Details

analyze935.0ms (10.3%)

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
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
49.9%	49.9%	0.2%	8
49.9%	49.9%	0.2%	9
49.9%	49.9%	0.2%	10
74.8%	24.9%	0.2%	11
74.8%	24.9%	0.2%	12
74.8%	24.9%	0.2%	13
74.8%	24.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.6s (17.4%)

Results

1.5s	8255×	body	128	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify204.0ms (2.3%)

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

prune11.0ms (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
	11.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
▶	1.0b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize16.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	1.0b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series121.0ms (1.3%)

Counts

2 → 96

Calls

2 calls:

78.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
43.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

rewrite31.0ms (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:

23.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
1.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

simplify252.0ms (2.8%)

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

prune253.0ms (2.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	134	4	138
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	134	6	140

Error

0.0b

Counts

140 → 6

Alt Table

Status	Error	Program
▶	1.0b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
	11.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
	35.7b	(-.f64 (+.f64 (.f64 (/.f64 z a) (.f64 (/.f64 y a) (+.f64 t (/.f64 (.f64 t t) a)))) (+.f64 x (/.f64 (.f64 y z) a))) (.f64 (/.f64 y a) (+.f64 t (/.f64 (.f64 t t) a))))
✓	1.0b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	1.4b	(fma.f64 y (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t)))) x)
	3.6b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))

Compiler

Compiled 3449 to 1164 computations (66.3% saved)

localize35.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a t) (-.f64 z t))
✓	0.5b	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))
✓	1.0b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

series162.0ms (1.8%)

Counts

3 → 132

Calls

3 calls:

81.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
41.0ms	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))
39.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

rewrite77.0ms (0.9%)

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:

17.0ms	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))
16.0ms	(/.f64 (-.f64 a t) (-.f64 z t))
1.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

simplify372.0ms (4.1%)

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

prune515.0ms (5.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	336	1	337
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	338	5	343

Error

0.0b

Counts

343 → 5

Alt Table

Status	Error	Program
	1.5b	(fma.f64 y (/.f64 1 (-.f64 (/.f64 a (-.f64 z t)) (/.f64 t (-.f64 z t)))) x)
	11.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
✓	1.0b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
▶	1.4b	(fma.f64 y (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t)))) x)
	3.6b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))

Compiler

Compiled 8671 to 2781 computations (67.9% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t))))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))
✓	0.5b	(cbrt.f64 (-.f64 a t))
✓	1.0b	(fma.f64 y (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t)))) x)

series301.0ms (3.3%)

Counts

4 → 144

Calls

4 calls:

103.0ms	(*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))
91.0ms	(fma.f64 y (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t)))) x)
62.0ms	(cbrt.f64 (-.f64 a t))
45.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t))))

rewrite133.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`add-sqr-sqrt_binary64`
79×	`*-un-lft-identity_binary64`
61×	`cbrt-prod_binary64`
55×	`times-frac_binary64`
54×	`associate-r_binary64`

Counts

4 → 189

Calls

4 calls:

61.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t))))
19.0ms	(*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))
6.0ms	(cbrt.f64 (-.f64 a t))
1.0ms	(fma.f64 y (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t)))) x)

simplify352.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

406×	`associate-r_binary64`
296×	`associate-l_binary64`
263×	`times-frac_binary64`
256×	`associate-/l*_binary64`
206×	`associate-/r*_binary64`

Counts

333 → 377

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	553	10086
1	1509	8678
2	5021	8678

prune779.0ms (8.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	477	0	477
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	477	5	482

Error

0.0b

Counts

482 → 5

Alt Table

Status	Error	Program
▶	1.5b	(fma.f64 y (/.f64 1 (-.f64 (/.f64 a (-.f64 z t)) (/.f64 t (-.f64 z t)))) x)
	11.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
✓	1.0b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
✓	1.4b	(fma.f64 y (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t)))) x)
	3.6b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))

Compiler

Compiled 16901 to 5818 computations (65.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 z t))
✓	0.0b	(/.f64 a (-.f64 z t))
✓	0.5b	(/.f64 1 (-.f64 (/.f64 a (-.f64 z t)) (/.f64 t (-.f64 z t))))
✓	1.0b	(fma.f64 y (/.f64 1 (-.f64 (/.f64 a (-.f64 z t)) (/.f64 t (-.f64 z t)))) x)

series495.0ms (5.5%)

Counts

4 → 144

Calls

4 calls:

317.0ms	(fma.f64 y (/.f64 1 (-.f64 (/.f64 a (-.f64 z t)) (/.f64 t (-.f64 z t)))) x)
129.0ms	(/.f64 1 (-.f64 (/.f64 a (-.f64 z t)) (/.f64 t (-.f64 z t))))
32.0ms	(/.f64 a (-.f64 z t))
16.0ms	(/.f64 t (-.f64 z t))

rewrite104.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

175×	`*-un-lft-identity_binary64`
156×	`times-frac_binary64`
135×	`add-sqr-sqrt_binary64`
56×	`distribute-lft-out--_binary64`
55×	`add-cube-cbrt_binary64`

Counts

4 → 185

Calls

4 calls:

45.0ms	(/.f64 1 (-.f64 (/.f64 a (-.f64 z t)) (/.f64 t (-.f64 z t))))
7.0ms	(/.f64 a (-.f64 z t))
7.0ms	(/.f64 t (-.f64 z t))
1.0ms	(fma.f64 y (/.f64 1 (-.f64 (/.f64 a (-.f64 z t)) (/.f64 t (-.f64 z t)))) x)

simplify317.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

290×	`fma-def_binary64`
249×	`associate-*l/_binary64`
231×	`associate-*r/_binary64`
223×	`+-commutative_binary64`
207×	`associate-l_binary64`

Counts

329 → 343

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	793	11354
1	2535	11048
2	4990	11048

prune595.0ms (6.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	342	1	343
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	343	5	348

Error

Counts

348 → 5

Alt Table

Status	Error	Program
	11.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
✓	1.0b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	1.5b	(+.f64 (/.f64 y (-.f64 (/.f64 a (-.f64 z t)) (/.f64 t (-.f64 z t)))) x)
✓	1.4b	(fma.f64 y (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t)))) x)
	3.6b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))

Compiler

Compiled 13518 to 5396 computations (60.1% saved)

regimes1.2s (13.4%)

Accuracy

Total 1.2b remaining (99.5%)

Threshold costs 0b (0%)

Counts

110 → 1

Compiler

Compiled 15325 to 9382 computations (38.8% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	13	14
2	19	14
3	21	14
4	22	14
5	22	14

end149.0ms (1.6%)

Compiler: Compiled 125 to 72 computations (42.4% saved)

Details

analyze935.0ms (10.3%)

sample1.6s (17.4%)

simplify204.0ms (2.3%)

prune11.0ms (0.1%)

localize16.0ms (0.2%)

series121.0ms (1.3%)

rewrite31.0ms (0.3%)

simplify252.0ms (2.8%)

prune253.0ms (2.8%)

localize35.0ms (0.4%)

series162.0ms (1.8%)

rewrite77.0ms (0.9%)

simplify372.0ms (4.1%)

prune515.0ms (5.7%)

localize25.0ms (0.3%)

series301.0ms (3.3%)

rewrite133.0ms (1.5%)

simplify352.0ms (3.9%)

prune779.0ms (8.6%)

localize16.0ms (0.2%)

series495.0ms (5.5%)

rewrite104.0ms (1.1%)

simplify317.0ms (3.5%)

prune595.0ms (6.6%)

regimes1.2s (13.4%)

simplify5.0ms (0.1%)

end149.0ms (1.6%)

Profiling