Details

analyze2.1s (20.3%)

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
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%	69.4%	3.3%	12
36.6%	56.5%	6.8%	13
40.5%	52%	7.4%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample77.0ms (0.7%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
5.0ms	82×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify52.0ms (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

prune6.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	7.9b	(.f64 y (.f64 t (-.f64 x z)))
▶	5.5b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

Compiler

Compiled 68 to 41 computations (39.7% saved)

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(-.f64 (.f64 x y) (.f64 z y))
✓	5.3b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

series51.0ms (0.5%)

Counts

2 → 84

Calls

2 calls:

37.0ms	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
14.0ms	(-.f64 (.f64 x y) (.f64 z y))

rewrite19.0ms (0.2%)

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:

10.0ms	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
5.0ms	(-.f64 (.f64 x y) (.f64 z y))

simplify128.0ms (1.2%)

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

prune103.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	78	5	83
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	78	7	85

Error

0.0b

Counts

85 → 7

Alt Table

Status	Error	Program
	6.4b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
✓	5.5b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
▶	6.4b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (-.f64 x z))) (cbrt.f64 (.f64 y (-.f64 x z)))) (cbrt.f64 (.f64 y (-.f64 x z)))) t)
	21.5b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (sqrt.f64 t)) (sqrt.f64 t))
	7.9b	(.f64 y (.f64 t (-.f64 x z)))
	6.5b	(.f64 (-.f64 x z) (.f64 y t))
	27.4b	(/.f64 (.f64 (-.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (.f64 z y) (.f64 z y))) t) (+.f64 (.f64 x y) (*.f64 z y)))

Compiler

Compiled 1426 to 376 computations (73.6% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 y (-.f64 x z))) (cbrt.f64 (.f64 y (-.f64 x z)))) (cbrt.f64 (*.f64 y (-.f64 x z))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 y (-.f64 x z))) (cbrt.f64 (*.f64 y (-.f64 x z))))
✓	5.3b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (-.f64 x z))) (cbrt.f64 (.f64 y (-.f64 x z)))) (cbrt.f64 (.f64 y (-.f64 x z)))) t)
✓	7.2b	(cbrt.f64 (*.f64 y (-.f64 x z)))

series1.4s (12.9%)

Counts

4 → 156

Calls

4 calls:

699.0ms	(.f64 (cbrt.f64 (.f64 y (-.f64 x z))) (cbrt.f64 (*.f64 y (-.f64 x z))))
510.0ms	(cbrt.f64 (*.f64 y (-.f64 x z)))
76.0ms	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (-.f64 x z))) (cbrt.f64 (.f64 y (-.f64 x z)))) (cbrt.f64 (.f64 y (-.f64 x z)))) t)
64.0ms	(.f64 (.f64 (cbrt.f64 (.f64 y (-.f64 x z))) (cbrt.f64 (.f64 y (-.f64 x z)))) (cbrt.f64 (*.f64 y (-.f64 x z))))

rewrite135.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`associate-*r/_binary64`
122×	`cbrt-div_binary64`
61×	`flip--_binary64`
61×	`flip3--_binary64`
60×	`frac-times_binary64`

Counts

4 → 164

Calls

4 calls:

34.0ms	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (-.f64 x z))) (cbrt.f64 (.f64 y (-.f64 x z)))) (cbrt.f64 (.f64 y (-.f64 x z)))) t)
21.0ms	(.f64 (.f64 (cbrt.f64 (.f64 y (-.f64 x z))) (cbrt.f64 (.f64 y (-.f64 x z)))) (cbrt.f64 (*.f64 y (-.f64 x z))))
11.0ms	(.f64 (cbrt.f64 (.f64 y (-.f64 x z))) (cbrt.f64 (*.f64 y (-.f64 x z))))
8.0ms	(cbrt.f64 (*.f64 y (-.f64 x z)))

simplify343.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

463×	`associate-l_binary64`
421×	`associate-r_binary64`
288×	`*-commutative_binary64`
200×	`fma-neg_binary64`
168×	`fma-def_binary64`

Counts

320 → 354

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	496	8541
1	1256	8047
2	4427	7657
3	4964	7657

prune604.0ms (5.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	498	2	500
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	499	8	507

Error

0.0b

Counts

507 → 8

Alt Table

Status	Error	Program
▶	6.4b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
✓	5.5b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
✓	6.4b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (-.f64 x z))) (cbrt.f64 (.f64 y (-.f64 x z)))) (cbrt.f64 (.f64 y (-.f64 x z)))) t)
	6.7b	(.f64 (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (.f64 y (-.f64 x z))) (cbrt.f64 (.f64 y (-.f64 x z))))) (cbrt.f64 (.f64 (cbrt.f64 (.f64 y (-.f64 x z))) (cbrt.f64 (.f64 y (-.f64 x z)))))) (cbrt.f64 (.f64 (cbrt.f64 (.f64 y (-.f64 x z))) (cbrt.f64 (.f64 y (-.f64 x z)))))) (cbrt.f64 (.f64 y (-.f64 x z)))) t)
	21.5b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (sqrt.f64 t)) (sqrt.f64 t))
	7.9b	(.f64 y (.f64 t (-.f64 x z)))
	30.0b	(.f64 (/.f64 (.f64 y (-.f64 (.f64 x x) (.f64 z z))) (+.f64 x z)) t)
	6.5b	(.f64 (-.f64 x z) (.f64 y t))

Compiler

Compiled 19489 to 6854 computations (64.8% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
✓	0.6b	(cbrt.f64 t)
✓	1.7b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
✓	3.9b	(.f64 (-.f64 (.f64 x y) (.f64 z y)) (.f64 (cbrt.f64 t) (cbrt.f64 t)))

series1.2s (11.1%)

Counts

4 → 120

Calls

4 calls:

971.0ms	(.f64 (-.f64 (.f64 x y) (.f64 z y)) (.f64 (cbrt.f64 t) (cbrt.f64 t)))
76.0ms	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
59.0ms	(cbrt.f64 t)
57.0ms	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))

rewrite67.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
22×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 107

Calls

4 calls:

21.0ms	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
21.0ms	(.f64 (-.f64 (.f64 x y) (.f64 z y)) (.f64 (cbrt.f64 t) (cbrt.f64 t)))
11.0ms	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
1.0ms	(cbrt.f64 t)

simplify218.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

357×	`distribute-rgt-in_binary64`
340×	`distribute-lft-in_binary64`
310×	`associate-r_binary64`
310×	`associate-l_binary64`
279×	`exp-prod_binary64`

Counts

227 → 176

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	155	2920
1	388	2569
2	1536	2412
3	3785	2384
4	4943	2384
5	4948	2384

prune203.0ms (1.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	210	2	212
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	211	9	220

Error

0.0b

Counts

220 → 9

Alt Table

Status	Error	Program
✓	6.4b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (-.f64 x z))) (cbrt.f64 (.f64 y (-.f64 x z)))) (cbrt.f64 (.f64 y (-.f64 x z)))) t)
	21.7b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (*.f64 (sqrt.f64 (cbrt.f64 t)) (sqrt.f64 t))) (cbrt.f64 t))
✓	6.4b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))
✓	5.5b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
	6.7b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)))) (cbrt.f64 (*.f64 (cbrt.f64 t) (cbrt.f64 t))))) (cbrt.f64 t))
	21.5b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (sqrt.f64 t)) (sqrt.f64 t))
	7.9b	(.f64 y (.f64 t (-.f64 x z)))
	30.0b	(.f64 (/.f64 (.f64 y (-.f64 (.f64 x x) (.f64 z z))) (+.f64 x z)) t)
▶	6.5b	(.f64 (-.f64 x z) (.f64 y t))

Compiler

Compiled 4628 to 1118 computations (75.8% saved)

localize11.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.3b	(.f64 (-.f64 x z) (.f64 y t))

series30.0ms (0.3%)

Counts

1 → 32

Calls

1 calls:

30.0ms

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

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
5×	`associate-l_binary64`
4×	`*-un-lft-identity_binary64`

Counts

1 → 24

Calls

1 calls:

14.0ms

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

simplify83.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

568×	`associate-l_binary64`
483×	`fma-def_binary64`
414×	`associate-r_binary64`
378×	`distribute-rgt-neg-out_binary64`
327×	`unsub-neg_binary64`

Counts

56 → 42

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	66	661
1	178	598
2	527	598
3	1835	598
4	3260	598
5	5376	598

prune45.0ms (0.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	1	4	5
Picked	0	1	1
Done	1	2	3
Total	42	9	51

Error

Counts

51 → 9

Alt Table

Status	Error	Program
✓	6.4b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (-.f64 x z))) (cbrt.f64 (.f64 y (-.f64 x z)))) (cbrt.f64 (.f64 y (-.f64 x z)))) t)
	21.7b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (*.f64 (sqrt.f64 (cbrt.f64 t)) (sqrt.f64 t))) (cbrt.f64 t))
	6.7b	(.f64 (.f64 (-.f64 (.f64 x y) (.f64 z y)) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)))) (cbrt.f64 (*.f64 (cbrt.f64 t) (cbrt.f64 t))))) (cbrt.f64 t))
	7.9b	(.f64 y (.f64 t (-.f64 x z)))
✓	5.5b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
	30.0b	(.f64 (/.f64 (.f64 y (-.f64 (.f64 x x) (.f64 z z))) (+.f64 x z)) t)
✓	6.5b	(.f64 (-.f64 x z) (.f64 y t))
	50.0b	(.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 z)) (.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 z)) (*.f64 y t)))
	38.2b	(.f64 (sqrt.f64 (-.f64 x z)) (.f64 (sqrt.f64 (-.f64 x z)) (*.f64 y t)))

Compiler

Compiled 716 to 226 computations (68.4% saved)

regimes1.6s (15%)

Accuracy

Total 0.3b remaining (90.4%)

Threshold costs 0.3b (90.4%)

Counts

67 → 5

Compiler

Compiled 8611 to 4495 computations (47.8% saved)

bsearch4.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	110
1	42	110
2	53	110
3	59	110
4	63	110
5	64	110
6	64	110

end14.0ms (0.1%)

Compiler: Compiled 237 to 78 computations (67.1% saved)

sample2.0s (19.1%)

Algorithm

1×

intervals

Results

581.0ms	8000×	body	128	valid
139.0ms	1929×	body	128	invalid

Compiler

Compiled 269 to 129 computations (52% 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

analyze2.1s (20.3%)

sample77.0ms (0.7%)

simplify52.0ms (0.5%)

prune6.0ms (0.1%)

localize12.0ms (0.1%)

series51.0ms (0.5%)

rewrite19.0ms (0.2%)

simplify128.0ms (1.2%)

prune103.0ms (1%)

localize17.0ms (0.2%)

series1.4s (12.9%)

rewrite135.0ms (1.3%)

simplify343.0ms (3.3%)

prune604.0ms (5.8%)

localize19.0ms (0.2%)

series1.2s (11.1%)

rewrite67.0ms (0.6%)

simplify218.0ms (2.1%)

prune203.0ms (1.9%)

localize11.0ms (0.1%)

series30.0ms (0.3%)

rewrite17.0ms (0.2%)

simplify83.0ms (0.8%)

prune45.0ms (0.4%)

regimes1.6s (15%)

bsearch4.0ms (0%)

simplify12.0ms (0.1%)

end14.0ms (0.1%)

sample2.0s (19.1%)

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