Details

analyze551.0ms (15.3%)

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
0%	81.1%	18.9%	7
6.2%	74.9%	18.9%	8
9.4%	65.5%	25.1%	9
15.6%	48.4%	36%	10
20.3%	43.1%	36.6%	11
22.6%	36%	41.4%	12
27.1%	25.1%	47.8%	13
29.5%	22.5%	48%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.8s (49%)

Results

1.1s	8256×	body	128	valid
379.0ms	2691×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify192.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

767×	`unsub-neg_binary64`
741×	`*-commutative_binary64`
699×	`fma-def_binary64`
598×	`fma-neg_binary64`
465×	`distribute-neg-out_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	19	15
2	29	15
3	57	15
4	118	15
5	278	15
6	529	15
7	1007	15
8	1781	15
9	2585	15
10	2834	15
11	3141	15
12	3371	15
13	3485	15
14	3485	15
15	4444	15
16	4284	15
17	4604	15
18	4604	15
19	5103	15

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

25.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	25.1b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
✓	2.2b	(-.f64 (.f64 y y) (.f64 z z))
✓	24.4b	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

series64.0ms (1.8%)

Counts

3 → 84

Calls

3 calls:

41.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
16.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
7.0ms	(-.f64 (.f64 y y) (.f64 z z))

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 62

Calls

3 calls:

6.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
5.0ms	(-.f64 (.f64 y y) (.f64 z z))
3.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

simplify111.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

638×	`fma-def_binary64`
337×	`fma-neg_binary64`
316×	`cancel-sign-sub-inv_binary64`
268×	`neg-mul-1_binary64`
187×	`distribute-rgt-neg-in_binary64`

Counts

146 → 179

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	2931
1	582	2842
2	2289	2771
3	4556	2771
4	5028	2771

prune107.0ms (3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	174	5	179
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	175	5	180

Error

0.1b

Counts

180 → 5

Alt Table

Status	Error	Program
▶	25.1b	(.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 (.f64 z z)))))
	40.0b	(fma.f64 y x (fma.f64 (.f64 (/.f64 (.f64 z z) y) x) -1/2 (.f64 (.f64 (/.f64 (pow.f64 z 4) (pow.f64 y 3)) x) -1/8)))
	29.0b	(*.f64 x (neg.f64 y))
	32.4b	(*.f64 x y)
	35.9b	(.f64 (.f64 (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)) (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x))) (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)))

Compiler

Compiled 3739 to 1667 computations (55.4% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 (.f64 z z)))))
✓	2.7b	(fma.f64 y y (neg.f64 (*.f64 z z)))
✓	24.4b	(sqrt.f64 (fma.f64 y y (neg.f64 (*.f64 z z))))

series74.0ms (2.1%)

Counts

3 → 84

Calls

3 calls:

45.0ms	(.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 (.f64 z z)))))
21.0ms	(sqrt.f64 (fma.f64 y y (neg.f64 (*.f64 z z))))
7.0ms	(fma.f64 y y (neg.f64 (*.f64 z z)))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
7×	`sqrt-prod_binary64`
7×	`add-cube-cbrt_binary64`
6×	`associate-r_binary64`

Counts

3 → 49

Calls

3 calls:

3.0ms	(.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 (.f64 z z)))))
1.0ms	(sqrt.f64 (fma.f64 y y (neg.f64 (*.f64 z z))))
0.0ms	(fma.f64 y y (neg.f64 (*.f64 z z)))

simplify98.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

705×	`associate-/r*_binary64`
524×	`fma-def_binary64`
364×	`fma-neg_binary64`
268×	`cancel-sign-sub-inv_binary64`
142×	`associate-/r/_binary64`

Counts

133 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	2728
1	510	2646
2	1862	2573
3	4760	2573
4	5125	2573

prune75.0ms (2.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	161	5	166

Error

0.1b

Counts

166 → 5

Alt Table

Status	Error	Program
✓	25.1b	(.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 (.f64 z z)))))
	40.0b	(fma.f64 y x (fma.f64 (.f64 (/.f64 (.f64 z z) y) x) -1/2 (.f64 (.f64 (/.f64 (pow.f64 z 4) (pow.f64 y 3)) x) -1/8)))
▶	29.0b	(*.f64 x (neg.f64 y))
	32.4b	(*.f64 x y)
	35.9b	(.f64 (.f64 (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)) (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x))) (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)))

Compiler

Compiled 3341 to 1539 computations (53.9% saved)

localize3.0ms (0.1%)

prune4.0ms (0.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	1	1
Total	5	5

Error

0.1b

Counts

5 → 5

Alt Table

Status	Error	Program
✓	25.1b	(.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 (.f64 z z)))))
	40.0b	(fma.f64 y x (fma.f64 (.f64 (/.f64 (.f64 z z) y) x) -1/2 (.f64 (.f64 (/.f64 (pow.f64 z 4) (pow.f64 y 3)) x) -1/8)))
✓	29.0b	(*.f64 x (neg.f64 y))
▶	32.4b	(*.f64 x y)
	35.9b	(.f64 (.f64 (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)) (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x))) (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)))

Compiler

Compiled 154 to 77 computations (50% saved)

localize2.0ms (0.1%)

prune4.0ms (0.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	2	2
Total	5	5

Error

0.1b

Counts

5 → 5

Alt Table

Status	Error	Program
✓	25.1b	(.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 (.f64 z z)))))
	40.0b	(fma.f64 y x (fma.f64 (.f64 (/.f64 (.f64 z z) y) x) -1/2 (.f64 (.f64 (/.f64 (pow.f64 z 4) (pow.f64 y 3)) x) -1/8)))
✓	29.0b	(*.f64 x (neg.f64 y))
✓	32.4b	(*.f64 x y)
	35.9b	(.f64 (.f64 (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)) (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x))) (cbrt.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)))

Compiler

Compiled 87 to 45 computations (48.3% saved)

regimes385.0ms (10.7%)

Accuracy

Total 0.3b remaining (55.2%)

Threshold costs 0.3b (55.2%)

Counts

20 → 2

Compiler

Compiled 3231 to 1853 computations (42.6% saved)

bsearch43.0ms (1.2%)

Steps

Iters	Range		Point
2	-3.924711085373417e-270	6.93388403477893e-222	-1.8331389015440094e-301

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
6×	`+-commutative_binary64`
5×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	29
1	25	29
2	34	29
3	41	29
4	47	29
5	50	29
6	51	29
7	51	29

end73.0ms (2%)

Compiler: Compiled 131 to 73 computations (44.3% saved)

Details

analyze551.0ms (15.3%)

sample1.8s (49%)

simplify192.0ms (5.3%)

prune2.0ms (0%)

localize8.0ms (0.2%)

series64.0ms (1.8%)

rewrite16.0ms (0.5%)

simplify111.0ms (3.1%)

prune107.0ms (3%)

localize7.0ms (0.2%)

series74.0ms (2.1%)

rewrite7.0ms (0.2%)

simplify98.0ms (2.7%)

prune75.0ms (2.1%)

localize3.0ms (0.1%)

prune4.0ms (0.1%)

localize2.0ms (0.1%)

prune4.0ms (0.1%)

regimes385.0ms (10.7%)

bsearch43.0ms (1.2%)

simplify6.0ms (0.2%)

end73.0ms (2%)

Profiling