Details

analyze1.3s (24.7%)

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 (23%)

Results

1.0s	8255×	body	128	valid
91.0ms	750×	body	128	invalid
0.0ms	1×	body	2048	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify139.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1627×	`fma-def_binary64`
927×	`div-sub_binary64`
619×	`times-frac_binary64`
541×	`fma-neg_binary64`
386×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	21	14
2	40	14
3	78	14
4	161	14
5	302	14
6	659	14
7	1591	14
8	3045	14
9	3070	14
10	3380	14
11	3469	14
12	3480	14
13	4892	14
14	5124	14

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

1.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

Compiler

Compiled 56 to 29 computations (48.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series61.0ms (1.2%)

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))

rewrite15.0ms (0.3%)

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:

11.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

simplify112.0ms (2.2%)

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

prune101.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	134	4	138
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	134	5	139

Error

0.0b

Counts

139 → 5

Alt Table

Status	Error	Program
▶	1.3b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	3.2b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	10.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
	28.5b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)))

Compiler

Compiled 3381 to 1128 computations (66.6% saved)

localize8.0ms (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)))
✓	1.3b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

series89.0ms (1.7%)

Counts

3 → 120

Calls

3 calls:

57.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
23.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
8.0ms	(/.f64 1 (-.f64 a t))

rewrite23.0ms (0.5%)

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:

13.0ms	(*.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)

simplify134.0ms (2.6%)

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

prune150.0ms (2.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	227	0	227
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	227	5	232

Error

0.0b

Counts

232 → 5

Alt Table

Status	Error	Program
✓	1.3b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
▶	3.2b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	10.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
	28.5b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)))

Compiler

Compiled 5310 to 1956 computations (63.2% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 a t))
✓	0.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	10.0b	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))

series113.0ms (2.2%)

Counts

3 → 132

Calls

3 calls:

49.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
47.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
18.0ms	(/.f64 y (-.f64 a t))

rewrite34.0ms (0.7%)

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:

11.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
4.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
4.0ms	(/.f64 y (-.f64 a t))

simplify214.0ms (4.1%)

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

prune211.0ms (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

0.0b

Counts

313 → 5

Alt Table

Status	Error	Program
✓	1.3b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	10.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
▶	3.2b	(+.f64 (fma.f64 z (/.f64 y (-.f64 a t)) x) (*.f64 (neg.f64 t) (/.f64 y (-.f64 a t))))
	33.2b	(+.f64 x (*.f64 (/.f64 (/.f64 y (sqrt.f64 (-.f64 a t))) (sqrt.f64 (-.f64 a t))) (-.f64 z t)))

Compiler

Compiled 8052 to 2073 computations (74.3% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 y (-.f64 a t))
✓	2.8b	(fma.f64 z (/.f64 y (-.f64 a t)) x)
✓	8.3b	(*.f64 (neg.f64 t) (/.f64 y (-.f64 a t)))

series47.0ms (0.9%)

Counts

2 → 96

Calls

2 calls:

27.0ms	(fma.f64 z (/.f64 y (-.f64 a t)) x)
20.0ms	(*.f64 (neg.f64 t) (/.f64 y (-.f64 a t)))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
21×	`associate-r_binary64`
20×	`*-un-lft-identity_binary64`
16×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`

Counts

2 → 60

Calls

2 calls:

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

simplify92.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

506×	`fma-def_binary64`
292×	`div-sub_binary64`
195×	`cancel-sign-sub-inv_binary64`
188×	`associate-/r/_binary64`
176×	`distribute-lft-neg-out_binary64`

Counts

156 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	211	2651
1	553	2565
2	1993	2298
3	4653	2298
4	5288	2298

prune175.0ms (3.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	256	5	261

Error

0.0b

Counts

261 → 5

Alt Table

Status	Error	Program
✓	1.3b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	10.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
✓	3.2b	(+.f64 (fma.f64 z (/.f64 y (-.f64 a t)) x) (*.f64 (neg.f64 t) (/.f64 y (-.f64 a t))))
	33.2b	(+.f64 x (*.f64 (/.f64 (/.f64 y (sqrt.f64 (-.f64 a t))) (sqrt.f64 (-.f64 a t))) (-.f64 z t)))

Compiler

Compiled 6768 to 1498 computations (77.9% saved)

regimes873.0ms (16.9%)

Accuracy

Total 1.3b remaining (99%)

Threshold costs 0b (0%)

Counts

105 → 1

Compiler

Compiled 15216 to 9320 computations (38.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	16	16
2	22	16
3	24	16
4	25	16
5	25	16

end67.0ms (1.3%)

Compiler: Compiled 130 to 75 computations (42.3% saved)

Details

analyze1.3s (24.7%)

sample1.2s (23%)

simplify139.0ms (2.7%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series61.0ms (1.2%)

rewrite15.0ms (0.3%)

simplify112.0ms (2.2%)

prune101.0ms (1.9%)

localize8.0ms (0.2%)

series89.0ms (1.7%)

rewrite23.0ms (0.5%)

simplify134.0ms (2.6%)

prune150.0ms (2.9%)

localize9.0ms (0.2%)

series113.0ms (2.2%)

rewrite34.0ms (0.7%)

simplify214.0ms (4.1%)

prune211.0ms (4.1%)

localize10.0ms (0.2%)

series47.0ms (0.9%)

rewrite14.0ms (0.3%)

simplify92.0ms (1.8%)

prune175.0ms (3.4%)

regimes873.0ms (16.9%)

simplify3.0ms (0.1%)

end67.0ms (1.3%)

Profiling