Details

analyze2.0ms (0%)

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)

sample958.0ms (20.8%)

Infinites

49.5% of outputs are infinite.

Results

708.0ms

8256×

body

128

valid

Compiler

Compiled 53 to 35 computations (34% saved)

simplify65.0ms (1.4%)

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)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.4b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

series33.0ms (0.7%)

Counts

1 → 48

Calls

1 calls:

33.0ms

(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))

simplify103.0ms (2.2%)

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

prune25.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	30	3	33
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	4	34

Error

2.4b

Counts

34 → 4

Alt Table

Status	Error	Program
	24.6b	(.f64 4 (.f64 y (-.f64 t (*.f64 z z))))
▶	6.2b	(.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))))
✓	5.6b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	19.5b	(fma.f64 x x (.f64 4 (.f64 y t)))

Compiler

Compiled 654 to 278 computations (57.5% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.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))))
✓	0.4b	(.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))))
	5.4b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
✓	30.7b	(cbrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x)))

series647.0ms (14.1%)

Counts

3 → 144

Calls

3 calls:

422.0ms

(*.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))))

188.0ms

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

37.0ms

(*.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))))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

9.0ms

(*.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))))

6.0ms

(*.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))))

1.0ms

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

simplify286.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

478×	`*-commutative_binary64`
220×	`+-commutative_binary64`
212×	`cancel-sign-sub-inv_binary64`
207×	`fma-def_binary64`
195×	`sub-neg_binary64`

Counts

237 → 282

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1128	19837
1	3968	19315
2	5082	19315

prune964.0ms (21%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	569	0	569
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	569	4	573

Error

2.4b

Counts

573 → 4

Alt Table

Status	Error	Program
	24.6b	(.f64 4 (.f64 y (-.f64 t (*.f64 z z))))
✓	6.2b	(.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))))
✓	5.6b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
▶	19.5b	(fma.f64 x x (.f64 4 (.f64 y t)))

Compiler

Compiled 51302 to 29772 computations (42% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 4 (.f64 y t))
✓	0.2b	(fma.f64 x x (.f64 4 (.f64 y t)))

series15.0ms (0.3%)

Counts

2 → 36

Calls

2 calls:

11.0ms	(fma.f64 x x (.f64 4 (.f64 y t)))
4.0ms	(.f64 4 (.f64 y t))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
3×	`associate-l_binary64`
3×	`cbrt-unprod_binary64`

Counts

2 → 30

Calls

2 calls:

4.0ms	(.f64 4 (.f64 y t))
0.0ms	(fma.f64 x x (.f64 4 (.f64 y t)))

simplify86.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

828×	`distribute-rgt-in_binary64`
818×	`distribute-lft-in_binary64`
667×	`fma-def_binary64`
383×	`*-commutative_binary64`
355×	`associate-l_binary64`

Counts

66 → 42

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	55	716
1	106	657
2	304	657
3	810	657
4	1261	657
5	2498	657
6	4543	657
7	4964	657
8	4932	657

prune28.0ms (0.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	41	5	46

Error

2.4b

Counts

46 → 5

Alt Table

Status	Error	Program
▶	24.6b	(.f64 4 (.f64 y (-.f64 t (*.f64 z z))))
	29.7b	(expm1.f64 (log1p.f64 (fma.f64 x x (.f64 4 (.f64 y t)))))
✓	6.2b	(.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))))
✓	5.6b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
✓	19.5b	(fma.f64 x x (.f64 4 (.f64 y t)))

Compiler

Compiled 667 to 344 computations (48.4% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 4 (.f64 y (-.f64 t (*.f64 z z))))
✓	4.5b	(.f64 y (-.f64 t (.f64 z z)))

series37.0ms (0.8%)

Counts

2 → 72

Calls

2 calls:

21.0ms	(.f64 4 (.f64 y (-.f64 t (*.f64 z z))))
16.0ms	(.f64 y (-.f64 t (.f64 z z)))

rewrite15.0ms (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:

6.0ms	(.f64 4 (.f64 y (-.f64 t (*.f64 z z))))
4.0ms	(.f64 y (-.f64 t (.f64 z z)))

simplify127.0ms (2.8%)

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

prune72.0ms (1.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	0	1	1
Picked	1	0	1
Done	0	3	3
Total	116	6	122

Error

0.8b

Counts

122 → 6

Alt Table

Status	Error	Program
✓	5.6b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	43.4b	(.f64 4 (.f64 (*.f64 y (+.f64 (sqrt.f64 t) z)) (-.f64 (sqrt.f64 t) z)))
	24.6b	(.f64 (.f64 4 y) (-.f64 t (*.f64 z z)))
	29.7b	(expm1.f64 (log1p.f64 (fma.f64 x x (.f64 4 (.f64 y t)))))
✓	6.2b	(.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))))
✓	19.5b	(fma.f64 x x (.f64 4 (.f64 y t)))

Compiler

Compiled 2007 to 703 computations (65% saved)

regimes961.0ms (20.9%)

Accuracy

Total 2.8b remaining (67.8%)

Threshold costs 0b (0%)

Counts

72 → 2

Compiler

Compiled 21483 to 12575 computations (41.5% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 17 to 11 computations (35.3% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

48×	`distribute-rgt-neg-in_binary64`
31×	`distribute-lft-neg-in_binary64`
31×	`cancel-sign-sub-inv_binary64`
29×	`neg-sub0_binary64`
29×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	52
1	39	52
2	64	52
3	81	52
4	98	52
5	113	52
6	124	52
7	140	52
8	159	52
9	173	52
10	185	52
11	197	52
12	205	52
13	222	52
14	234	52
15	238	52
16	232	52

end94.0ms (2%)

Compiler: Compiled 197 to 113 computations (42.6% saved)

Iter	Nodes	Cost
0	22	52
1	39	52
2	64	52
3	81	52
4	98	52
5	113	52
6	124	52
7	140	52
8	159	52
9	173	52
10	185	52
11	197	52
12	205	52
13	222	52
14	234	52
15	238	52
16	232	52

Iter	Nodes	Cost
0	22	52
1	39	52
2	64	52
3	81	52
4	98	52
5	113	52
6	124	52
7	140	52
8	159	52
9	173	52
10	185	52
11	197	52
12	205	52
13	222	52
14	234	52
15	238	52
16	232	52

Details

analyze2.0ms (0%)

sample958.0ms (20.8%)

simplify65.0ms (1.4%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series33.0ms (0.7%)

rewrite1.0ms (0%)

simplify103.0ms (2.2%)

prune25.0ms (0.5%)

localize12.0ms (0.3%)

series647.0ms (14.1%)

rewrite25.0ms (0.5%)

simplify286.0ms (6.2%)

prune964.0ms (21%)

localize5.0ms (0.1%)

series15.0ms (0.3%)

rewrite5.0ms (0.1%)

simplify86.0ms (1.9%)

prune28.0ms (0.6%)

localize5.0ms (0.1%)

series37.0ms (0.8%)

rewrite15.0ms (0.3%)

simplify127.0ms (2.8%)

prune72.0ms (1.6%)

regimes961.0ms (20.9%)

bsearch4.0ms (0.1%)

simplify10.0ms (0.2%)

end94.0ms (2%)

Profiling

Iter	Nodes	Cost
0	22	52
1	39	52
2	64	52
3	81	52
4	98	52
5	113	52
6	124	52
7	140	52
8	159	52
9	173	52
10	185	52
11	197	52
12	205	52
13	222	52
14	234	52
15	238	52
16	232	52