Details

analyze344.0ms (8.4%)

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
31.2%	68.6%	0.1%	7
40.6%	59.3%	0.1%	8
43.7%	56.2%	0.1%	9
56.6%	43.3%	0.1%	10
61%	37.3%	1.7%	11
62.1%	34.8%	3.1%	12
68.6%	25.6%	5.8%	13
70.6%	22.1%	7.4%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample251.0ms (6.1%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	44×	body	128	invalid

Compiler

Compiled 24 to 16 computations (33.3% saved)

simplify31.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

377×	`fma-neg_binary64`
309×	`fma-def_binary64`
112×	`cancel-sign-sub-inv_binary64`
77×	`distribute-rgt-in_binary64`
56×	`unsub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	42	10
4	80	10
5	138	10
6	302	10
7	420	10
8	581	10
9	647	10
10	718	10
11	740	10
12	744	10
13	699	10

prune8.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 x (/.f64 (-.f64 y x) z))

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series25.0ms (0.6%)

Counts

2 → 64

Calls

2 calls:

13.0ms	(/.f64 (-.f64 y x) z)
11.0ms	(+.f64 x (/.f64 (-.f64 y x) z))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`
5×	`associate-/l*_binary64`

Counts

2 → 58

Calls

2 calls:

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

simplify83.0ms (2%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-neg_binary64`
599×	`times-frac_binary64`
572×	`associate-/l*_binary64`
274×	`div-sub_binary64`
243×	`distribute-rgt-in_binary64`

Counts

122 → 74

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	1378
1	273	1269
2	636	1260
3	1893	1260
4	4435	1260
5	5003	1260

prune41.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	71	4	75

Error

Counts

75 → 4

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 x (/.f64 (-.f64 y x) z))
▶	24.1b	(*.f64 (-.f64 1 (/.f64 1 z)) x)
	55.8b	(+.f64 x (*.f64 (/.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z)) (/.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z))))
	40.7b	(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (/.f64 (-.f64 y x) z) 3)) (+.f64 (.f64 x x) (-.f64 (.f64 (/.f64 (-.f64 y x) z) (/.f64 (-.f64 y x) z)) (*.f64 x (/.f64 (-.f64 y x) z)))))

Compiler

Compiled 1131 to 354 computations (68.7% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (/.f64 1 z))
✓	0.1b	(*.f64 (-.f64 1 (/.f64 1 z)) x)

series8.0ms (0.2%)

Counts

2 → 15

Calls

2 calls:

7.0ms	(*.f64 (-.f64 1 (/.f64 1 z)) x)
1.0ms	(-.f64 1 (/.f64 1 z))

rewrite23.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`add-sqr-sqrt_binary64`
62×	`*-un-lft-identity_binary64`
46×	`add-cube-cbrt_binary64`
44×	`times-frac_binary64`
39×	`prod-diff_binary64`

Counts

2 → 106

Calls

2 calls:

8.0ms	(-.f64 1 (/.f64 1 z))
8.0ms	(*.f64 (-.f64 1 (/.f64 1 z)) x)

simplify82.0ms (2%)

Algorithm

1×	egg-herbie

Rules

811×	`unsub-neg_binary64`
374×	`associate-l_binary64`
324×	`fma-neg_binary64`
291×	`associate-/l*_binary64`
260×	`associate-r_binary64`

Counts

121 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1494
1	225	1313
2	607	1038
3	1890	1025
4	3974	1025
5	5325	1025

prune89.0ms (2.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	140	4	144

Error

Counts

144 → 4

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 x (/.f64 (-.f64 y x) z))
✓	24.1b	(*.f64 (-.f64 1 (/.f64 1 z)) x)
	55.8b	(+.f64 x (*.f64 (/.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z)) (/.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z))))
▶	40.7b	(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (/.f64 (-.f64 y x) z) 3)) (+.f64 (.f64 x x) (-.f64 (.f64 (/.f64 (-.f64 y x) z) (/.f64 (-.f64 y x) z)) (*.f64 x (/.f64 (-.f64 y x) z)))))

Compiler

Compiled 3105 to 2214 computations (28.7% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.6b	(+.f64 (.f64 x x) (-.f64 (.f64 (/.f64 (-.f64 y x) z) (/.f64 (-.f64 y x) z)) (*.f64 x (/.f64 (-.f64 y x) z))))
✓	3.9b	(-.f64 (.f64 (/.f64 (-.f64 y x) z) (/.f64 (-.f64 y x) z)) (.f64 x (/.f64 (-.f64 y x) z)))
✓	4.8b	(+.f64 (pow.f64 x 3) (pow.f64 (/.f64 (-.f64 y x) z) 3))
✓	39.4b	(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (/.f64 (-.f64 y x) z) 3)) (+.f64 (.f64 x x) (-.f64 (.f64 (/.f64 (-.f64 y x) z) (/.f64 (-.f64 y x) z)) (*.f64 x (/.f64 (-.f64 y x) z)))))

series820.0ms (20%)

Counts

4 → 144

Calls

4 calls:

594.0ms	(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (/.f64 (-.f64 y x) z) 3)) (+.f64 (.f64 x x) (-.f64 (.f64 (/.f64 (-.f64 y x) z) (/.f64 (-.f64 y x) z)) (*.f64 x (/.f64 (-.f64 y x) z)))))
79.0ms	(+.f64 (.f64 x x) (-.f64 (.f64 (/.f64 (-.f64 y x) z) (/.f64 (-.f64 y x) z)) (*.f64 x (/.f64 (-.f64 y x) z))))
77.0ms	(-.f64 (.f64 (/.f64 (-.f64 y x) z) (/.f64 (-.f64 y x) z)) (.f64 x (/.f64 (-.f64 y x) z)))
69.0ms	(+.f64 (pow.f64 x 3) (pow.f64 (/.f64 (-.f64 y x) z) 3))

rewrite112.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`*-un-lft-identity_binary64`
27×	`times-frac_binary64`
25×	`distribute-lft-out_binary64`
23×	`cube-prod_binary64`
23×	`unpow-prod-down_binary64`

Counts

4 → 129

Calls

4 calls:

40.0ms	(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (/.f64 (-.f64 y x) z) 3)) (+.f64 (.f64 x x) (-.f64 (.f64 (/.f64 (-.f64 y x) z) (/.f64 (-.f64 y x) z)) (*.f64 x (/.f64 (-.f64 y x) z)))))
31.0ms	(+.f64 (pow.f64 x 3) (pow.f64 (/.f64 (-.f64 y x) z) 3))
14.0ms	(+.f64 (.f64 x x) (-.f64 (.f64 (/.f64 (-.f64 y x) z) (/.f64 (-.f64 y x) z)) (*.f64 x (/.f64 (-.f64 y x) z))))
9.0ms	(-.f64 (.f64 (/.f64 (-.f64 y x) z) (/.f64 (-.f64 y x) z)) (.f64 x (/.f64 (-.f64 y x) z)))

simplify258.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

686×	`associate-/l*_binary64`
641×	`fma-def_binary64`
237×	`+-commutative_binary64`
227×	`*-commutative_binary64`
190×	`associate-+r+_binary64`

Counts

273 → 256

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	806	18874
1	2701	17892
2	5708	17892

prune326.0ms (8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	256	4	260

Error

Counts

260 → 4

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 x (/.f64 (-.f64 y x) z))
✓	24.1b	(*.f64 (-.f64 1 (/.f64 1 z)) x)
▶	55.8b	(+.f64 x (*.f64 (/.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z)) (/.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z))))
✓	40.7b	(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (/.f64 (-.f64 y x) z) 3)) (+.f64 (.f64 x x) (-.f64 (.f64 (/.f64 (-.f64 y x) z) (/.f64 (-.f64 y x) z)) (*.f64 x (/.f64 (-.f64 y x) z)))))

Compiler

Compiled 22503 to 10323 computations (54.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (/.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z)) (/.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z))))
✓	0.0b	(/.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z))
✓	0.1b	(/.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z))
✓	0.1b	(*.f64 (/.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z)) (/.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z)))

series415.0ms (10.1%)

Counts

4 → 39

Calls

4 calls:

288.0ms	(/.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z))
58.0ms	(*.f64 (/.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z)) (/.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z)))
42.0ms	(/.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z))
27.0ms	(+.f64 x (*.f64 (/.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z)) (/.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z))))

rewrite96.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

227×	`add-sqr-sqrt_binary64`
200×	`sqrt-prod_binary64`
197×	`*-un-lft-identity_binary64`
180×	`times-frac_binary64`
93×	`add-cube-cbrt_binary64`

Counts

4 → 282

Calls

4 calls:

39.0ms	(*.f64 (/.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z)) (/.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z)))
8.0ms	(/.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z))
6.0ms	(/.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z))
4.0ms	(+.f64 x (*.f64 (/.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z)) (/.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z))))

simplify170.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

600×	`distribute-rgt-in_binary64`
581×	`distribute-lft-in_binary64`
353×	`fma-def_binary64`
283×	`times-frac_binary64`
163×	`associate-*r/_binary64`

Counts

321 → 283

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	234	8557
1	641	7098
2	1988	7096
3	5429	7096

prune83.0ms (2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	283	0	283
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	283	4	287

Error

Counts

287 → 4

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 x (/.f64 (-.f64 y x) z))
✓	24.1b	(*.f64 (-.f64 1 (/.f64 1 z)) x)
✓	55.8b	(+.f64 x (*.f64 (/.f64 (+.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z)) (/.f64 (-.f64 (sqrt.f64 y) (sqrt.f64 x)) (sqrt.f64 z))))
✓	40.7b	(/.f64 (+.f64 (pow.f64 x 3) (pow.f64 (/.f64 (-.f64 y x) z) 3)) (+.f64 (.f64 x x) (-.f64 (.f64 (/.f64 (-.f64 y x) z) (/.f64 (-.f64 y x) z)) (*.f64 x (/.f64 (-.f64 y x) z)))))

Compiler

Compiled 7966 to 1278 computations (84% saved)

regimes133.0ms (3.2%)

Accuracy

Total 0.0b remaining (23.7%)

Threshold costs 0.0b (23.7%)

Counts

21 → 1

Compiler

Compiled 1568 to 830 computations (47.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`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	7	10
1	10	10
2	15	10
3	17	10
4	18	10
5	18	10

end0.0ms (0%)

Compiler: Compiled 10 to 6 computations (40% saved)

sample649.0ms (15.8%)

Algorithm

1×

intervals

Results

261.0ms	8000×	body	128	valid
47.0ms	1348×	body	128	invalid

Compiler

Compiled 104 to 58 computations (44.2% saved)

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	42	10
4	80	10
5	138	10
6	302	10
7	420	10
8	581	10
9	647	10
10	718	10
11	740	10
12	744	10
13	699	10

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	42	10
4	80	10
5	138	10
6	302	10
7	420	10
8	581	10
9	647	10
10	718	10
11	740	10
12	744	10
13	699	10

Details

analyze344.0ms (8.4%)

sample251.0ms (6.1%)

simplify31.0ms (0.7%)

prune8.0ms (0.2%)

localize5.0ms (0.1%)

series25.0ms (0.6%)

rewrite14.0ms (0.3%)

simplify83.0ms (2%)

prune41.0ms (1%)

localize4.0ms (0.1%)

series8.0ms (0.2%)

rewrite23.0ms (0.6%)

simplify82.0ms (2%)

prune89.0ms (2.2%)

localize18.0ms (0.4%)

series820.0ms (20%)

rewrite112.0ms (2.7%)

simplify258.0ms (6.3%)

prune326.0ms (8%)

localize10.0ms (0.2%)

series415.0ms (10.1%)

rewrite96.0ms (2.4%)

simplify170.0ms (4.2%)

prune83.0ms (2%)

regimes133.0ms (3.2%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample649.0ms (15.8%)

Profiling

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	42	10
4	80	10
5	138	10
6	302	10
7	420	10
8	581	10
9	647	10
10	718	10
11	740	10
12	744	10
13	699	10