Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
99.8%	0%	0.2%	1

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.6s (20.9%)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify119.0ms (1.6%)

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

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

2.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	3.2b	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))
▶	2.4b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

Compiler

Compiled 95 to 57 computations (40% saved)

localize16.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 t (*.f64 z z))
✓	2.4b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series74.0ms (1%)

Counts

2 → 72

Calls

2 calls:

64.0ms	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
10.0ms	(-.f64 t (*.f64 z z))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 31

Calls

2 calls:

5.0ms	(-.f64 t (*.f64 z z))
1.0ms	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

simplify130.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

703×	`distribute-rgt-in_binary64`
653×	`distribute-lft-in_binary64`
495×	`fma-neg_binary64`
369×	`exp-prod_binary64`
193×	`fma-def_binary64`

Counts

103 → 64

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	80	1591
1	187	1301
2	431	1282
3	1535	1282
4	4588	1282
5	5085	1282

prune86.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	60	4	64
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	61	5	66

Error

1.9b

Counts

66 → 5

Alt Table

Status	Error	Program
	22.6b	(.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))))
	22.8b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)) (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
▶	21.9b	(+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2))
	22.3b	(.f64 4 (.f64 y (-.f64 t (*.f64 z z))))
✓	2.4b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

Compiler

Compiled 1251 to 491 computations (60.8% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 4 (.f64 y t))
✓	0.8b	(+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2))

series24.0ms (0.3%)

Counts

2 → 9

Calls

2 calls:

19.0ms	(+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2))
6.0ms	(.f64 4 (.f64 y t))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
4×	`add-log-exp_binary64`
3×	`associate-l_binary64`

Counts

2 → 34

Calls

2 calls:

8.0ms	(+.f64 (.f64 4 (.f64 y t)) (pow.f64 x 2))
7.0ms	(.f64 4 (.f64 y t))

simplify140.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-neg_binary64`
506×	`associate-l_binary64`
372×	`associate-r_binary64`
288×	`distribute-rgt-in_binary64`
268×	`distribute-lft-in_binary64`

Counts

43 → 46

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	477
1	168	448
2	519	441
3	1733	441
4	3834	441
5	4897	441
6	4999	441
7	4939	441

prune69.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	45	1	46
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	46	5	51

Error

1.9b

Counts

51 → 5

Alt Table

Status	Error	Program
✓	2.4b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	32.6b	(exp.f64 (log.f64 (fma.f64 x x (.f64 4 (.f64 y t)))))
	22.6b	(.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))))
	22.8b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)) (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
▶	22.3b	(.f64 4 (.f64 y (-.f64 t (*.f64 z z))))

Compiler

Compiled 919 to 541 computations (41.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 4 (.f64 y (-.f64 t (*.f64 z z))))
	0.0b	(-.f64 t (*.f64 z z))
✓	2.9b	(.f64 y (-.f64 t (.f64 z z)))

series41.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

21.0ms	(.f64 4 (.f64 y (-.f64 t (*.f64 z z))))
19.0ms	(.f64 y (-.f64 t (.f64 z z)))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`distribute-lft-in_binary64`
25×	`distribute-rgt-in_binary64`
18×	`prod-diff_binary64`
14×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`

Counts

2 → 75

Calls

2 calls:

8.0ms	(.f64 4 (.f64 y (-.f64 t (*.f64 z z))))
5.0ms	(.f64 y (-.f64 t (.f64 z z)))

simplify230.0ms (3%)

Algorithm

1×	egg-herbie

Rules

379×	`distribute-rgt-in_binary64`
358×	`distribute-lft-in_binary64`
323×	`*-commutative_binary64`
300×	`distribute-lft-neg-out_binary64`
298×	`distribute-rgt-neg-out_binary64`

Counts

147 → 117

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	143	2159
1	299	1973
2	922	1865
3	2664	1811
4	4725	1811
5	4984	1811
6	4995	1811
7	4787	1811

prune306.0ms (4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	147	6	153

Error

0.5b

Counts

153 → 6

Alt Table

Status	Error	Program
✓	2.4b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	22.7b	(.f64 4 (.f64 (.f64 (cbrt.f64 (.f64 y (-.f64 t (.f64 z z)))) (cbrt.f64 (.f64 y (-.f64 t (.f64 z z))))) (cbrt.f64 (.f64 y (-.f64 t (*.f64 z z))))))
	22.7b	(.f64 4 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (-.f64 t (*.f64 z z)))))
▶	22.6b	(.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))))
	22.8b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)) (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
	40.3b	(.f64 4 (.f64 (*.f64 y (+.f64 (sqrt.f64 t) z)) (-.f64 (sqrt.f64 t) z)))

Compiler

Compiled 2636 to 935 computations (64.5% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 t (*.f64 z z))
✓	0.1b	(.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))))
	2.4b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
✓	17.5b	(sqrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)))

series325.0ms (4.2%)

Counts

2 → 80

Calls

2 calls:

287.0ms

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

38.0ms

(*.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))))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

6.0ms

(*.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))))

1.0ms

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

simplify206.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

617×	`cancel-sign-sub-inv_binary64`
264×	`fma-neg_binary64`
249×	`sub-neg_binary64`
201×	`associate-r_binary64`
187×	`unswap-sqr_binary64`

Counts

148 → 147

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	254	5290
1	784	4698
2	3338	4601
3	5058	4601

prune644.0ms (8.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	346	0	346
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	346	6	352

Error

0.5b

Counts

352 → 6

Alt Table

Status	Error	Program
✓	2.4b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	22.7b	(.f64 4 (.f64 (.f64 (cbrt.f64 (.f64 y (-.f64 t (.f64 z z)))) (cbrt.f64 (.f64 y (-.f64 t (.f64 z z))))) (cbrt.f64 (.f64 y (-.f64 t (*.f64 z z))))))
	22.7b	(.f64 4 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (-.f64 t (*.f64 z z)))))
✓	22.6b	(.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))))
	22.8b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x)) (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (.f64 x x))) (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))))
	40.3b	(.f64 4 (.f64 (*.f64 y (+.f64 (sqrt.f64 t) z)) (-.f64 (sqrt.f64 t) z)))

Compiler

Compiled 15171 to 7351 computations (51.5% saved)

regimes3.3s (42.9%)

Accuracy

Total 2.6b remaining (48.3%)

Threshold costs 0b (0%)

Counts

152 → 1

Compiler

Compiled 28927 to 19352 computations (33.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	17	17
2	24	17
3	28	17
4	30	17
5	30	17

end243.0ms (3.2%)

Compiler: Compiled 191 to 100 computations (47.6% saved)

Details

analyze5.0ms (0.1%)

sample1.6s (20.9%)

simplify119.0ms (1.6%)

prune6.0ms (0.1%)

localize16.0ms (0.2%)

series74.0ms (1%)

rewrite8.0ms (0.1%)

simplify130.0ms (1.7%)

prune86.0ms (1.1%)

localize10.0ms (0.1%)

series24.0ms (0.3%)

rewrite17.0ms (0.2%)

simplify140.0ms (1.8%)

prune69.0ms (0.9%)

localize6.0ms (0.1%)

series41.0ms (0.5%)

rewrite20.0ms (0.3%)

simplify230.0ms (3%)

prune306.0ms (4%)

localize22.0ms (0.3%)

series325.0ms (4.2%)

rewrite20.0ms (0.3%)

simplify206.0ms (2.7%)

prune644.0ms (8.4%)

regimes3.3s (42.9%)

simplify3.0ms (0%)

end243.0ms (3.2%)

Profiling