Details

analyze526.0ms (8.5%)

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
12.5%	87.4%	0.1%	7
31.2%	68.6%	0.1%	8
35.9%	60.8%	3.3%	9
44.1%	48%	7.9%	10
54.8%	36.9%	8.3%	11
57.6%	31.5%	10.9%	12
61.9%	24%	14.1%	13
67.2%	18.6%	14.2%	14

Compiler

Compiled 13 to 10 computations (23.1% saved)

sample22.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	24×	body	128	invalid

Compiler

Compiled 28 to 22 computations (21.4% saved)

simplify43.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-def_binary64`
419×	`fma-neg_binary64`
210×	`distribute-rgt-in_binary64`
164×	`distribute-lft-in_binary64`
139×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	20	13
2	47	11
3	132	11
4	334	11
5	640	11
6	965	11
7	1254	11
8	1262	11
9	1262	11
10	1191	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

5.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	5.1b	(*.f64 x (-.f64 (fma.f64 y z 1) z))
	5.1b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))

Compiler

Compiled 66 to 45 computations (31.8% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 y z 1) z)
✓	4.8b	(*.f64 x (-.f64 (fma.f64 y z 1) z))

series14.0ms (0.2%)

Counts

2 → 60

Calls

2 calls:

10.0ms	(*.f64 x (-.f64 (fma.f64 y z 1) z))
4.0ms	(-.f64 (fma.f64 y z 1) z)

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
27×	`prod-diff_binary64`
26×	`add-cube-cbrt_binary64`
14×	`distribute-lft-in_binary64`

Counts

2 → 83

Calls

2 calls:

7.0ms	(*.f64 x (-.f64 (fma.f64 y z 1) z))
3.0ms	(-.f64 (fma.f64 y z 1) z)

simplify168.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

486×	`fma-def_binary64`
425×	`distribute-rgt-in_binary64`
399×	`distribute-lft-in_binary64`
324×	`exp-prod_binary64`
249×	`fma-neg_binary64`

Counts

143 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	1823
1	251	1705
2	904	1620
3	2834	1535
4	4552	1535
5	5143	1535

prune88.0ms (1.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	115	4	119
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	116	5	121

Error

0.0b

Counts

121 → 5

Alt Table

Status	Error	Program
▶	1.2b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
✓	5.1b	(*.f64 x (-.f64 (fma.f64 y z 1) z))
	18.2b	(/.f64 (.f64 x (-.f64 (.f64 (fma.f64 y z 1) (fma.f64 y z 1)) (*.f64 z z))) (+.f64 (fma.f64 y z 1) z))
	28.1b	(.f64 (-.f64 y 1) (.f64 z x))
	5.6b	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))

Compiler

Compiled 2321 to 1093 computations (52.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 y (.f64 z x)) x)
✓	0.0b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
✓	3.3b	(.f64 y (.f64 z x))

series31.0ms (0.5%)

Counts

3 → 60

Calls

3 calls:

14.0ms	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
9.0ms	(.f64 y (.f64 z x))
8.0ms	(+.f64 (.f64 y (.f64 z x)) x)

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`

Counts

3 → 56

Calls

3 calls:

7.0ms	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
4.0ms	(+.f64 (.f64 y (.f64 z x)) x)
4.0ms	(.f64 y (.f64 z x))

simplify88.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

816×	`fma-neg_binary64`
502×	`fma-def_binary64`
318×	`cancel-sign-sub-inv_binary64`
279×	`distribute-rgt-in_binary64`
247×	`distribute-lft-in_binary64`

Counts

116 → 103

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1397
1	285	1233
2	896	1196
3	2752	1195
4	4487	1195
5	4963	1195

prune97.0ms (1.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	103	5	108

Error

Counts

108 → 5

Alt Table

Status	Error	Program
✓	1.2b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
✓	5.1b	(*.f64 x (-.f64 (fma.f64 y z 1) z))
	28.1b	(.f64 (-.f64 y 1) (.f64 z x))
	28.6b	(.f64 (-.f64 (.f64 y x) x) z)
▶	5.6b	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))

Compiler

Compiled 1845 to 503 computations (72.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
✓	0.3b	(*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
✓	0.9b	(.f64 x (.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z))))
✓	5.1b	(cbrt.f64 (-.f64 (fma.f64 y z 1) z))

series784.0ms (12.6%)

Counts

4 → 120

Calls

4 calls:

644.0ms	(.f64 x (.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z))))
93.0ms	(*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
30.0ms	(cbrt.f64 (-.f64 (fma.f64 y z 1) z))
16.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))

rewrite70.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`cbrt-div_binary64`
44×	`associate-*r/_binary64`
40×	`flip--_binary64`
40×	`flip3--_binary64`
38×	`cbrt-prod_binary64`

Counts

4 → 158

Calls

4 calls:

17.0ms	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
17.0ms	(.f64 x (.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z))))
9.0ms	(*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))
2.0ms	(cbrt.f64 (-.f64 (fma.f64 y z 1) z))

simplify457.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

975×	`fma-def_binary64`
704×	`times-frac_binary64`
347×	`*-commutative_binary64`
234×	`+-commutative_binary64`
149×	`associate-+r+_binary64`

Counts

278 → 394

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	950	16210
1	3205	15465
2	4983	15465
3	4978	15465

prune1.6s (25.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	544	0	544
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	544	5	549

Error

Counts

549 → 5

Alt Table

Status	Error	Program
✓	1.2b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
✓	5.1b	(*.f64 x (-.f64 (fma.f64 y z 1) z))
▶	28.1b	(.f64 (-.f64 y 1) (.f64 z x))
	28.6b	(.f64 (-.f64 (.f64 y x) x) z)
✓	5.6b	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))

Compiler

Compiled 33642 to 22436 computations (33.3% saved)

localize14.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.3b	(.f64 (-.f64 y 1) (.f64 z x))

series22.0ms (0.4%)

Counts

1 → 20

Calls

1 calls:

22.0ms

(*.f64 (-.f64 y 1) (*.f64 z x))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`associate-l_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`

Counts

1 → 26

Calls

1 calls:

16.0ms

(*.f64 (-.f64 y 1) (*.f64 z x))

simplify91.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

925×	`fma-def_binary64`
502×	`associate-l_binary64`
369×	`associate-r_binary64`
291×	`distribute-rgt-neg-in_binary64`
274×	`distribute-lft-neg-in_binary64`

Counts

46 → 45

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	63	620
1	158	494
2	446	494
3	1509	494
4	2442	494
5	4707	494
6	4978	494

prune50.0ms (0.8%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	45	5	50

Error

Counts

50 → 5

Alt Table

Status	Error	Program
✓	1.2b	(-.f64 (+.f64 (.f64 y (.f64 z x)) x) (*.f64 z x))
✓	5.1b	(*.f64 x (-.f64 (fma.f64 y z 1) z))
✓	28.1b	(.f64 (-.f64 y 1) (.f64 z x))
	28.6b	(.f64 (-.f64 (.f64 y x) x) z)
✓	5.6b	(.f64 (.f64 x (*.f64 (cbrt.f64 (-.f64 (fma.f64 y z 1) z)) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))) (cbrt.f64 (-.f64 (fma.f64 y z 1) z)))

Compiler

Compiled 631 to 314 computations (50.2% saved)

regimes744.0ms (12%)

Accuracy

Total 0.1b remaining (81.6%)

Threshold costs 0.1b (81.6%)

Counts

41 → 3

Compiler

Compiled 4625 to 3045 computations (34.2% saved)

bsearch2.0ms (0%)

Compiler: Compiled 12 to 9 computations (25% saved)

simplify25.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

64×	`distribute-rgt-neg-in_binary64`
56×	`cancel-sign-sub-inv_binary64`
40×	`distribute-lft-neg-in_binary64`
40×	`distribute-lft-neg-out_binary64`
37×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	71
1	48	71
2	73	71
3	91	71
4	106	71
5	117	71
6	133	71
7	148	71
8	170	71
9	203	71
10	245	71
11	285	71
12	310	71
13	321	71
14	323	71
15	319	71

end5.0ms (0.1%)

Compiler: Compiled 52 to 31 computations (40.4% saved)

sample1.2s (19.9%)

Algorithm

1×

intervals

Results

566.0ms	8000×	body	128	valid
44.0ms	660×	body	128	invalid

Compiler

Compiled 141 to 89 computations (36.9% saved)

Iter	Nodes	Cost
0	25	71
1	48	71
2	73	71
3	91	71
4	106	71
5	117	71
6	133	71
7	148	71
8	170	71
9	203	71
10	245	71
11	285	71
12	310	71
13	321	71
14	323	71
15	319	71

Iter	Nodes	Cost
0	25	71
1	48	71
2	73	71
3	91	71
4	106	71
5	117	71
6	133	71
7	148	71
8	170	71
9	203	71
10	245	71
11	285	71
12	310	71
13	321	71
14	323	71
15	319	71

Details

analyze526.0ms (8.5%)

sample22.0ms (0.3%)

simplify43.0ms (0.7%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series14.0ms (0.2%)

rewrite15.0ms (0.2%)

simplify168.0ms (2.7%)

prune88.0ms (1.4%)

localize9.0ms (0.1%)

series31.0ms (0.5%)

rewrite17.0ms (0.3%)

simplify88.0ms (1.4%)

prune97.0ms (1.6%)

localize10.0ms (0.2%)

series784.0ms (12.6%)

rewrite70.0ms (1.1%)

simplify457.0ms (7.3%)

prune1.6s (25.1%)

localize14.0ms (0.2%)

series22.0ms (0.4%)

rewrite18.0ms (0.3%)

simplify91.0ms (1.5%)

prune50.0ms (0.8%)

regimes744.0ms (12%)

bsearch2.0ms (0%)

simplify25.0ms (0.4%)

end5.0ms (0.1%)

sample1.2s (19.9%)

Profiling

Iter	Nodes	Cost
0	25	71
1	48	71
2	73	71
3	91	71
4	106	71
5	117	71
6	133	71
7	148	71
8	170	71
9	203	71
10	245	71
11	285	71
12	310	71
13	321	71
14	323	71
15	319	71