Details

analyze182.0ms (6.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 32 to 20 computations (37.5% saved)

sample98.0ms (3.3%)

Algorithm

1×

intervals

Results

20.0ms

256×

body

128

valid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify57.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
556×	`cancel-sign-sub-inv_binary64`
552×	`unswap-sqr_binary64`
357×	`unsub-neg_binary64`
344×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	57	37
2	168	37
3	492	37
4	1604	33
5	2891	33
6	4309	33
7	5214	33

prune5.0ms (0.2%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)

Status

Error

Program

▶

0.0b

(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))

0.2b

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a))))) 1)

Compiler

Compiled 166 to 104 computations (37.3% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	0.1b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	1.0b	(.f64 (.f64 b b) (+.f64 a 3))

series89.0ms (3%)

Counts

4 → 96

Calls

4 calls:

35.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
34.0ms	(pow.f64 (hypot.f64 a b) 4)
12.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
8.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
9×	`add-cube-cbrt_binary64`

Counts

4 → 78

Calls

4 calls:

7.0ms	(.f64 (.f64 b b) (+.f64 a 3))
4.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
1.0ms	(pow.f64 (hypot.f64 a b) 4)
0.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))

simplify80.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

574×	`associate-+l+_binary64`
469×	`distribute-rgt-in_binary64`
453×	`distribute-lft-in_binary64`
338×	`associate--l+_binary64`
219×	`cancel-sign-sub-inv_binary64`

Counts

174 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	3413
1	464	3143
2	1556	3045
3	5074	3045

prune168.0ms (5.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	162	2	164

Error

0.0b

Counts

164 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
▶	13.6b	(+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))

Status

Error

Program

✓

0.0b

(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))

▶

13.6b

(+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))

Compiler

Compiled 4851 to 2830 computations (41.7% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	0.2b	(pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)
	1.0b	(.f64 (.f64 b b) (+.f64 a 3))
✓	25.5b	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3))

series67.0ms (2.3%)

Counts

2 → 48

Calls

2 calls:

35.0ms	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3))
32.0ms	(pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`unpow-prod-down_binary64`
20×	`cbrt-prod_binary64`
14×	`cube-prod_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`

Counts

2 → 66

Calls

2 calls:

4.0ms	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3))
2.0ms	(pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)

simplify111.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

597×	`fma-def_binary64`
554×	`unswap-sqr_binary64`
435×	`log-prod_binary64`
406×	`sqr-pow_binary64`
400×	`exp-prod_binary64`

Counts

114 → 91

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	119	1921
1	267	1844
2	801	1704
3	1600	1642
4	2717	1642
5	4642	1642
6	4942	1642
7	4845	1642

prune177.0ms (6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	163	3	166

Error

Counts

166 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
▶	13.7b	(+.f64 (cbrt.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4) 3) (pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4) 3))) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
✓	13.6b	(+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))

Compiler

Compiled 5357 to 3259 computations (39.2% saved)

localize18.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4) 3)
✓	0.8b	(pow.f64 (sqrt.f64 (hypot.f64 a b)) 4)
	1.0b	(.f64 (.f64 b b) (+.f64 a 3))
✓	25.5b	(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4) 3) (pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4) 3)))

series179.0ms (6%)

Counts

3 → 40

Calls

3 calls:

74.0ms

(pow.f64 (sqrt.f64 (hypot.f64 a b)) 4)

70.0ms

(pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4) 3)

34.0ms

(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4) 3) (pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4) 3)))

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`unpow-prod-down_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
10×	`cube-prod_binary64`

Counts

3 → 78

Calls

3 calls:

8.0ms

(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4) 3) (pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4) 3)))

4.0ms

(pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4) 3)

2.0ms

(pow.f64 (sqrt.f64 (hypot.f64 a b)) 4)

simplify103.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

413×	`sqr-pow_binary64`
383×	`log-prod_binary64`
369×	`exp-prod_binary64`
350×	`distribute-rgt-in_binary64`
347×	`fma-def_binary64`

Counts

118 → 121

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	114	1929
1	249	1597
2	695	1480
3	1198	1352
4	2225	1297
5	4178	1297
6	4588	1297
7	4836	1297

prune338.0ms (11.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	260	0	260
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	260	3	263

Error

Counts

263 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	13.7b	(+.f64 (cbrt.f64 (.f64 (pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4) 3) (pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 a b)) 4) 3))) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
✓	13.6b	(+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))

Compiler

Compiled 10641 to 6110 computations (42.6% saved)

regimes281.0ms (9.4%)

Accuracy

Total 0.0b remaining (17.8%)

Threshold costs 0.0b (17.8%)

Counts

50 → 1

Compiler

Compiled 5963 to 4290 computations (28.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	33
1	24	33
2	27	33
3	29	33
4	30	33
5	29	33

end1.0ms (0%)

Compiler: Compiled 25 to 17 computations (32% saved)

sample945.0ms (31.7%)

Algorithm

1×

intervals

Results

630.0ms	8000×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 150 to 102 computations (32% saved)

Details

analyze182.0ms (6.1%)

sample98.0ms (3.3%)

simplify57.0ms (1.9%)

prune5.0ms (0.2%)

localize14.0ms (0.5%)

series89.0ms (3%)

rewrite16.0ms (0.5%)

simplify80.0ms (2.7%)

prune168.0ms (5.6%)

localize15.0ms (0.5%)

series67.0ms (2.3%)

rewrite10.0ms (0.3%)

simplify111.0ms (3.7%)

prune177.0ms (6%)

localize18.0ms (0.6%)

series179.0ms (6%)

rewrite18.0ms (0.6%)

simplify103.0ms (3.5%)

prune338.0ms (11.3%)

regimes281.0ms (9.4%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample945.0ms (31.7%)

Profiling