Details

analyze956.0ms (22.5%)

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)

sample1.6s (36.9%)

Results

966.0ms	8256×	body	128	valid
377.0ms	3181×	body	128	invalid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify62.0ms (1.5%)

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

6.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.5b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

Compiler

Compiled 61 to 35 computations (42.6% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	6.2b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series31.0ms (0.7%)

Counts

1 → 48

Calls

1 calls:

31.0ms

(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))

simplify101.0ms (2.4%)

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 (0.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	28	5	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	5	34

Error

5.9b

Counts

34 → 5

Alt Table

Status	Error	Program
	33.7b	(.f64 4 (.f64 y t))
▶	6.5b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 y (pow.f64 z 2))))
	43.4b	(pow.f64 x 2)
	24.2b	(.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))))
	7.7b	(.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 724 to 324 computations (55.2% 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 y (pow.f64 z 2)))
✓	0.0b	(.f64 4 (.f64 y t))
✓	10.4b	(*.f64 y (pow.f64 z 2))

series42.0ms (1%)

Counts

4 → 9

Calls

4 calls:

15.0ms	(+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2))
10.0ms	(.f64 4 (.f64 y (pow.f64 z 2)))
9.0ms	(.f64 4 (.f64 y t))
8.0ms	(*.f64 y (pow.f64 z 2))

rewrite21.0ms (0.5%)

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:

7.0ms	(+.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))
3.0ms	(.f64 4 (.f64 y t))

simplify65.0ms (1.5%)

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

prune127.0ms (3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	114	6	120
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	117	8	125

Error

0.0b

Counts

125 → 8

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (*.f64 y z) z)))
✓	6.5b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 y (pow.f64 z 2))))
	33.5b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (sqrt.f64 y) (.f64 z (.f64 z (sqrt.f64 y))))))
	35.5b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (pow.f64 z 2)))))
	32.1b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (.f64 z (sqrt.f64 y)) (.f64 z (sqrt.f64 y)))))
	28.4b	(-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 4 (.f64 y t))) (sqrt.f64 (.f64 4 (.f64 y t)))) (pow.f64 x 2)) (.f64 4 (*.f64 y (pow.f64 z 2))))
	29.6b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (*.f64 y z) (pow.f64 (sqrt.f64 z) 2))))
	24.2b	(.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))))

Compiler

Compiled 3117 to 1975 computations (36.6% 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)

series18.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(.f64 4 (.f64 (*.f64 y z) z))
8.0ms	(.f64 (.f64 y z) z)

rewrite12.0ms (0.3%)

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:

7.0ms	(.f64 4 (.f64 (*.f64 y z) z))
4.0ms	(.f64 (.f64 y z) z)

simplify75.0ms (1.8%)

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

prune110.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	109	6	115

Error

0.0b

Counts

115 → 6

Alt Table

Status	Error	Program
	32.1b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (.f64 z (sqrt.f64 y)) (.f64 z (sqrt.f64 y)))))
▶	0.1b	(-.f64 (+.f64 (.f64 (.f64 4 y) t) (pow.f64 x 2)) (.f64 4 (.f64 (*.f64 y z) z)))
	35.5b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (pow.f64 z 2)))))
	30.5b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (*.f64 y (pow.f64 z 3/2)) (sqrt.f64 z))))
	28.4b	(-.f64 (+.f64 (.f64 (sqrt.f64 (.f64 4 (.f64 y t))) (sqrt.f64 (.f64 4 (.f64 y t)))) (pow.f64 x 2)) (.f64 4 (*.f64 y (pow.f64 z 2))))
✓	6.5b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 y (pow.f64 z 2))))

Compiler

Compiled 2694 to 1422 computations (47.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series44.0ms (1%)

Counts

2 → 84

Calls

2 calls:

34.0ms	(-.f64 (+.f64 (.f64 (.f64 4 y) t) (pow.f64 x 2)) (.f64 4 (.f64 (*.f64 y z) z)))
9.0ms	(+.f64 (.f64 (.f64 4 y) t) (pow.f64 x 2))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`fma-neg_binary64`

Counts

2 → 36

Calls

2 calls:

7.0ms	(-.f64 (+.f64 (.f64 (.f64 4 y) t) (pow.f64 x 2)) (.f64 4 (.f64 (*.f64 y z) z)))
5.0ms	(+.f64 (.f64 (.f64 4 y) t) (pow.f64 x 2))

simplify94.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
579×	`fma-neg_binary64`
564×	`cancel-sign-sub-inv_binary64`
328×	`*-commutative_binary64`
216×	`distribute-rgt-in_binary64`

Counts

120 → 75

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	2230
1	266	1924
2	1050	1760
3	3290	1753
4	4939	1753
5	4930	1753

prune110.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	137	5	142

Error

0.0b

Counts

142 → 5

Alt Table

Status	Error	Program
	0.1b	(-.f64 (fma.f64 (.f64 4 y) t (pow.f64 x 2)) (.f64 4 (.f64 (.f64 y z) z)))
	35.5b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (pow.f64 z 2)))))
	32.1b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (.f64 z (sqrt.f64 y)) (.f64 z (sqrt.f64 y)))))
	30.5b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 (*.f64 y (pow.f64 z 3/2)) (sqrt.f64 z))))
✓	6.5b	(-.f64 (+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2)) (.f64 4 (.f64 y (pow.f64 z 2))))

Compiler

Compiled 3299 to 1798 computations (45.5% saved)

regimes617.0ms (14.5%)

Accuracy

Total 0.1b remaining (64.3%)

Threshold costs 0.1b (64.3%)

Counts

61 → 1

Compiler

Compiled 14024 to 9595 computations (31.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
6×	`+-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	14	23
1	24	23
2	32	23
3	42	23
4	54	23
5	61	23
6	65	23
7	66	23
8	65	23

end101.0ms (2.4%)

Compiler: Compiled 155 to 110 computations (29% saved)

Details

analyze956.0ms (22.5%)

sample1.6s (36.9%)

simplify62.0ms (1.5%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series31.0ms (0.7%)

rewrite1.0ms (0%)

simplify101.0ms (2.4%)

prune32.0ms (0.8%)

localize10.0ms (0.2%)

series42.0ms (1%)

rewrite21.0ms (0.5%)

simplify65.0ms (1.5%)

prune127.0ms (3%)

localize10.0ms (0.2%)

series18.0ms (0.4%)

rewrite12.0ms (0.3%)

simplify75.0ms (1.8%)

prune110.0ms (2.6%)

localize11.0ms (0.3%)

series44.0ms (1%)

rewrite15.0ms (0.4%)

simplify94.0ms (2.2%)

prune110.0ms (2.6%)

regimes617.0ms (14.5%)

simplify3.0ms (0.1%)

end101.0ms (2.4%)

Profiling