
6	5293	623

prune14.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	20	3	23
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	20	4	24

Error

0.0b

Counts

24 → 4

Alt Table

Status	Error	Program
▶	3.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))
	32.6b	(*.f64 (-.f64 (/.f64 z y) (/.f64 t y)) x)
	6.5b	(-.f64 (+.f64 t (/.f64 (.f64 z x) y)) (/.f64 (.f64 t x) y))
✓	2.2b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

Compiler

Compiled 392 to 123 computations (68.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))
✓	0.6b	(cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))
	2.1b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

series532.0ms (7.1%)

Counts

3 → 144

Calls

3 calls:

393.0ms

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

121.0ms

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

17.0ms

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

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

6.0ms

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

4.0ms

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

1.0ms

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

simplify278.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

974×	`fma-def_binary64`
500×	`*-commutative_binary64`
223×	`+-commutative_binary64`
205×	`associate-r_binary64`
151×	`associate-+r+_binary64`

Counts

237 → 275

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1180	19736
1	4348	19386
2	5129	19386

prune575.0ms (7.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	525	3	528
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	526	6	532

Error

0.0b

Counts

532 → 6

Alt Table

Status	Error	Program
	6.5b	(+.f64 t (/.f64 (*.f64 x (-.f64 z t)) y))
✓	2.2b	(fma.f64 (/.f64 x y) (-.f64 z t) t)
✓	3.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))
	32.6b	(*.f64 (-.f64 (/.f64 z y) (/.f64 t y)) x)
	3.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))))) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))
▶	3.5b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))))

Compiler

Compiled 44891 to 18880 computations (57.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))
✓	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))
✓	0.6b	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))))
	2.1b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

series518.0ms (6.9%)

Counts

2 → 96

Calls

2 calls:

392.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))))
126.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`cbrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 27

Calls

2 calls:

2.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))))
1.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))

simplify246.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

517×	`*-commutative_binary64`
227×	`+-commutative_binary64`
206×	`associate-r_binary64`
197×	`sub-neg_binary64`
196×	`sqr-pow_binary64`

Counts

123 → 181

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1233	18092
1	4525	17966
2	5091	17966

prune845.0ms (11.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	756	0	756
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	756	6	762

Error

0.0b

Counts

762 → 6

Alt Table

Status	Error	Program
	6.5b	(+.f64 t (/.f64 (*.f64 x (-.f64 z t)) y))
✓	2.2b	(fma.f64 (/.f64 x y) (-.f64 z t) t)
✓	3.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))
	32.6b	(*.f64 (-.f64 (/.f64 z y) (/.f64 t y)) x)
▶	3.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))))) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))
✓	3.5b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))))

Compiler

Compiled 84019 to 29621 computations (64.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (.f64 (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))))
	0.6b	(cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))
	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))
	2.1b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

series395.0ms (5.3%)

Counts

1 → 48

Calls

1 calls:

394.0ms

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

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`pow1_binary64`
10×	`add-exp-log_binary64`
10×	`pow1/3_binary64`
9×	`pow-prod-down_binary64`
6×	`associate-l_binary64`

Counts

1 → 30

Calls

1 calls:

11.0ms

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

simplify188.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

670×	`fma-def_binary64`
365×	`associate-*l/_binary64`
352×	`*-commutative_binary64`
163×	`associate-r_binary64`
158×	`+-commutative_binary64`

Counts

78 → 123

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	823	12639
1	3051	11865
2	5432	11865

prune1.0s (14.1%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	971	0	971
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	971	6	977

Error

0.0b

Counts

977 → 6

Alt Table

Status	Error	Program
	6.5b	(+.f64 t (/.f64 (*.f64 x (-.f64 z t)) y))
✓	2.2b	(fma.f64 (/.f64 x y) (-.f64 z t) t)
✓	3.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))
	32.6b	(*.f64 (-.f64 (/.f64 z y) (/.f64 t y)) x)
✓	3.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))))) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)))
✓	3.5b	(.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t)) (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))))) (cbrt.f64 (cbrt.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t))))

Compiler

Compiled 103755 to 36028 computations (65.3% saved)

regimes773.0ms (10.4%)

Accuracy

Total 1.4b remaining (98.1%)

Threshold costs 0b (0%)

Counts

57 → 2

Compiler

Compiled 11888 to 4606 computations (61.3% saved)

bsearch3.0ms (0%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-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	16	39
1	21	39
2	26	39
3	28	39
4	29	39
5	29	39

end1.0ms (0%)

Compiler: Compiled 31 to 14 computations (54.8% saved)

sample829.0ms (11.1%)

Algorithm

1×

intervals

Results

330.0ms	8000×	body	128	valid
84.0ms	2223×	body	128	invalid

Compiler

Compiled 231 to 86 computations (62.8% saved)

Details

analyze759.0ms (10.2%)

sample220.0ms (3%)

simplify67.0ms (0.9%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series15.0ms (0.2%)

rewrite1.0ms (0%)

simplify64.0ms (0.9%)

prune14.0ms (0.2%)

localize12.0ms (0.2%)

series532.0ms (7.1%)

rewrite21.0ms (0.3%)

simplify278.0ms (3.7%)

prune575.0ms (7.7%)

localize12.0ms (0.2%)

series518.0ms (6.9%)

rewrite5.0ms (0.1%)

simplify246.0ms (3.3%)

prune845.0ms (11.3%)

localize12.0ms (0.2%)

series395.0ms (5.3%)

rewrite15.0ms (0.2%)

simplify188.0ms (2.5%)

prune1.0s (14.1%)

regimes773.0ms (10.4%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end1.0ms (0%)

sample829.0ms (11.1%)

Profiling