Details

analyze976.0ms (18%)

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
6.2%	82.7%	11.1%	10
12.5%	73.7%	13.8%	11
15.6%	59.5%	25%	12
17.9%	53.3%	28.8%	13
22.4%	47.2%	30.4%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.9s (35.1%)

Results

1.3s	8256×	body	128	valid
387.0ms	3051×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify63.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-neg_binary64`
525×	`fma-def_binary64`
182×	`cancel-sign-sub-inv_binary64`
160×	`associate-l_binary64`
154×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	25	17
2	72	17
3	227	17
4	512	17
5	1044	17
6	1436	17
7	1492	17
8	1573	17
9	1615	17
10	1631	17
11	1631	17
12	1550	17

prune3.0ms (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

5.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.6b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

Compiler

Compiled 61 to 35 computations (42.6% saved)

localize9.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.2b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series36.0ms (0.7%)

Counts

1 → 48

Calls

1 calls:

36.0ms

(fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))

simplify107.0ms (2%)

Algorithm

1×	egg-herbie

Rules

656×	`associate-l_binary64`
618×	`exp-prod_binary64`
546×	`associate-r_binary64`
433×	`distribute-rgt-in_binary64`
424×	`distribute-lft-in_binary64`

Counts

58 → 33

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	1181
1	101	928
2	231	928
3	721	928
4	3522	928
5	4742	928
6	4963	928
7	4910	928

prune32.0ms (0.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	27	6	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	6	34

Error

4.9b

Counts

34 → 6

Alt Table

Status	Error	Program
	39.2b	(cbrt.f64 (pow.f64 (fma.f64 4 (.f64 y (-.f64 t (.f64 z z))) (*.f64 x x)) 3))
▶	5.6b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 y (pow.f64 z 2))))
	40.3b	(pow.f64 x 2)
	38.4b	(.f64 4 (.f64 y t))
	23.2b	(.f64 (sqrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (sqrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
	6.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))

Compiler

Compiled 762 to 350 computations (54.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2))
✓	0.0b	(.f64 4 (.f64 y (pow.f64 z 2)))
✓	0.0b	(.f64 4 (.f64 y t))
✓	9.1b	(*.f64 y (pow.f64 z 2))

series41.0ms (0.8%)

Counts

4 → 9

Calls

4 calls:

13.0ms	(*.f64 y (pow.f64 z 2))
13.0ms	(.f64 4 (.f64 y (pow.f64 z 2)))
10.0ms	(+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2))
5.0ms	(.f64 4 (.f64 y t))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`prod-exp_binary64`
11×	`pow1_binary64`

Counts

4 → 84

Calls

4 calls:

6.0ms	(.f64 4 (.f64 y t))
5.0ms	(+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2))
4.0ms	(.f64 4 (.f64 y (pow.f64 z 2)))
4.0ms	(*.f64 y (pow.f64 z 2))

simplify74.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

713×	`unswap-sqr_binary64`
384×	`*-commutative_binary64`
311×	`fma-neg_binary64`
216×	`fma-def_binary64`
206×	`sqr-pow_binary64`

Counts

93 → 120

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	1086
1	293	943
2	940	931
3	1861	931
4	3534	931
5	5046	931

prune143.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	116	4	120
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	119	7	126

Error

0.0b

Counts

126 → 7

Alt Table

Status	Error	Program
	39.2b	(cbrt.f64 (pow.f64 (fma.f64 4 (.f64 y (-.f64 t (.f64 z z))) (*.f64 x x)) 3))
▶	0.1b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (*.f64 y z) z)))
✓	5.6b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 y (pow.f64 z 2))))
	1.8b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (.f64 y (.f64 z (cbrt.f64 z))) (pow.f64 (cbrt.f64 z) 2))))
	5.8b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (.f64 y (.f64 (cbrt.f64 (pow.f64 z 2)) (cbrt.f64 (pow.f64 z 2)))) (cbrt.f64 (pow.f64 z 2)))))
	35.3b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (*.f64 y z) (pow.f64 (sqrt.f64 z) 2))))
	6.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))

Compiler

Compiled 3093 to 1955 computations (36.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2))
✓	0.0b	(.f64 4 (.f64 (*.f64 y z) z))
	0.0b	(.f64 4 (.f64 y t))
✓	0.2b	(.f64 (.f64 y z) z)

series22.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(.f64 4 (.f64 (*.f64 y z) z))
9.0ms	(.f64 (.f64 y z) z)

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

2 → 43

Calls

2 calls:

5.0ms	(.f64 4 (.f64 (*.f64 y z) z))
4.0ms	(.f64 (.f64 y z) z)

simplify81.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

749×	`fma-def_binary64`
436×	`associate-/l/_binary64`
369×	`log-div_binary64`
359×	`associate-/l*_binary64`
316×	`*-commutative_binary64`

Counts

91 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	968
1	154	851
2	562	851
3	883	849
4	1218	849
5	2122	849
6	4007	849
7	4935	849

prune152.0ms (2.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	103	4	107
Fresh	4	1	5
Picked	0	1	1
Done	0	1	1
Total	107	7	114

Error

0.0b

Counts

114 → 7

Alt Table

Status	Error	Program
▶	0.4b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (.f64 (.f64 y z) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))))
✓	0.1b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (*.f64 y z) z)))
✓	5.6b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 y (pow.f64 z 2))))
	0.4b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (cbrt.f64 4) (.f64 (*.f64 y z) z))))
	0.4b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 (.f64 (cbrt.f64 (.f64 4 (.f64 (.f64 y z) z))) (cbrt.f64 (.f64 4 (.f64 (.f64 y z) z)))) (cbrt.f64 (.f64 4 (.f64 (*.f64 y z) z)))))
	36.3b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (*.f64 y (pow.f64 z 3/2)) (sqrt.f64 z))))
	6.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))

Compiler

Compiled 2797 to 1467 computations (47.6% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 y z) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
✓	0.3b	(.f64 (.f64 (.f64 y z) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)

series488.0ms (9%)

Counts

4 → 72

Calls

4 calls:

388.0ms	(.f64 (.f64 y z) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
41.0ms	(cbrt.f64 z)
36.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
23.0ms	(.f64 (.f64 (.f64 y z) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))

rewrite33.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`pow1_binary64`
36×	`add-exp-log_binary64`
23×	`pow-prod-down_binary64`
23×	`add-sqr-sqrt_binary64`
22×	`cbrt-unprod_binary64`

Counts

4 → 111

Calls

4 calls:

11.0ms	(.f64 (.f64 (.f64 y z) (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))
11.0ms	(.f64 (.f64 y z) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))
4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
1.0ms	(cbrt.f64 z)

simplify138.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

500×	`*-commutative_binary64`
399×	`sqr-pow_binary64`
371×	`log-prod_binary64`
354×	`exp-prod_binary64`
292×	`associate-l_binary64`

Counts

183 → 149

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	125	1908
1	266	1583
2	1042	1476
3	1880	1448
4	3762	1300
5	4505	1296
6	4778	1296
7	4837	1296

prune208.0ms (3.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	184	1	185
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	185	7	192

Error

0.0b

Counts

192 → 7

Alt Table

Status	Error	Program
✓	0.4b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (.f64 (.f64 y z) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))))
✓	0.1b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (*.f64 y z) z)))
✓	5.6b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 y (pow.f64 z 2))))
	5.7b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (.f64 (.f64 y z) (cbrt.f64 (*.f64 z z))) (cbrt.f64 z))))
	0.4b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 (.f64 (cbrt.f64 (.f64 4 (.f64 (.f64 y z) z))) (cbrt.f64 (.f64 4 (.f64 (.f64 y z) z)))) (cbrt.f64 (.f64 4 (.f64 (*.f64 y z) z)))))
	36.3b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (*.f64 y (pow.f64 z 3/2)) (sqrt.f64 z))))
	6.7b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)))) (cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))

Compiler

Compiled 5407 to 2388 computations (55.8% saved)

regimes707.0ms (13%)

Accuracy

Total 0.1b remaining (69.9%)

Threshold costs 0.1b (69.9%)

Counts

60 → 1

Compiler

Compiled 15805 to 10610 computations (32.9% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
7×	`+-commutative_binary64`
6×	`distribute-lft-neg-in_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	27	25
2	35	25
3	45	25
4	57	25
5	64	25
6	68	25
7	69	25
8	68	25

end125.0ms (2.3%)

Compiler: Compiled 248 to 161 computations (35.1% saved)

Details

analyze976.0ms (18%)

sample1.9s (35.1%)

simplify63.0ms (1.2%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series36.0ms (0.7%)

rewrite1.0ms (0%)

simplify107.0ms (2%)

prune32.0ms (0.6%)

localize11.0ms (0.2%)

series41.0ms (0.8%)

rewrite23.0ms (0.4%)

simplify74.0ms (1.4%)

prune143.0ms (2.6%)

localize10.0ms (0.2%)

series22.0ms (0.4%)

rewrite11.0ms (0.2%)

simplify81.0ms (1.5%)

prune152.0ms (2.8%)

localize14.0ms (0.3%)

series488.0ms (9%)

rewrite33.0ms (0.6%)

simplify138.0ms (2.6%)

prune208.0ms (3.8%)

regimes707.0ms (13%)

simplify5.0ms (0.1%)

end125.0ms (2.3%)

Profiling