Details

analyze1.5s (22.3%)

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
7.8%	92%	0.2%	9
11.7%	88.1%	0.2%	10
24.2%	64.7%	11.1%	11
27.9%	59.8%	12.3%	12
35%	52.5%	12.5%	13
38.6%	48.2%	13.2%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample46.0ms (0.7%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
6.0ms	69×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify14.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

22×	`fma-def_binary64`
8×	`+-commutative_binary64`
4×	`associate-+r+_binary64`
4×	`associate-+l+_binary64`
3×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	9
1	15	9
2	25	9
3	38	9
4	52	9
5	52	9

prune6.0ms (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
	0.1b	(fma.f64 y (fma.f64 x y z) t)
▶	0.1b	(+.f64 (.f64 (+.f64 (.f64 x y) z) y) t)

Compiler

Compiled 68 to 38 computations (44.1% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series64.0ms (1%)

Counts

3 → 120

Calls

3 calls:

34.0ms	(+.f64 (.f64 (+.f64 (.f64 x y) z) y) t)
19.0ms	(.f64 (+.f64 (.f64 x y) z) y)
10.0ms	(+.f64 (*.f64 x y) z)

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
7×	`add-log-exp_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 50

Calls

3 calls:

14.0ms	(.f64 (+.f64 (.f64 x y) z) y)
11.0ms	(+.f64 (.f64 (+.f64 (.f64 x y) z) y) t)
6.0ms	(+.f64 (*.f64 x y) z)

simplify226.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

914×	`fma-neg_binary64`
664×	`associate-+l+_binary64`
377×	`associate-l_binary64`
325×	`fma-def_binary64`
309×	`associate-r_binary64`

Counts

170 → 101

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	1684
1	242	1391
2	671	1381
3	2360	1381
4	4783	1381
5	5523	1381

prune103.0ms (1.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	95	6	101
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	97	6	103

Error

0.0b

Counts

103 → 6

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 (+.f64 (*.f64 x y) z) y t)
	4.4b	(+.f64 (+.f64 (.f64 y z) (.f64 (pow.f64 y 2) x)) t)
	19.2b	(+.f64 (/.f64 (.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 z z)) y) (-.f64 (.f64 x y) z)) t)
	0.7b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (fma.f64 y x z))) (cbrt.f64 (.f64 y (fma.f64 y x z)))) (cbrt.f64 (*.f64 y (fma.f64 y x z)))) t)
	34.2b	(+.f64 (.f64 (.f64 (fma.f64 y x z) (sqrt.f64 y)) (sqrt.f64 y)) t)
	22.0b	(+.f64 (cbrt.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 x y) z) y) (.f64 (+.f64 (.f64 x y) z) y)) (.f64 (+.f64 (.f64 x y) z) y))) t)

Compiler

Compiled 1717 to 477 computations (72.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series17.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

17.0ms

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

simplify74.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

775×	`associate-+l+_binary64`
772×	`associate-+r+_binary64`
678×	`unswap-sqr_binary64`
551×	`*-commutative_binary64`
296×	`distribute-lft-in_binary64`

Counts

58 → 31

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	697
1	49	499
2	85	499
3	257	499
4	1272	499
5	3520	499
6	4213	499
7	5348	499

prune42.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	58	6	64

Error

0.0b

Counts

64 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (+.f64 (*.f64 x y) z) y t)
	4.4b	(+.f64 (+.f64 (.f64 y z) (.f64 (pow.f64 y 2) x)) t)
	19.2b	(+.f64 (/.f64 (.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 z z)) y) (-.f64 (.f64 x y) z)) t)
▶	0.7b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (fma.f64 y x z))) (cbrt.f64 (.f64 y (fma.f64 y x z)))) (cbrt.f64 (*.f64 y (fma.f64 y x z)))) t)
	34.2b	(+.f64 (.f64 (.f64 (fma.f64 y x z) (sqrt.f64 y)) (sqrt.f64 y)) t)
	22.0b	(+.f64 (cbrt.f64 (.f64 (.f64 (.f64 (+.f64 (.f64 x y) z) y) (.f64 (+.f64 (.f64 x y) z) y)) (.f64 (+.f64 (.f64 x y) z) y))) t)

Compiler

Compiled 912 to 284 computations (68.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 y (fma.f64 y x z))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 y (fma.f64 y x z))) (cbrt.f64 (.f64 y (fma.f64 y x z)))) (cbrt.f64 (*.f64 y (fma.f64 y x z))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 y (fma.f64 y x z))) (cbrt.f64 (*.f64 y (fma.f64 y x z))))
✓	7.2b	(cbrt.f64 (*.f64 y (fma.f64 y x z)))

series243.0ms (3.7%)

Counts

4 → 144

Calls

4 calls:

130.0ms	(.f64 (cbrt.f64 (.f64 y (fma.f64 y x z))) (cbrt.f64 (*.f64 y (fma.f64 y x z))))
55.0ms	(cbrt.f64 (*.f64 y (fma.f64 y x z)))
38.0ms	(.f64 (.f64 (cbrt.f64 (.f64 y (fma.f64 y x z))) (cbrt.f64 (.f64 y (fma.f64 y x z)))) (cbrt.f64 (*.f64 y (fma.f64 y x z))))
20.0ms	(*.f64 y (fma.f64 y x z))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`
16×	`pow1/3_binary64`
13×	`add-exp-log_binary64`
11×	`associate-r_binary64`

Counts

4 → 101

Calls

4 calls:

13.0ms	(.f64 (.f64 (cbrt.f64 (.f64 y (fma.f64 y x z))) (cbrt.f64 (.f64 y (fma.f64 y x z)))) (cbrt.f64 (*.f64 y (fma.f64 y x z))))
9.0ms	(.f64 (cbrt.f64 (.f64 y (fma.f64 y x z))) (cbrt.f64 (*.f64 y (fma.f64 y x z))))
6.0ms	(*.f64 y (fma.f64 y x z))
3.0ms	(cbrt.f64 (*.f64 y (fma.f64 y x z)))

simplify320.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

509×	`fma-def_binary64`
475×	`times-frac_binary64`
408×	`associate-l_binary64`
364×	`associate-/r*_binary64`
308×	`associate-/l*_binary64`

Counts

245 → 251

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	506	7168
1	1569	6470
2	4753	6450
3	4999	6450

prune870.0ms (13.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	447	2	449
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	448	7	455

Error

Counts

455 → 7

Alt Table

Status	Error	Program
	19.2b	(+.f64 (/.f64 (.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 z z)) y) (-.f64 (.f64 x y) z)) t)
▶	0.6b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (fma.f64 y x z))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (fma.f64 y x z))))) (cbrt.f64 (*.f64 y (fma.f64 y x z)))) t)
✓	0.1b	(fma.f64 (+.f64 (*.f64 x y) z) y t)
	4.4b	(+.f64 (+.f64 (.f64 y z) (.f64 (pow.f64 y 2) x)) t)
	23.0b	(+.f64 (.f64 (cbrt.f64 (.f64 y (.f64 y (.f64 (fma.f64 y x z) (fma.f64 y x z))))) (cbrt.f64 (*.f64 y (fma.f64 y x z)))) t)
✓	0.7b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (fma.f64 y x z))) (cbrt.f64 (.f64 y (fma.f64 y x z)))) (cbrt.f64 (*.f64 y (fma.f64 y x z)))) t)
	34.2b	(+.f64 (.f64 (.f64 (fma.f64 y x z) (sqrt.f64 y)) (sqrt.f64 y)) t)

Compiler

Compiled 21528 to 9538 computations (55.7% saved)

localize31.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (.f64 y (fma.f64 y x z))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (fma.f64 y x z)))))
✓	0.7b	(cbrt.f64 y)
	7.2b	(cbrt.f64 (*.f64 y (fma.f64 y x z)))
✓	7.2b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (fma.f64 y x z))))

series395.0ms (6.1%)

Counts

3 → 84

Calls

3 calls:

187.0ms

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

136.0ms

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

71.0ms

(cbrt.f64 y)

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`cbrt-prod_binary64`
6×	`add-cube-cbrt_binary64`
5×	`add-exp-log_binary64`

Counts

3 → 47

Calls

3 calls:

12.0ms

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

10.0ms

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

1.0ms

(cbrt.f64 y)

simplify264.0ms (4%)

Algorithm

1×	egg-herbie

Rules

490×	`fma-def_binary64`
475×	`times-frac_binary64`
366×	`associate-/r*_binary64`
343×	`associate-l_binary64`
308×	`associate-/l*_binary64`

Counts

131 → 210

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	479	5789
1	1517	5385
2	4641	5365
3	4938	5365

prune594.0ms (9.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	402	0	402
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	402	7	409

Error

Counts

409 → 7

Alt Table

Status	Error	Program
	19.2b	(+.f64 (/.f64 (.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 z z)) y) (-.f64 (.f64 x y) z)) t)
✓	0.6b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (fma.f64 y x z))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (fma.f64 y x z))))) (cbrt.f64 (*.f64 y (fma.f64 y x z)))) t)
✓	0.1b	(fma.f64 (+.f64 (*.f64 x y) z) y t)
	4.4b	(+.f64 (+.f64 (.f64 y z) (.f64 (pow.f64 y 2) x)) t)
	23.0b	(+.f64 (.f64 (cbrt.f64 (.f64 y (.f64 y (.f64 (fma.f64 y x z) (fma.f64 y x z))))) (cbrt.f64 (*.f64 y (fma.f64 y x z)))) t)
✓	0.7b	(+.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (fma.f64 y x z))) (cbrt.f64 (.f64 y (fma.f64 y x z)))) (cbrt.f64 (*.f64 y (fma.f64 y x z)))) t)
	34.2b	(+.f64 (.f64 (.f64 (fma.f64 y x z) (sqrt.f64 y)) (sqrt.f64 y)) t)

Compiler

Compiled 22026 to 9470 computations (57% saved)

regimes478.0ms (7.3%)

Accuracy

Total 0.0b remaining (77.6%)

Threshold costs 0.0b (77.6%)

Counts

74 → 1

Compiler

Compiled 8244 to 4430 computations (46.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
2	10	11

end0.0ms (0%)

Compiler: Compiled 12 to 7 computations (41.7% saved)

sample1.1s (17.4%)

Algorithm

1×

intervals

Results

393.0ms	8000×	body	128	valid
96.0ms	1901×	body	128	invalid

Compiler

Compiled 191 to 96 computations (49.7% saved)

Details

analyze1.5s (22.3%)

sample46.0ms (0.7%)

simplify14.0ms (0.2%)

prune6.0ms (0.1%)

localize12.0ms (0.2%)

series64.0ms (1%)

rewrite34.0ms (0.5%)

simplify226.0ms (3.5%)

prune103.0ms (1.6%)

localize6.0ms (0.1%)

series17.0ms (0.3%)

rewrite1.0ms (0%)

simplify74.0ms (1.1%)

prune42.0ms (0.6%)

localize9.0ms (0.1%)

series243.0ms (3.7%)

rewrite43.0ms (0.7%)

simplify320.0ms (4.9%)

prune870.0ms (13.4%)

localize31.0ms (0.5%)

series395.0ms (6.1%)

rewrite30.0ms (0.5%)

simplify264.0ms (4%)

prune594.0ms (9.1%)

regimes478.0ms (7.3%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.1s (17.4%)

Profiling