Details

analyze205.0ms (4.7%)

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)

sample101.0ms (2.3%)

Algorithm

1×

intervals

Results

23.0ms

256×

body

128

valid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify60.0ms (1.4%)

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
▶	0.1b	(+.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

▶

0.1b

(+.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)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 a b)
✓	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)))
✓	0.6b	(.f64 (.f64 b b) (+.f64 a 3))

series68.0ms (1.6%)

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))
13.0ms	(hypot.f64 a b)
11.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
9.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`

Counts

4 → 68

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))
0.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
0.0ms	(hypot.f64 a b)

simplify78.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

510×	`times-frac_binary64`
487×	`distribute-rgt-in_binary64`
460×	`distribute-lft-in_binary64`
304×	`cancel-sign-sub-inv_binary64`
229×	`fma-neg_binary64`

Counts

164 → 172

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	3345
1	567	3091
2	1963	3016
3	5271	3016

prune218.0ms (5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	169	3	172
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	169	5	174

Error

0.0b

Counts

174 → 5

Alt Table

Status	Error	Program
	49.6b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (pow.f64 a 4) (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))))) (.f64 4 (pow.f64 a 3)))
	17.4b	(/.f64 (+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3) (pow.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1) 3)) (+.f64 (.f64 (pow.f64 (hypot.f64 a b) 4) (pow.f64 (hypot.f64 a b) 4)) (-.f64 (.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1)) (.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)))))
	6.3b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (exp.f64 (log.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))))) -1))
✓	0.1b	(+.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 5635 to 3353 computations (40.5% saved)

localize14.0ms (0.3%)

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)))))
✓	0.1b	(.f64 (.f64 a a) (-.f64 1 a))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
✓	0.6b	(.f64 (.f64 b b) (+.f64 3 a))

series54.0ms (1.3%)

Counts

4 → 84

Calls

4 calls:

29.0ms	(+.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)))))
12.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
10.0ms	(.f64 (.f64 b b) (+.f64 3 a))
3.0ms	(.f64 (.f64 a a) (-.f64 1 a))

rewrite33.0ms (0.7%)

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:

9.0ms	(.f64 (.f64 b b) (+.f64 3 a))
7.0ms	(.f64 (.f64 a a) (-.f64 1 a))
6.0ms	(+.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)))))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify129.0ms (3%)

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

prune339.0ms (7.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	208	1	209
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	210	4	214

Error

0.0b

Counts

214 → 4

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 4 (.f64 a a) (*.f64 (pow.f64 a 3) (+.f64 a -4)))) 1)
	17.4b	(/.f64 (+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3) (pow.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1) 3)) (+.f64 (.f64 (pow.f64 (hypot.f64 a b) 4) (pow.f64 (hypot.f64 a b) 4)) (-.f64 (.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1)) (.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)))))
	6.3b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (exp.f64 (log.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))))) -1))
✓	0.1b	(+.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))

Compiler

Compiled 7960 to 4106 computations (48.4% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 a (+.f64 4 (.f64 2 a)))
✓	0.1b	(fma.f64 4 (.f64 a a) (.f64 (pow.f64 a 3) (+.f64 a -4)))
✓	0.1b	(*.f64 (pow.f64 a 3) (+.f64 a -4))
✓	1.4b	(.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (*.f64 2 a)))))

series30.0ms (0.7%)

Counts

4 → 60

Calls

4 calls:

21.0ms	(.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (*.f64 2 a)))))
3.0ms	(fma.f64 4 (.f64 a a) (.f64 (pow.f64 a 3) (+.f64 a -4)))
3.0ms	(*.f64 (pow.f64 a 3) (+.f64 a -4))
3.0ms	(.f64 a (+.f64 4 (.f64 2 a)))

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
16×	`associate-l_binary64`
16×	`add-exp-log_binary64`
14×	`associate-*r/_binary64`
13×	`*-un-lft-identity_binary64`

Counts

4 → 101

Calls

4 calls:

11.0ms	(.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (*.f64 2 a)))))
6.0ms	(*.f64 (pow.f64 a 3) (+.f64 a -4))
4.0ms	(.f64 a (+.f64 4 (.f64 2 a)))
0.0ms	(fma.f64 4 (.f64 a a) (.f64 (pow.f64 a 3) (+.f64 a -4)))

simplify101.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

494×	`exp-prod_binary64`
481×	`associate-l_binary64`
439×	`associate-r_binary64`
288×	`fma-neg_binary64`
268×	`unswap-sqr_binary64`

Counts

161 → 177

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	225	3098
1	676	2444
2	3162	2442
3	4632	2412
4	5040	2412

prune303.0ms (7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	177	4	181

Error

0.0b

Counts

181 → 4

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 4 (.f64 a a) (*.f64 (pow.f64 a 3) (+.f64 a -4)))) 1)
	17.4b	(/.f64 (+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3) (pow.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1) 3)) (+.f64 (.f64 (pow.f64 (hypot.f64 a b) 4) (pow.f64 (hypot.f64 a b) 4)) (-.f64 (.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1)) (.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)))))
▶	6.3b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (exp.f64 (log.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))))) -1))
✓	0.1b	(+.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))

Compiler

Compiled 7467 to 4661 computations (37.6% saved)

localize16.0ms (0.4%)

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)))
	0.6b	(.f64 (.f64 b b) (+.f64 a 3))
✓	4.0b	(exp.f64 (log.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))))
✓	8.8b	(log.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))))

series58.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

46.0ms	(log.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))))
11.0ms	(exp.f64 (log.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`log-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`exp-prod_binary64`

Counts

2 → 31

Calls

2 calls:

3.0ms	(exp.f64 (log.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))))
1.0ms	(log.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))))

simplify110.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

339×	`cancel-sign-sub-inv_binary64`
314×	`fma-neg_binary64`
247×	`distribute-neg-in_binary64`
244×	`distribute-rgt-in_binary64`
240×	`sub-neg_binary64`

Counts

79 → 112

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	229	2908
1	650	2705
2	2514	2676
3	4689	2673
4	4995	2673
5	4939	2673

prune278.0ms (6.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	185	4	189

Error

0.0b

Counts

189 → 4

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 4 (.f64 a a) (*.f64 (pow.f64 a 3) (+.f64 a -4)))) 1)
	17.4b	(/.f64 (+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3) (pow.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1) 3)) (+.f64 (.f64 (pow.f64 (hypot.f64 a b) 4) (pow.f64 (hypot.f64 a b) 4)) (-.f64 (.f64 (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1)) (.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)))))
✓	6.3b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (exp.f64 (log.f64 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))))) -1))
✓	0.1b	(+.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))

Compiler

Compiled 7051 to 4478 computations (36.5% saved)

regimes1.0s (24.2%)

Accuracy

Total 0.0b remaining (62.2%)

Threshold costs 0.0b (62.2%)

Counts

178 → 1

Compiler

Compiled 27118 to 18530 computations (31.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
3×	`*-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	18	35
1	27	35
2	30	35
3	32	35
4	33	35
5	32	35

end1.0ms (0%)

Compiler: Compiled 26 to 18 computations (30.8% saved)

sample1.0s (23.3%)

Algorithm

1×

intervals

Results

657.0ms	8000×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 247 to 159 computations (35.6% saved)

Details

analyze205.0ms (4.7%)

sample101.0ms (2.3%)

simplify60.0ms (1.4%)

prune5.0ms (0.1%)

localize13.0ms (0.3%)

series68.0ms (1.6%)

rewrite13.0ms (0.3%)

simplify78.0ms (1.8%)

prune218.0ms (5%)

localize14.0ms (0.3%)

series54.0ms (1.3%)

rewrite33.0ms (0.7%)

simplify129.0ms (3%)

prune339.0ms (7.8%)

localize18.0ms (0.4%)

series30.0ms (0.7%)

rewrite33.0ms (0.8%)

simplify101.0ms (2.3%)

prune303.0ms (7%)

localize16.0ms (0.4%)

series58.0ms (1.3%)

rewrite5.0ms (0.1%)

simplify110.0ms (2.5%)

prune278.0ms (6.4%)

regimes1.0s (24.2%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.0s (23.3%)

Profiling