Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample899.0ms (42%)

Symmetry

(sort y z)

Results

782.0ms

8256×

body

128

valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify28.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

335×	`fma-def_binary64`
126×	`fma-neg_binary64`
60×	`cancel-sign-sub-inv_binary64`
40×	`distribute-rgt-neg-in_binary64`
28×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	19	11
2	45	11
3	91	11
4	120	11
5	179	11
6	240	11
7	294	11
8	377	11
9	396	11
10	450	11
11	462	11
12	413	11

prune5.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

0.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.8b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) z))

Compiler

Compiled 44 to 27 computations (38.6% saved)

localize11.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.6b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) z))

series16.0ms (0.8%)

Counts

1 → 36

Calls

1 calls:

16.0ms

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

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
1×	`cancel-sign-sub-inv_binary64`
1×	`flip--_binary64`
1×	`sub-neg_binary64`
1×	`*-un-lft-identity_binary64`

Counts

1 → 16

Calls

1 calls:

5.0ms

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

simplify89.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

974×	`fma-def_binary64`
507×	`associate-l_binary64`
406×	`associate-r_binary64`
356×	`distribute-rgt-neg-in_binary64`
346×	`distribute-lft-neg-in_binary64`

Counts

52 → 33

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	649
1	128	606
2	473	595
3	2020	593
4	4542	593
5	4918	593

prune44.0ms (2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	30	3	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	31	3	34

Error

Counts

34 → 3

Alt Table

Status	Error	Program
	50.0b	(/.f64 (fma.f64 (.f64 y y) (.f64 (.f64 z z) -16) (pow.f64 x 4)) (fma.f64 z (.f64 y 4) (*.f64 x x)))
▶	0.8b	(fma.f64 x x (neg.f64 (.f64 (.f64 y 4) z)))
	29.6b	(pow.f64 x 2)

Compiler

Compiled 573 to 298 computations (48% saved)

localize11.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.8b	(fma.f64 x x (neg.f64 (.f64 (.f64 y 4) z)))

series20.0ms (0.9%)

Counts

1 → 36

Calls

1 calls:

20.0ms

(fma.f64 x x (neg.f64 (*.f64 (*.f64 y 4) z)))

rewrite1.0ms (0.1%)

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:

1.0ms

(fma.f64 x x (neg.f64 (*.f64 (*.f64 y 4) z)))

simplify106.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

400×	`neg-sub0_binary64`
371×	`neg-mul-1_binary64`
363×	`associate-l_binary64`
323×	`associate-r_binary64`
228×	`distribute-rgt-neg-out_binary64`

Counts

46 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	586
1	51	485
2	109	485
3	351	485
4	1659	485
5	3911	485
6	4499	485
7	4950	485

prune25.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	22	3	25

Error

Counts

25 → 3

Alt Table

Status	Error	Program
	50.0b	(/.f64 (fma.f64 (.f64 y y) (.f64 (.f64 z z) -16) (pow.f64 x 4)) (fma.f64 z (.f64 y 4) (*.f64 x x)))
✓	0.8b	(fma.f64 x x (neg.f64 (.f64 (.f64 y 4) z)))
▶	29.6b	(pow.f64 x 2)

Compiler

Compiled 361 to 201 computations (44.3% saved)

localize3.0ms (0.1%)

prune4.0ms (0.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	1	1
Total	3	3

Error

Counts

3 → 3

Alt Table

Status	Error	Program
▶	50.0b	(/.f64 (fma.f64 (.f64 y y) (.f64 (.f64 z z) -16) (pow.f64 x 4)) (fma.f64 z (.f64 y 4) (*.f64 x x)))
✓	0.8b	(fma.f64 x x (neg.f64 (.f64 (.f64 y 4) z)))
✓	29.6b	(pow.f64 x 2)

Compiler

Compiled 66 to 43 computations (34.8% saved)

localize23.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 z z) -16)
✓	0.2b	(fma.f64 z (.f64 y 4) (.f64 x x))
✓	16.1b	(fma.f64 (.f64 y y) (.f64 (*.f64 z z) -16) (pow.f64 x 4))
✓	36.0b	(/.f64 (fma.f64 (.f64 y y) (.f64 (.f64 z z) -16) (pow.f64 x 4)) (fma.f64 z (.f64 y 4) (*.f64 x x)))

series173.0ms (8.1%)

Counts

4 → 120

Calls

4 calls:

88.0ms	(/.f64 (fma.f64 (.f64 y y) (.f64 (.f64 z z) -16) (pow.f64 x 4)) (fma.f64 z (.f64 y 4) (*.f64 x x)))
63.0ms	(fma.f64 (.f64 y y) (.f64 (*.f64 z z) -16) (pow.f64 x 4))
17.0ms	(fma.f64 z (.f64 y 4) (.f64 x x))
4.0ms	(.f64 (.f64 z z) -16)

rewrite21.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

8.0ms	(.f64 (.f64 z z) -16)
4.0ms	(/.f64 (fma.f64 (.f64 y y) (.f64 (.f64 z z) -16) (pow.f64 x 4)) (fma.f64 z (.f64 y 4) (*.f64 x x)))
1.0ms	(fma.f64 (.f64 y y) (.f64 (*.f64 z z) -16) (pow.f64 x 4))
1.0ms	(fma.f64 z (.f64 y 4) (.f64 x x))

simplify228.0ms (10.7%)

Algorithm

1×	egg-herbie

Rules

709×	`exp-prod_binary64`
488×	`associate-l_binary64`
417×	`fma-def_binary64`
381×	`associate-r_binary64`
263×	`distribute-rgt-in_binary64`

Counts

190 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	3443
1	234	3117
2	631	3108
3	2079	3108
4	4644	3108
5	5148	3108

prune136.0ms (6.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	125	3	128

Error

Counts

128 → 3

Alt Table

Status	Error	Program
✓	50.0b	(/.f64 (fma.f64 (.f64 y y) (.f64 (.f64 z z) -16) (pow.f64 x 4)) (fma.f64 z (.f64 y 4) (*.f64 x x)))
✓	0.8b	(fma.f64 x x (neg.f64 (.f64 (.f64 y 4) z)))
✓	29.6b	(pow.f64 x 2)

Compiler

Compiled 3810 to 1889 computations (50.4% saved)

regimes165.0ms (7.7%)

Accuracy

Total 0.7b remaining (95.4%)

Threshold costs 0.7b (95.4%)

Counts

10 → 1

Compiler

Compiled 1028 to 694 computations (32.5% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	19	11
2	34	11
3	41	11
4	45	11
5	46	11
6	45	11

end119.0ms (5.5%)

Remove: (sort y z)
Compiler: Compiled 86 to 56 computations (34.9% saved)

Iter	Nodes	Cost
0	9	13
1	19	11
2	45	11
3	91	11
4	120	11
5	179	11
6	240	11
7	294	11
8	377	11
9	396	11
10	450	11
11	462	11
12	413	11

Iter	Nodes	Cost
0	9	13
1	19	11
2	45	11
3	91	11
4	120	11
5	179	11
6	240	11
7	294	11
8	377	11
9	396	11
10	450	11
11	462	11
12	413	11

Details

analyze4.0ms (0.2%)

sample899.0ms (42%)

simplify28.0ms (1.3%)

prune5.0ms (0.2%)

localize11.0ms (0.5%)

series16.0ms (0.8%)

rewrite6.0ms (0.3%)

simplify89.0ms (4.2%)

prune44.0ms (2%)

localize11.0ms (0.5%)

series20.0ms (0.9%)

rewrite1.0ms (0.1%)

simplify106.0ms (4.9%)

prune25.0ms (1.2%)

localize3.0ms (0.1%)

prune4.0ms (0.2%)

localize23.0ms (1.1%)

series173.0ms (8.1%)

rewrite21.0ms (1%)

simplify228.0ms (10.7%)

prune136.0ms (6.4%)

regimes165.0ms (7.7%)

simplify5.0ms (0.2%)

end119.0ms (5.5%)

Profiling

Iter	Nodes	Cost
0	9	13
1	19	11
2	45	11
3	91	11
4	120	11
5	179	11
6	240	11
7	294	11
8	377	11
9	396	11
10	450	11
11	462	11
12	413	11