Details

analyze983.0ms (18.9%)

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)

sample152.0ms (2.9%)

Algorithm

1×

intervals

Symmetry

(sort y t)

Results

9.0ms	256×	body	128	valid
2.0ms	61×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify38.0ms (0.7%)

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 (0.1%)

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
▶	7.6b	(.f64 y (.f64 t (-.f64 x z)))
	7.8b	(.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 t (-.f64 x z))
✓	7.2b	(.f64 y (.f64 t (-.f64 x z)))

series19.0ms (0.4%)

Counts

2 → 84

Calls

2 calls:

13.0ms	(.f64 y (.f64 t (-.f64 x z)))
6.0ms	(*.f64 t (-.f64 x z))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`distribute-lft-in_binary64`
65×	`distribute-rgt-in_binary64`
54×	`prod-diff_binary64`
51×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`

Counts

2 → 124

Calls

2 calls:

8.0ms	(*.f64 t (-.f64 x z))
7.0ms	(.f64 y (.f64 t (-.f64 x z)))

simplify108.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

449×	`*-commutative_binary64`
402×	`distribute-rgt-in_binary64`
400×	`distribute-rgt-neg-out_binary64`
379×	`distribute-lft-in_binary64`
309×	`fma-def_binary64`

Counts

208 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	219	2765
1	326	2564
2	1079	2402
3	3077	2078
4	4965	2078
5	4751	2078

prune82.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	145	8	153
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	146	9	155

Error

0.0b

Counts

155 → 9

Alt Table

Status	Error	Program
	33.3b	(.f64 y (cbrt.f64 (pow.f64 (.f64 t (-.f64 x z)) 3)))
▶	4.3b	(.f64 (-.f64 x z) (.f64 y t))
✓	7.6b	(.f64 y (.f64 t (-.f64 x z)))
	6.9b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))
	37.5b	(.f64 y (.f64 (*.f64 t (sqrt.f64 (-.f64 x z))) (sqrt.f64 (-.f64 x z))))
	7.8b	(+.f64 (.f64 t (.f64 x y)) (neg.f64 (.f64 t (.f64 z y))))
	34.7b	(.f64 (sqrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (sqrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))
	8.6b	(.f64 (.f64 (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z))))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))))
	30.5b	(.f64 y (/.f64 (.f64 t (-.f64 (.f64 x x) (.f64 z z))) (+.f64 x z)))

Compiler

Compiled 3255 to 856 computations (73.7% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.3b	(.f64 (-.f64 x z) (.f64 y t))

series13.0ms (0.2%)

Counts

1 → 32

Calls

1 calls:

13.0ms

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

rewrite7.0ms (0.1%)

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:

5.0ms

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

simplify52.0ms (1%)

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

prune36.0ms (0.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	41	10	51

Error

0.0b

Counts

51 → 10

Alt Table

Status	Error	Program
	33.3b	(.f64 y (cbrt.f64 (pow.f64 (.f64 t (-.f64 x z)) 3)))
✓	4.3b	(.f64 (-.f64 x z) (.f64 y t))
✓	7.6b	(.f64 y (.f64 t (-.f64 x z)))
	6.9b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))
	37.5b	(.f64 y (.f64 (*.f64 t (sqrt.f64 (-.f64 x z))) (sqrt.f64 (-.f64 x z))))
	7.8b	(+.f64 (.f64 t (.f64 x y)) (neg.f64 (.f64 t (.f64 z y))))
	34.7b	(.f64 (sqrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (sqrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))
	8.6b	(.f64 (.f64 (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z))))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))))
▶	5.2b	(.f64 (.f64 (cbrt.f64 (-.f64 x z)) (cbrt.f64 (-.f64 x z))) (.f64 (cbrt.f64 (-.f64 x z)) (.f64 y t)))
	30.5b	(.f64 y (/.f64 (.f64 t (-.f64 (.f64 x x) (.f64 z z))) (+.f64 x z)))

Compiler

Compiled 880 to 308 computations (65% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 x z)) (cbrt.f64 (-.f64 x z)))
✓	0.6b	(cbrt.f64 (-.f64 x z))
✓	2.1b	(.f64 (cbrt.f64 (-.f64 x z)) (.f64 y t))
✓	2.4b	(.f64 (.f64 (cbrt.f64 (-.f64 x z)) (cbrt.f64 (-.f64 x z))) (.f64 (cbrt.f64 (-.f64 x z)) (.f64 y t)))

series662.0ms (12.8%)

Counts

4 → 144

Calls

4 calls:

564.0ms	(.f64 (cbrt.f64 (-.f64 x z)) (.f64 y t))
45.0ms	(*.f64 (cbrt.f64 (-.f64 x z)) (cbrt.f64 (-.f64 x z)))
30.0ms	(cbrt.f64 (-.f64 x z))
24.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 x z)) (cbrt.f64 (-.f64 x z))) (.f64 (cbrt.f64 (-.f64 x z)) (.f64 y t)))

rewrite110.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`cbrt-div_binary64`
38×	`cbrt-prod_binary64`
37×	`pow1_binary64`
36×	`associate-*l/_binary64`
35×	`flip--_binary64`

Counts

4 → 158

Calls

4 calls:

15.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 x z)) (cbrt.f64 (-.f64 x z))) (.f64 (cbrt.f64 (-.f64 x z)) (.f64 y t)))
8.0ms	(*.f64 (cbrt.f64 (-.f64 x z)) (cbrt.f64 (-.f64 x z)))
6.0ms	(.f64 (cbrt.f64 (-.f64 x z)) (.f64 y t))
2.0ms	(cbrt.f64 (-.f64 x z))

simplify158.0ms (3%)

Algorithm

1×	egg-herbie

Rules

796×	`associate-r_binary64`
659×	`associate-l_binary64`
409×	`fma-neg_binary64`
349×	`*-commutative_binary64`
194×	`fma-def_binary64`

Counts

302 → 300

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	421	7402
1	1206	6796
2	4363	6753
3	4966	6753

prune251.0ms (4.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	404	0	404
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	404	10	414

Error

0.0b

Counts

414 → 10

Alt Table

Status	Error	Program
	33.3b	(.f64 y (cbrt.f64 (pow.f64 (.f64 t (-.f64 x z)) 3)))
✓	4.3b	(.f64 (-.f64 x z) (.f64 y t))
✓	7.6b	(.f64 y (.f64 t (-.f64 x z)))
▶	6.9b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))
	37.5b	(.f64 y (.f64 (*.f64 t (sqrt.f64 (-.f64 x z))) (sqrt.f64 (-.f64 x z))))
	7.8b	(+.f64 (.f64 t (.f64 x y)) (neg.f64 (.f64 t (.f64 z y))))
	34.7b	(.f64 (sqrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (sqrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))
	8.6b	(.f64 (.f64 (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z))))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))))
✓	5.2b	(.f64 (.f64 (cbrt.f64 (-.f64 x z)) (cbrt.f64 (-.f64 x z))) (.f64 (cbrt.f64 (-.f64 x z)) (.f64 y t)))
	30.5b	(.f64 y (/.f64 (.f64 t (-.f64 (.f64 x x) (.f64 z z))) (+.f64 x z)))

Compiler

Compiled 13473 to 4726 computations (64.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(cbrt.f64 y)
✓	1.4b	(.f64 t (.f64 (-.f64 x z) (cbrt.f64 y)))
✓	4.5b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))

series437.0ms (8.4%)

Counts

4 → 120

Calls

4 calls:

341.0ms	(.f64 t (.f64 (-.f64 x z) (cbrt.f64 y)))
37.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
32.0ms	(cbrt.f64 y)
26.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`pow1_binary64`
32×	`add-exp-log_binary64`
22×	`add-sqr-sqrt_binary64`
21×	`add-cbrt-cube_binary64`
20×	`pow-prod-down_binary64`

Counts

4 → 109

Calls

4 calls:

13.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))
6.0ms	(.f64 t (.f64 (-.f64 x z) (cbrt.f64 y)))
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify77.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

709×	`distribute-rgt-in_binary64`
697×	`distribute-lft-in_binary64`
346×	`associate-r_binary64`
331×	`associate-l_binary64`
193×	`fma-def_binary64`

Counts

229 → 158

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	157	3043
1	372	2345
2	1605	2289
3	5437	2289

prune81.0ms (1.6%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	194	10	204

Error

0.0b

Counts

204 → 10

Alt Table

Status	Error	Program
	33.3b	(.f64 y (cbrt.f64 (pow.f64 (.f64 t (-.f64 x z)) 3)))
✓	4.3b	(.f64 (-.f64 x z) (.f64 y t))
✓	7.6b	(.f64 y (.f64 t (-.f64 x z)))
✓	6.9b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 t (.f64 (-.f64 x z) (cbrt.f64 y))))
	37.5b	(.f64 y (.f64 (*.f64 t (sqrt.f64 (-.f64 x z))) (sqrt.f64 (-.f64 x z))))
	7.8b	(+.f64 (.f64 t (.f64 x y)) (neg.f64 (.f64 t (.f64 z y))))
	34.7b	(.f64 (sqrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (sqrt.f64 (.f64 t (*.f64 y (-.f64 x z)))))
	8.6b	(.f64 (.f64 (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z))))) (cbrt.f64 (.f64 t (.f64 y (-.f64 x z)))))
✓	5.2b	(.f64 (.f64 (cbrt.f64 (-.f64 x z)) (cbrt.f64 (-.f64 x z))) (.f64 (cbrt.f64 (-.f64 x z)) (.f64 y t)))
	30.5b	(.f64 y (/.f64 (.f64 t (-.f64 (.f64 x x) (.f64 z z))) (+.f64 x z)))

Compiler

Compiled 3796 to 863 computations (77.3% saved)

regimes623.0ms (12%)

Accuracy

Total 2.2b remaining (99%)

Threshold costs 0b (0%)

Counts

63 → 3

Compiler

Compiled 6628 to 3758 computations (43.3% saved)

bsearch2.0ms (0%)

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-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	19	61
1	33	61
2	44	61
3	50	61
4	54	61
5	55	61
6	55	61

end7.0ms (0.1%)

Compiler: Compiled 135 to 54 computations (60% saved)

sample1.2s (23%)

Algorithm

1×

intervals

Results

295.0ms	8000×	body	128	valid
73.0ms	1995×	body	128	invalid

Compiler

Compiled 242 to 124 computations (48.8% 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

analyze983.0ms (18.9%)

sample152.0ms (2.9%)

simplify38.0ms (0.7%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series19.0ms (0.4%)

rewrite25.0ms (0.5%)

simplify108.0ms (2.1%)

prune82.0ms (1.6%)

localize8.0ms (0.2%)

series13.0ms (0.2%)

rewrite7.0ms (0.1%)

simplify52.0ms (1%)

prune36.0ms (0.7%)

localize9.0ms (0.2%)

series662.0ms (12.8%)

rewrite110.0ms (2.1%)

simplify158.0ms (3%)

prune251.0ms (4.8%)

localize9.0ms (0.2%)

series437.0ms (8.4%)

rewrite32.0ms (0.6%)

simplify77.0ms (1.5%)

prune81.0ms (1.6%)

regimes623.0ms (12%)

bsearch2.0ms (0%)

simplify6.0ms (0.1%)

end7.0ms (0.1%)

sample1.2s (23%)

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