Details

analyze905.0ms (10.8%)

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
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
23.4%	74.9%	1.8%	11
27.3%	69%	3.7%	12
36.6%	56.5%	6.8%	13
40.5%	52%	7.4%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.3s (14.9%)

Symmetry

(sort y t)

Results

898.0ms	8256×	body	128	valid
203.0ms	1936×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify39.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

998×	`fma-def_binary64`
304×	`fma-neg_binary64`
112×	`distribute-rgt-in_binary64`
90×	`associate-l_binary64`
87×	`associate-r_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	20	10
2	43	10
3	96	10
4	172	10
5	252	10
6	398	10
7	581	10
8	846	10
9	910	10
10	943	10
11	949	10
12	949	10
13	886	10

prune3.0ms (0%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	6.0b	(.f64 y (.f64 t (-.f64 x z)))
▶	4.0b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

Compiler

Compiled 68 to 41 computations (39.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x y) (.f64 z y))
✓	3.9b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

series23.0ms (0.3%)

Counts

2 → 84

Calls

2 calls:

16.0ms	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
7.0ms	(-.f64 (.f64 x y) (.f64 z y))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`associate-l_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 40

Calls

2 calls:

5.0ms	(-.f64 (.f64 x y) (.f64 z y))
4.0ms	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

simplify75.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

919×	`fma-def_binary64`
443×	`neg-mul-1_binary64`
246×	`*-commutative_binary64`
223×	`fma-neg_binary64`
217×	`distribute-lft-neg-out_binary64`

Counts

124 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	1269
1	221	1209
2	783	1202
3	1981	1199
4	4246	1199
5	5104	1199

prune53.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	78	5	83
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	79	6	85

Error

Counts

85 → 6

Alt Table

Status	Error	Program
	8.4b	(.f64 (-.f64 x z) (.f64 y t))
	5.1b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z y))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z y)))) (.f64 t (cbrt.f64 (.f64 y (-.f64 x z)))))
	6.0b	(-.f64 (.f64 y (.f64 t x)) (.f64 y (.f64 t z)))
✓	4.0b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
▶	4.9b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) t)) (cbrt.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) t))) (cbrt.f64 (.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)))
	34.3b	(cbrt.f64 (.f64 (.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) t) (.f64 (-.f64 (.f64 x y) (.f64 z y)) t)) (.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)))

Compiler

Compiled 1450 to 366 computations (74.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) t)) (cbrt.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) t))) (cbrt.f64 (.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)))
✓	0.4b	(.f64 (cbrt.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) t)) (cbrt.f64 (.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)))
	3.9b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
✓	7.7b	(cbrt.f64 (.f64 (-.f64 (.f64 x y) (*.f64 z y)) t))

series1.7s (20.2%)

Counts

3 → 144

Calls

3 calls:

1.1s

(*.f64 (cbrt.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t)) (cbrt.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t)))

545.0ms

(cbrt.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t))

39.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t)) (cbrt.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t))) (cbrt.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t)))

rewrite45.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`associate-*l/_binary64`
68×	`cbrt-div_binary64`
34×	`flip--_binary64`
34×	`flip3--_binary64`
32×	`frac-times_binary64`

Counts

3 → 115

Calls

3 calls:

9.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t)) (cbrt.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t))) (cbrt.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t)))

8.0ms

(cbrt.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t))

5.0ms

(*.f64 (cbrt.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t)) (cbrt.f64 (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t)))

simplify214.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

363×	`associate-r_binary64`
344×	`associate-l_binary64`
268×	`fma-neg_binary64`
258×	`*-commutative_binary64`
204×	`fma-def_binary64`

Counts

259 → 291

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	491	9131
1	1357	8772
2	4494	8274
3	5090	8274

prune346.0ms (4.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	595	0	595
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	595	6	601

Error

Counts

601 → 6

Alt Table

Status	Error	Program
	8.4b	(.f64 (-.f64 x z) (.f64 y t))
▶	5.1b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z y))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z y)))) (.f64 t (cbrt.f64 (.f64 y (-.f64 x z)))))
	6.0b	(-.f64 (.f64 y (.f64 t x)) (.f64 y (.f64 t z)))
✓	4.0b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
✓	4.9b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) t)) (cbrt.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) t))) (cbrt.f64 (.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)))
	34.3b	(cbrt.f64 (.f64 (.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) t) (.f64 (-.f64 (.f64 x y) (.f64 z y)) t)) (.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)))

Compiler

Compiled 28309 to 6767 computations (76.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 t (cbrt.f64 (.f64 y (-.f64 x z))))
✓	0.4b	(.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z y))) (cbrt.f64 (-.f64 (.f64 x y) (*.f64 z y))))
✓	6.0b	(cbrt.f64 (*.f64 y (-.f64 x z)))
✓	6.0b	(cbrt.f64 (-.f64 (.f64 x y) (.f64 z y)))

series1.3s (15.4%)

Counts

4 → 156

Calls

4 calls:

579.0ms	(.f64 t (cbrt.f64 (.f64 y (-.f64 x z))))
310.0ms	(.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z y))) (cbrt.f64 (-.f64 (.f64 x y) (*.f64 z y))))
206.0ms	(cbrt.f64 (-.f64 (.f64 x y) (.f64 z y)))
199.0ms	(cbrt.f64 (*.f64 y (-.f64 x z)))

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`cbrt-prod_binary64`
25×	`add-sqr-sqrt_binary64`
18×	`cbrt-div_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`

Counts

4 → 105

Calls

4 calls:

9.0ms	(.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z y))) (cbrt.f64 (-.f64 (.f64 x y) (*.f64 z y))))
3.0ms	(.f64 t (cbrt.f64 (.f64 y (-.f64 x z))))
3.0ms	(cbrt.f64 (*.f64 y (-.f64 x z)))
3.0ms	(cbrt.f64 (-.f64 (.f64 x y) (.f64 z y)))

simplify147.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

584×	`associate-r_binary64`
417×	`associate-l_binary64`
284×	`fma-def_binary64`
250×	`times-frac_binary64`
208×	`*-commutative_binary64`

Counts

261 → 311

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	578	8934
1	1583	8319
2	5422	8319

prune262.0ms (3.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	389	0	389
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	389	6	395

Error

Counts

395 → 6

Alt Table

Status	Error	Program
	8.4b	(.f64 (-.f64 x z) (.f64 y t))
✓	5.1b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z y))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z y)))) (.f64 t (cbrt.f64 (.f64 y (-.f64 x z)))))
▶	6.0b	(-.f64 (.f64 y (.f64 t x)) (.f64 y (.f64 t z)))
✓	4.0b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
✓	4.9b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) t)) (cbrt.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) t))) (cbrt.f64 (.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)))
	34.3b	(cbrt.f64 (.f64 (.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) t) (.f64 (-.f64 (.f64 x y) (.f64 z y)) t)) (.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)))

Compiler

Compiled 17291 to 6130 computations (64.5% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 y (.f64 t x)) (.f64 y (.f64 t z)))
✓	4.5b	(.f64 y (.f64 t x))
✓	5.1b	(.f64 y (.f64 t z))

series43.0ms (0.5%)

Counts

3 → 30

Calls

3 calls:

25.0ms	(-.f64 (.f64 y (.f64 t x)) (.f64 y (.f64 t z)))
10.0ms	(.f64 y (.f64 t x))
8.0ms	(.f64 y (.f64 t z))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
13×	`pow1_binary64`
6×	`associate-l_binary64`
6×	`cbrt-unprod_binary64`

Counts

3 → 57

Calls

3 calls:

4.0ms	(-.f64 (.f64 y (.f64 t x)) (.f64 y (.f64 t z)))
4.0ms	(.f64 y (.f64 t z))
3.0ms	(.f64 y (.f64 t x))

simplify70.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

623×	`fma-neg_binary64`
456×	`cancel-sign-sub-inv_binary64`
405×	`fma-def_binary64`
402×	`*-commutative_binary64`
367×	`distribute-rgt-neg-in_binary64`

Counts

87 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	106	950
1	285	914
2	967	898
3	2492	898
4	4590	898
5	4892	898

prune66.0ms (0.8%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	1	2
Picked	0	1	1
Done	0	3	3
Total	97	6	103

Error

Counts

103 → 6

Alt Table

Status	Error	Program
	8.4b	(.f64 (-.f64 x z) (.f64 y t))
✓	5.1b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 x y) (.f64 z y))) (cbrt.f64 (-.f64 (.f64 x y) (.f64 z y)))) (.f64 t (cbrt.f64 (.f64 y (-.f64 x z)))))
✓	6.0b	(-.f64 (.f64 y (.f64 t x)) (.f64 y (.f64 t z)))
✓	4.0b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
✓	4.9b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) t)) (cbrt.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) t))) (cbrt.f64 (.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)))
	20.2b	(-.f64 (.f64 y (.f64 t x)) (cbrt.f64 (.f64 (.f64 (.f64 y (.f64 t z)) (.f64 y (.f64 t z))) (.f64 y (.f64 t z)))))

Compiler

Compiled 1657 to 385 computations (76.8% saved)

regimes1.5s (18.4%)

Accuracy

Total 1.2b remaining (97%)

Threshold costs 0b (0%)

Counts

120 → 5

Compiler

Compiled 18142 to 9544 computations (47.4% saved)

bsearch4.0ms (0%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	134
1	48	134
2	66	134
3	76	134
4	82	134
5	83	134
6	83	134

end224.0ms (2.7%)

Compiler: Compiled 513 to 169 computations (67.1% saved)

Iter	Nodes	Cost
0	9	10
1	20	10
2	43	10
3	96	10
4	172	10
5	252	10
6	398	10
7	581	10
8	846	10
9	910	10
10	943	10
11	949	10
12	949	10
13	886	10

Iter	Nodes	Cost
0	9	10
1	20	10
2	43	10
3	96	10
4	172	10
5	252	10
6	398	10
7	581	10
8	846	10
9	910	10
10	943	10
11	949	10
12	949	10
13	886	10

Details

analyze905.0ms (10.8%)

sample1.3s (14.9%)

simplify39.0ms (0.5%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series23.0ms (0.3%)

rewrite11.0ms (0.1%)

simplify75.0ms (0.9%)

prune53.0ms (0.6%)

localize9.0ms (0.1%)

series1.7s (20.2%)

rewrite45.0ms (0.5%)

simplify214.0ms (2.6%)

prune346.0ms (4.1%)

localize12.0ms (0.1%)

series1.3s (15.4%)

rewrite27.0ms (0.3%)

simplify147.0ms (1.8%)

prune262.0ms (3.1%)

localize7.0ms (0.1%)

series43.0ms (0.5%)

rewrite13.0ms (0.2%)

simplify70.0ms (0.8%)

prune66.0ms (0.8%)

regimes1.5s (18.4%)

bsearch4.0ms (0%)

simplify6.0ms (0.1%)

end224.0ms (2.7%)

Profiling

Iter	Nodes	Cost
0	9	10
1	20	10
2	43	10
3	96	10
4	172	10
5	252	10
6	398	10
7	581	10
8	846	10
9	910	10
10	943	10
11	949	10
12	949	10
13	886	10