Details

analyze1.1s (8.6%)

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
16.4%	83.4%	0.2%	9
21.4%	78.4%	0.2%	10
25.1%	74.7%	0.2%	11
28%	70.2%	1.9%	12
39.6%	55.8%	4.6%	13
43.9%	50.4%	5.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample32.0ms (0.2%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
3.0ms	69×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify75.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

973×	`fma-def_binary64`
752×	`fma-neg_binary64`
239×	`cancel-sign-sub-inv_binary64`
193×	`distribute-rgt-in_binary64`
133×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	33	11
3	64	11
4	125	11
5	238	11
6	414	11
7	791	11
8	1182	11
9	1373	11
10	1483	11
11	1532	11
12	1538	11
13	1543	11
14	1543	11
15	1458	11

prune3.0ms (0%)

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
▶	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	7.2b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.0b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series22.0ms (0.2%)

Counts

1 → 48

Calls

1 calls:

22.0ms

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

simplify69.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

539×	`distribute-rgt-neg-out_binary64`
515×	`distribute-lft-neg-out_binary64`
375×	`distribute-rgt-in_binary64`
373×	`distribute-lft-in_binary64`
270×	`times-frac_binary64`

Counts

58 → 31

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	946
1	88	635
2	194	623
3	469	623
4	2305	623
5	4632	623
6	5238	623

prune64.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	29	2	31
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	29	4	33

Error

0.0b

Counts

33 → 4

Alt Table

Status	Error	Program
	34.8b	(*.f64 z (/.f64 (-.f64 y x) t))
✓	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	7.2b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
▶	2.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))

Compiler

Compiled 480 to 136 computations (71.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
✓	0.5b	(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))
	1.0b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series645.0ms (4.8%)

Counts

3 → 144

Calls

3 calls:

447.0ms

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

174.0ms

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

24.0ms

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

rewrite25.0ms (0.2%)

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:

7.0ms

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

5.0ms

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

1.0ms

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

simplify562.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

938×	`fma-def_binary64`
540×	`*-commutative_binary64`
218×	`+-commutative_binary64`
210×	`associate-r_binary64`
141×	`associate-+r+_binary64`

Counts

237 → 277

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1216	19471
1	4389	19186
2	5141	19186

prune1.7s (13.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	553	1	554
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	553	5	558

Error

0.0b

Counts

558 → 5

Alt Table

Status	Error	Program
	34.8b	(*.f64 z (/.f64 (-.f64 y x) t))
▶	2.5b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))))
✓	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	7.2b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
✓	2.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))

Compiler

Compiled 45026 to 18371 computations (59.2% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	0.5b	(cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))
✓	0.5b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))
	1.0b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series303.0ms (2.3%)

Counts

1 → 48

Calls

1 calls:

303.0ms

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

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`rem-cbrt-cube_binary64`
1×	`pow3_binary64`
1×	`cbrt-prod_binary64`

Counts

1 → 12

Calls

1 calls:

15.0ms

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

simplify218.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

593×	`times-frac_binary64`
370×	`associate-/r*_binary64`
344×	`associate-/l*_binary64`
296×	`fma-def_binary64`
195×	`associate-*r/_binary64`

Counts

60 → 96

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	446	5390
1	1530	5195
2	5105	5195

prune5.2s (39.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	1770	0	1770
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	1770	5	1775

Error

0.0b

Counts

1775 → 5

Alt Table

Status	Error	Program
	34.8b	(*.f64 z (/.f64 (-.f64 y x) t))
✓	2.5b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))))
✓	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
▶	7.2b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
✓	2.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))

Compiler

Compiled 260110 to 66776 computations (74.3% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y x) z)
✓	0.0b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
✓	7.5b	(/.f64 (*.f64 (-.f64 y x) z) t)

series150.0ms (1.1%)

Counts

3 → 132

Calls

3 calls:

56.0ms	(*.f64 (-.f64 y x) z)
50.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
43.0ms	(/.f64 (*.f64 (-.f64 y x) z) t)

rewrite35.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 66

Calls

3 calls:

11.0ms	(/.f64 (*.f64 (-.f64 y x) z) t)
9.0ms	(*.f64 (-.f64 y x) z)
8.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

simplify149.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

546×	`times-frac_binary64`
512×	`associate-/l*_binary64`
379×	`div-sub_binary64`
319×	`distribute-rgt-in_binary64`
318×	`associate-*l/_binary64`

Counts

198 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	138	2596
1	365	2080
2	1123	1980
3	4594	1980
4	5596	1980

prune154.0ms (1.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	0	1	1
Picked	0	1	1
Done	1	2	3
Total	125	6	131

Error

Counts

131 → 6

Alt Table

Status	Error	Program
	36.5b	(+.f64 x (*.f64 (/.f64 (-.f64 y x) (sqrt.f64 t)) (/.f64 z (sqrt.f64 t))))
✓	2.5b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))))
	34.8b	(*.f64 z (/.f64 (-.f64 y x) t))
✓	1.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	7.2b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
	1.1b	(+.f64 x (/.f64 (-.f64 y x) (/.f64 t z)))

Compiler

Compiled 1965 to 527 computations (73.2% saved)

regimes915.0ms (6.9%)

Accuracy

Total 1.8b remaining (99.5%)

Threshold costs 0b (0%)

Counts

86 → 1

Compiler

Compiled 20391 to 5793 computations (71.6% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	12	13
2	17	13
3	19	13
4	20	13
5	20	13

end1.0ms (0%)

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

sample1.7s (12.6%)

Algorithm

1×

intervals

Results

681.0ms	8000×	body	128	valid
187.0ms	2108×	body	128	invalid

Compiler

Compiled 193 to 74 computations (61.7% saved)

Details

analyze1.1s (8.6%)

sample32.0ms (0.2%)

simplify75.0ms (0.6%)

prune3.0ms (0%)

localize6.0ms (0%)

series22.0ms (0.2%)

rewrite1.0ms (0%)

simplify69.0ms (0.5%)

prune64.0ms (0.5%)

localize10.0ms (0.1%)

series645.0ms (4.8%)

rewrite25.0ms (0.2%)

simplify562.0ms (4.2%)

prune1.7s (13.1%)

localize30.0ms (0.2%)

series303.0ms (2.3%)

rewrite16.0ms (0.1%)

simplify218.0ms (1.6%)

prune5.2s (39.4%)

localize13.0ms (0.1%)

series150.0ms (1.1%)

rewrite35.0ms (0.3%)

simplify149.0ms (1.1%)

prune154.0ms (1.2%)

regimes915.0ms (6.9%)

simplify5.0ms (0%)

end1.0ms (0%)

sample1.7s (12.6%)

Profiling