Details

analyze635.0ms (8.2%)

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)

sample1.2s (15.9%)

Results

1.1s	8255×	body	128	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify182.0ms (2.3%)

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

prune5.0ms (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

1.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.0b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

Compiler

Compiled 56 to 29 computations (48.2% saved)

localize14.0ms (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)

series122.0ms (1.6%)

Counts

2 → 96

Calls

2 calls:

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

rewrite15.0ms (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:

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

simplify163.0ms (2.1%)

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

prune144.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	133	5	138
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	133	6	139

Error

0.0b

Counts

139 → 6

Alt Table

Status	Error	Program
	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)
	11.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
	3.6b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	1.0b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	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 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

Compiler

Compiled 3461 to 1168 computations (66.3% saved)

localize14.0ms (0.2%)

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)

series138.0ms (1.8%)

Counts

3 → 132

Calls

3 calls:

73.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
34.0ms	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))
30.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

rewrite70.0ms (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:

20.0ms	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))
7.0ms	(/.f64 (-.f64 a t) (-.f64 z t))
1.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

simplify200.0ms (2.6%)

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

prune467.0ms (6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	335	2	337
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	337	6	343

Error

0.0b

Counts

343 → 6

Alt Table

Status	Error	Program
▶	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)
	11.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
	3.6b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	1.0b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	1.5b	(fma.f64 y (/.f64 1 (-.f64 (/.f64 a (-.f64 z t)) (/.f64 t (-.f64 z t)))) x)
	31.2b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)) (sqrt.f64 (fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)))

Compiler

Compiled 8747 to 2819 computations (67.8% 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)

series198.0ms (2.5%)

Counts

4 → 144

Calls

4 calls:

75.0ms	(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)
50.0ms	(cbrt.f64 (-.f64 a t))
41.0ms	(*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))
31.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t))))

rewrite72.0ms (0.9%)

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:

35.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t))))
9.0ms	(*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))
2.0ms	(cbrt.f64 (-.f64 a t))
0.0ms	(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)

simplify310.0ms (4%)

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

prune768.0ms (9.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	477	0	477
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	477	6	483

Error

0.0b

Counts

483 → 6

Alt Table

Status	Error	Program
✓	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)
	11.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
	3.6b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	1.0b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
▶	1.5b	(fma.f64 y (/.f64 1 (-.f64 (/.f64 a (-.f64 z t)) (/.f64 t (-.f64 z t)))) x)
	31.2b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)) (sqrt.f64 (fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)))

Compiler

Compiled 16977 to 5856 computations (65.5% saved)

localize27.0ms (0.3%)

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)

series386.0ms (5%)

Counts

4 → 144

Calls

4 calls:

235.0ms	(fma.f64 y (/.f64 1 (-.f64 (/.f64 a (-.f64 z t)) (/.f64 t (-.f64 z t)))) x)
123.0ms	(/.f64 1 (-.f64 (/.f64 a (-.f64 z t)) (/.f64 t (-.f64 z t))))
18.0ms	(/.f64 a (-.f64 z t))
10.0ms	(/.f64 t (-.f64 z t))

rewrite89.0ms (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:

30.0ms	(/.f64 1 (-.f64 (/.f64 a (-.f64 z t)) (/.f64 t (-.f64 z t))))
10.0ms	(/.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)

simplify274.0ms (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

prune599.0ms (7.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	342	1	343
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	344	5	349

Error

Counts

349 → 5

Alt Table

Status	Error	Program
✓	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)
	11.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
	1.5b	(+.f64 (/.f64 y (-.f64 (/.f64 a (-.f64 z t)) (/.f64 t (-.f64 z t)))) x)
✓	1.0b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	3.6b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))

Compiler

Compiled 13524 to 5398 computations (60.1% saved)

regimes1.5s (19.9%)

Accuracy

Total 1.2b remaining (99.5%)

Threshold costs 0b (0%)

Counts

126 → 1

Compiler

Compiled 20056 to 12298 computations (38.7% saved)

simplify7.0ms (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

end70.0ms (0.9%)

Compiler: Compiled 131 to 74 computations (43.5% saved)

Details

analyze635.0ms (8.2%)

sample1.2s (15.9%)

simplify182.0ms (2.3%)

prune5.0ms (0.1%)

localize14.0ms (0.2%)

series122.0ms (1.6%)

rewrite15.0ms (0.2%)

simplify163.0ms (2.1%)

prune144.0ms (1.9%)

localize14.0ms (0.2%)

series138.0ms (1.8%)

rewrite70.0ms (0.9%)

simplify200.0ms (2.6%)

prune467.0ms (6%)

localize25.0ms (0.3%)

series198.0ms (2.5%)

rewrite72.0ms (0.9%)

simplify310.0ms (4%)

prune768.0ms (9.9%)

localize27.0ms (0.3%)

series386.0ms (5%)

rewrite89.0ms (1.1%)

simplify274.0ms (3.5%)

prune599.0ms (7.7%)

regimes1.5s (19.9%)

simplify7.0ms (0.1%)

end70.0ms (0.9%)

Profiling