Details

analyze1.3s (24.4%)

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
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
23.5%	76.3%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (21.8%)

Results

1.0s	8255×	body	128	valid
89.0ms	729×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify113.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1894×	`fma-neg_binary64`
843×	`div-sub_binary64`
750×	`fma-def_binary64`
582×	`times-frac_binary64`
397×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	37	14
3	78	14
4	163	14
5	295	14
6	645	14
7	1554	14
8	3040	14
9	3228	14
10	3469	14
11	3370	14
12	3363	14
13	3398	14
14	4949	14

prune4.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.7b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	14.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	0.7b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series61.0ms (1.1%)

Counts

2 → 96

Calls

2 calls:

41.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
20.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

6.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

simplify112.0ms (2%)

Algorithm

1×	egg-herbie

Rules

690×	`cancel-sign-sub-inv_binary64`
647×	`times-frac_binary64`
542×	`fma-neg_binary64`
354×	`sub-neg_binary64`
188×	`neg-mul-1_binary64`

Counts

160 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	267	4118
1	740	4035
2	2434	3427
3	4231	3410
4	4964	3410

prune111.0ms (2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	133	5	138
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	135	5	140

Error

0.0b

Counts

140 → 5

Alt Table

Status	Error	Program
	3.3b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	14.6b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
	10.5b	(fma.f64 y (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 z t) (-.f64 a t)) (/.f64 (-.f64 z t) (-.f64 a t))) (/.f64 (-.f64 z t) (-.f64 a t)))) x)
▶	0.8b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
	0.8b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

Compiler

Compiled 3408 to 1143 computations (66.5% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a t))
✓	0.2b	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
✓	0.7b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

series69.0ms (1.2%)

Counts

3 → 120

Calls

3 calls:

40.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
19.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
10.0ms	(/.f64 1 (-.f64 a t))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

3 → 105

Calls

3 calls:

10.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
4.0ms	(/.f64 1 (-.f64 a t))
0.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

simplify138.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

700×	`cancel-sign-sub-inv_binary64`
675×	`times-frac_binary64`
380×	`fma-neg_binary64`
354×	`sub-neg_binary64`
192×	`+-commutative_binary64`

Counts

225 → 227

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	298	4903
1	792	4646
2	2764	4604
3	4923	4603
4	5113	4603

prune168.0ms (3.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	227	0	227
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	227	5	232

Error

0.0b

Counts

232 → 5

Alt Table

Status	Error	Program
	3.3b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	14.6b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
	10.5b	(fma.f64 y (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 z t) (-.f64 a t)) (/.f64 (-.f64 z t) (-.f64 a t))) (/.f64 (-.f64 z t) (-.f64 a t)))) x)
✓	0.8b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
▶	0.8b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

Compiler

Compiled 5337 to 1971 computations (63.1% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a t) (-.f64 z t))
✓	0.2b	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))
✓	0.7b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

series88.0ms (1.6%)

Counts

3 → 132

Calls

3 calls:

41.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
24.0ms	(/.f64 (-.f64 a t) (-.f64 z t))
22.0ms	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))

rewrite44.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
195×	`*-un-lft-identity_binary64`
195×	`add-sqr-sqrt_binary64`
91×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

3 → 214

Calls

3 calls:

9.0ms	(/.f64 (-.f64 a t) (-.f64 z t))
9.0ms	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))
0.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

simplify178.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

927×	`cancel-sign-sub-inv_binary64`
524×	`sub-neg_binary64`
249×	`associate--l+_binary64`
234×	`+-commutative_binary64`
217×	`fma-neg_binary64`

Counts

346 → 337

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	391	8735
1	1041	8263
2	3678	8083
3	5565	8083

prune230.0ms (4.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	337	0	337
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	337	5	342

Error

0.0b

Counts

342 → 5

Alt Table

Status	Error	Program
▶	3.3b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	14.6b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
	10.5b	(fma.f64 y (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 z t) (-.f64 a t)) (/.f64 (-.f64 z t) (-.f64 a t))) (/.f64 (-.f64 z t) (-.f64 a t)))) x)
✓	0.8b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
✓	0.8b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

Compiler

Compiled 8668 to 2770 computations (68% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	0.0b	(/.f64 y (-.f64 a t))
✓	11.9b	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))

series102.0ms (1.9%)

Counts

3 → 132

Calls

3 calls:

46.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
37.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
19.0ms	(/.f64 y (-.f64 a t))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64`
68×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
31×	`times-frac_binary64`

Counts

3 → 155

Calls

3 calls:

10.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
6.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
3.0ms	(/.f64 y (-.f64 a t))

simplify207.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

422×	`sub-neg_binary64`
404×	`fma-neg_binary64`
222×	`associate--l+_binary64`
218×	`+-commutative_binary64`
182×	`associate-l_binary64`

Counts

287 → 308

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	443	6869
1	1078	6148
2	3977	6052
3	4707	6051
4	4994	6051
5	4942	6051

prune226.0ms (4.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	306	2	308
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	308	5	313

Error

Counts

313 → 5

Alt Table

Status	Error	Program
	36.5b	(+.f64 x (/.f64 (.f64 y (-.f64 (.f64 z z) (.f64 t t))) (.f64 (-.f64 a t) (+.f64 z t))))
✓	0.8b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
	3.6b	(+.f64 x (*.f64 (/.f64 1 (/.f64 (-.f64 a t) y)) (-.f64 z t)))
	14.6b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
✓	0.8b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

Compiler

Compiled 7986 to 2043 computations (74.4% saved)

regimes932.0ms (17%)

Accuracy

Total 1.3b remaining (99%)

Threshold costs 0b (0%)

Counts

137 → 1

Compiler

Compiled 18174 to 11132 computations (38.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	15	20
2	24	20
3	28	20
4	30	20
5	30	20

end72.0ms (1.3%)

Compiler: Compiled 136 to 80 computations (41.2% saved)

Details

analyze1.3s (24.4%)

sample1.2s (21.8%)

simplify113.0ms (2.1%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series61.0ms (1.1%)

rewrite11.0ms (0.2%)

simplify112.0ms (2%)

prune111.0ms (2%)

localize10.0ms (0.2%)

series69.0ms (1.2%)

rewrite20.0ms (0.4%)

simplify138.0ms (2.5%)

prune168.0ms (3.1%)

localize9.0ms (0.2%)

series88.0ms (1.6%)

rewrite44.0ms (0.8%)

simplify178.0ms (3.2%)

prune230.0ms (4.2%)

localize10.0ms (0.2%)

series102.0ms (1.9%)

rewrite32.0ms (0.6%)

simplify207.0ms (3.8%)

prune226.0ms (4.1%)

regimes932.0ms (17%)

simplify2.0ms (0%)

end72.0ms (1.3%)

Profiling