Details

analyze157.0ms (4.9%)

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)

sample97.0ms (3.1%)

Algorithm

1×

intervals

Results

18.0ms

256×

body

128

valid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify58.0ms (1.8%)

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 (0.1%)

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

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))
	0.1b	(-.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))

0.1b

(-.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 (0.4%)

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))
✓	0.0b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	0.3b	(.f64 (.f64 b b) (+.f64 a 3))

series91.0ms (2.9%)

Counts

4 → 96

Calls

4 calls:

36.0ms	(pow.f64 (hypot.f64 a b) 4)
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))
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:

6.0ms	(.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)))

simplify78.0ms (2.5%)

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

prune212.0ms (6.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	161	3	164

Error

Counts

164 → 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))
▶	0.0b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 1 (*.f64 4 (pow.f64 a 3))))
	0.1b	(-.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 4951 to 2904 computations (41.3% saved)

localize25.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 4 (.f64 a (pow.f64 b 2)))
✓	0.2b	(*.f64 12 (pow.f64 b 2))
✓	0.2b	(*.f64 a (pow.f64 b 2))
✓	2.2b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series33.0ms (1%)

Counts

4 → 0

Calls

4 calls:

11.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))
10.0ms	(.f64 4 (.f64 a (pow.f64 b 2)))
9.0ms	(*.f64 a (pow.f64 b 2))
2.0ms	(*.f64 12 (pow.f64 b 2))

rewrite27.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
36×	`add-exp-log_binary64`
25×	`associate-r_binary64`
24×	`unswap-sqr_binary64`
22×	`unpow-prod-down_binary64`

Counts

4 → 132

Calls

4 calls:

7.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))
5.0ms	(.f64 4 (.f64 a (pow.f64 b 2)))
4.0ms	(*.f64 12 (pow.f64 b 2))
4.0ms	(*.f64 a (pow.f64 b 2))

simplify88.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-def_binary64`
369×	`*-commutative_binary64`
303×	`sqr-pow_binary64`
237×	`associate-/l/_binary64`
230×	`exp-prod_binary64`

Counts

132 → 186

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	162	1455
1	295	1266
2	859	1241
3	1567	1178
4	2616	1178
5	4804	1178
6	4941	1178

prune325.0ms (10.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	186	3	189

Error

Counts

189 → 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))
✓	0.0b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 1 (*.f64 4 (pow.f64 a 3))))
▶	0.1b	(-.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 9560 to 7372 computations (22.9% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.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)))))
✓	0.0b	(.f64 (.f64 a a) (-.f64 1 a))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
✓	0.3b	(.f64 (.f64 b b) (+.f64 3 a))

series52.0ms (1.6%)

Counts

4 → 84

Calls

4 calls:

27.0ms	(+.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)))))
14.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
8.0ms	(.f64 (.f64 b b) (+.f64 3 a))
3.0ms	(.f64 (.f64 a a) (-.f64 1 a))

rewrite35.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
24×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
15×	`distribute-lft-in_binary64`

Counts

4 → 121

Calls

4 calls:

8.0ms	(+.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)))))
8.0ms	(.f64 (.f64 b b) (+.f64 3 a))
8.0ms	(.f64 (.f64 a a) (-.f64 1 a))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify91.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

511×	`associate-+l+_binary64`
383×	`associate-l_binary64`
299×	`associate-r_binary64`
268×	`cancel-sign-sub-inv_binary64`
211×	`unswap-sqr_binary64`

Counts

205 → 209

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	241	3743
1	600	3419
2	2388	3054
3	4882	3054

prune272.0ms (8.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	209	0	209
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	209	3	212

Error

Counts

212 → 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))
✓	0.0b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 1 (*.f64 4 (pow.f64 a 3))))
✓	0.1b	(-.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 7714 to 3959 computations (48.7% saved)

regimes557.0ms (17.5%)

Accuracy

Total 0.0b remaining (49.1%)

Threshold costs 0.0b (49.1%)

Counts

97 → 1

Compiler

Compiled 14176 to 9792 computations (30.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	53
1	39	53
2	43	53
3	45	53
4	46	53
5	44	53

end1.0ms (0%)

Compiler: Compiled 38 to 25 computations (34.2% saved)

sample932.0ms (29.3%)

Algorithm

1×

intervals

Results

607.0ms	8000×	body	128	valid
1.0ms	7×	body	128	invalid

Compiler

Compiled 175 to 121 computations (30.9% saved)

Details

analyze157.0ms (4.9%)

sample97.0ms (3.1%)

simplify58.0ms (1.8%)

prune5.0ms (0.1%)

localize14.0ms (0.4%)

series91.0ms (2.9%)

rewrite16.0ms (0.5%)

simplify78.0ms (2.5%)

prune212.0ms (6.7%)

localize25.0ms (0.8%)

series33.0ms (1%)

rewrite27.0ms (0.9%)

simplify88.0ms (2.8%)

prune325.0ms (10.2%)

localize15.0ms (0.5%)

series52.0ms (1.6%)

rewrite35.0ms (1.1%)

simplify91.0ms (2.9%)

prune272.0ms (8.5%)

regimes557.0ms (17.5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample932.0ms (29.3%)

Profiling