Details

analyze1.4s (31.2%)

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
3.1%	96.7%	0.2%	8
7.8%	92%	0.2%	9
11.7%	88.1%	0.2%	10
24.2%	64.7%	11.1%	11
27.9%	59.8%	12.3%	12
35%	52.5%	12.5%	13
38.6%	48.2%	13.2%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample46.0ms (1%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
4.0ms	49×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

22×	`fma-def_binary64`
8×	`+-commutative_binary64`
4×	`associate-+r+_binary64`
4×	`associate-+l+_binary64`
3×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	9
1	15	9
2	25	9
3	38	9
4	52	9
5	52	9

prune6.0ms (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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 y (fma.f64 x y z) t)

Compiler

Compiled 42 to 22 computations (47.6% saved)

localize13.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (fma.f64 x y z) t)

series28.0ms (0.6%)

Counts

1 → 48

Calls

1 calls:

28.0ms

(fma.f64 y (fma.f64 x y z) t)

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:

1.0ms

(fma.f64 y (fma.f64 x y z) t)

simplify121.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

775×	`associate-+l+_binary64`
772×	`associate-+r+_binary64`
678×	`unswap-sqr_binary64`
551×	`*-commutative_binary64`
295×	`distribute-lft-in_binary64`

Counts

58 → 31

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	697
1	47	499
2	84	499
3	257	499
4	1272	499
5	3520	499
6	4213	499
7	5348	499

prune39.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	29	2	31
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	3	32

Error

0.0b

Counts

32 → 3

Alt Table

Status	Error	Program
▶	5.0b	(+.f64 (.f64 y z) (+.f64 t (.f64 (pow.f64 y 2) x)))
✓	0.1b	(fma.f64 y (fma.f64 x y z) t)
	41.7b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (fma.f64 x y z) t) (fma.f64 y (fma.f64 x y z) t)) (fma.f64 y (fma.f64 x y z) t)))

Compiler

Compiled 407 to 119 computations (70.8% saved)

localize19.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	8.9b	(*.f64 (pow.f64 y 2) x)

series14.0ms (0.3%)

Counts

1 → 0

Calls

1 calls:

13.0ms

(*.f64 (pow.f64 y 2) x)

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`associate-l_binary64`
6×	`add-exp-log_binary64`
4×	`unswap-sqr_binary64`
4×	`unpow-prod-down_binary64`

Counts

1 → 29

Calls

1 calls:

9.0ms

(*.f64 (pow.f64 y 2) x)

simplify80.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

872×	`fma-def_binary64`
362×	`distribute-rgt-in_binary64`
350×	`*-commutative_binary64`
325×	`distribute-lft-in_binary64`
281×	`associate-/l*_binary64`

Counts

29 → 45

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	51	331
1	98	253
2	260	253
3	784	253
4	1194	253
5	2034	253
6	4662	253
7	4851	253

prune62.0ms (1.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	44	4	48

Error

0.0b

Counts

48 → 4

Alt Table

Status	Error	Program
✓	5.0b	(+.f64 (.f64 y z) (+.f64 t (.f64 (pow.f64 y 2) x)))
	34.9b	(+.f64 (.f64 y z) (+.f64 t (.f64 (*.f64 (pow.f64 y 2) (sqrt.f64 x)) (sqrt.f64 x))))
✓	0.1b	(fma.f64 y (fma.f64 x y z) t)
▶	14.7b	(+.f64 (.f64 y z) (+.f64 t (cbrt.f64 (pow.f64 (.f64 (*.f64 y y) x) 3))))

Compiler

Compiled 843 to 409 computations (51.5% saved)

localize18.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (.f64 (.f64 y y) x) 3)
✓	8.9b	(.f64 (.f64 y y) x)
✓	27.5b	(cbrt.f64 (pow.f64 (.f64 (.f64 y y) x) 3))

series93.0ms (2.1%)

Counts

3 → 72

Calls

3 calls:

46.0ms	(pow.f64 (.f64 (.f64 y y) x) 3)
29.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 y y) x) 3))
18.0ms	(.f64 (.f64 y y) x)

rewrite26.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow1_binary64`
8×	`cbrt-prod_binary64`
7×	`add-sqr-sqrt_binary64`

Counts

3 → 67

Calls

3 calls:

9.0ms	(pow.f64 (.f64 (.f64 y y) x) 3)
8.0ms	(.f64 (.f64 y y) x)
3.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 y y) x) 3))

simplify133.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

582×	`sqr-pow_binary64`
478×	`log-prod_binary64`
399×	`exp-prod_binary64`
348×	`cube-prod_binary64`
338×	`*-commutative_binary64`

Counts

139 → 77

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	89	1336
1	158	1291
2	582	1267
3	1570	1243
4	3464	1240
5	4933	1240
6	4943	1240

prune102.0ms (2.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	77	4	81

Error

0.0b

Counts

81 → 4

Alt Table

Status	Error	Program
✓	5.0b	(+.f64 (.f64 y z) (+.f64 t (.f64 (pow.f64 y 2) x)))
▶	34.9b	(+.f64 (.f64 y z) (+.f64 t (.f64 (*.f64 (pow.f64 y 2) (sqrt.f64 x)) (sqrt.f64 x))))
✓	0.1b	(fma.f64 y (fma.f64 x y z) t)
✓	14.7b	(+.f64 (.f64 y z) (+.f64 t (cbrt.f64 (pow.f64 (.f64 (*.f64 y y) x) 3))))

Compiler

Compiled 1569 to 643 computations (59% saved)

localize18.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.7b	(*.f64 (pow.f64 y 2) (sqrt.f64 x))
✓	2.2b	(.f64 (.f64 (pow.f64 y 2) (sqrt.f64 x)) (sqrt.f64 x))

series55.0ms (1.2%)

Counts

2 → 20

Calls

2 calls:

30.0ms	(*.f64 (pow.f64 y 2) (sqrt.f64 x))
25.0ms	(.f64 (.f64 (pow.f64 y 2) (sqrt.f64 x)) (sqrt.f64 x))

rewrite30.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
17×	`add-exp-log_binary64`
12×	`associate-r_binary64`
10×	`sqrt-prod_binary64`
10×	`prod-exp_binary64`

Counts

2 → 60

Calls

2 calls:

12.0ms	(.f64 (.f64 (pow.f64 y 2) (sqrt.f64 x)) (sqrt.f64 x))
11.0ms	(*.f64 (pow.f64 y 2) (sqrt.f64 x))

simplify177.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

661×	`unswap-sqr_binary64`
367×	`distribute-rgt-in_binary64`
321×	`distribute-lft-in_binary64`
315×	`associate-/l*_binary64`
252×	`fma-def_binary64`

Counts

80 → 84

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	926
1	161	807
2	481	801
3	724	786
4	1178	786
5	2453	786
6	4486	786
7	4744	786

prune119.0ms (2.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	84	4	88

Error

0.0b

Counts

88 → 4

Alt Table

Status	Error	Program
✓	5.0b	(+.f64 (.f64 y z) (+.f64 t (.f64 (pow.f64 y 2) x)))
✓	34.9b	(+.f64 (.f64 y z) (+.f64 t (.f64 (*.f64 (pow.f64 y 2) (sqrt.f64 x)) (sqrt.f64 x))))
✓	0.1b	(fma.f64 y (fma.f64 x y z) t)
✓	14.7b	(+.f64 (.f64 y z) (+.f64 t (cbrt.f64 (pow.f64 (.f64 (*.f64 y y) x) 3))))

Compiler

Compiled 1774 to 715 computations (59.7% saved)

regimes379.0ms (8.4%)

Accuracy

Total 0.0b remaining (59.5%)

Threshold costs 0.0b (59.5%)

Counts

20 → 1

Compiler

Compiled 1754 to 1090 computations (37.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

end1.0ms (0%)

Compiler: Compiled 11 to 6 computations (45.5% saved)

sample1.5s (33.3%)

Algorithm

1×

intervals

Results

564.0ms	8000×	body	128	valid
185.0ms	1793×	body	128	invalid

Compiler

Compiled 92 to 59 computations (35.9% saved)

Details

analyze1.4s (31.2%)

sample46.0ms (1%)

simplify14.0ms (0.3%)

prune6.0ms (0.1%)

localize13.0ms (0.3%)

series28.0ms (0.6%)

rewrite1.0ms (0%)

simplify121.0ms (2.7%)

prune39.0ms (0.9%)

localize19.0ms (0.4%)

series14.0ms (0.3%)

rewrite11.0ms (0.2%)

simplify80.0ms (1.8%)

prune62.0ms (1.4%)

localize18.0ms (0.4%)

series93.0ms (2.1%)

rewrite26.0ms (0.6%)

simplify133.0ms (2.9%)

prune102.0ms (2.2%)

localize18.0ms (0.4%)

series55.0ms (1.2%)

rewrite30.0ms (0.7%)

simplify177.0ms (3.9%)

prune119.0ms (2.6%)

regimes379.0ms (8.4%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.5s (33.3%)

Profiling