Details

analyze198.0ms (3.2%)

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%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 34 to 22 computations (35.3% saved)

sample89.0ms (1.5%)

Algorithm

1×

intervals

Results

25.0ms

256×

body

128

valid

Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify68.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-def_binary64`
669×	`unsub-neg_binary64`
596×	`cancel-sign-sub-inv_binary64`
340×	`+-commutative_binary64`
277×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	42
1	63	40
2	170	36
3	542	36
4	1867	32
5	3281	32
6	4881	32
7	4958	32

prune6.0ms (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
	0.2b	(-.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 1 (.f64 3 a)))))) 1)
▶	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Status

Error

Program

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 1 (*.f64 3 a)))))) 1)

▶

0.0b

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

Compiler

Compiled 172 to 108 computations (37.2% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.0b	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
✓	0.1b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
✓	0.2b	(.f64 (.f64 b b) (fma.f64 a -3 1))

series99.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

39.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
36.0ms	(pow.f64 (hypot.f64 a b) 4)
14.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
10.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

6.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
2.0ms	(pow.f64 (hypot.f64 a b) 4)
0.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
0.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))

simplify128.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

821×	`fma-def_binary64`
417×	`fma-neg_binary64`
408×	`associate-+l+_binary64`
315×	`cancel-sign-sub-inv_binary64`
250×	`exp-prod_binary64`

Counts

159 → 140

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	149	3218
1	364	2814
2	1065	2628
3	3367	2622
4	4754	2618
5	4990	2618

prune245.0ms (4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	137	3	140
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	139	3	142

Error

Counts

142 → 3

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))))) (.f64 12 (*.f64 a (pow.f64 b 2)))) -1)
	0.2b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) -1)
	0.4b	(+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) -1)

Compiler

Compiled 4229 to 2340 computations (44.7% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 4 (pow.f64 b 2))
✓	0.2b	(.f64 12 (.f64 a (pow.f64 b 2)))
✓	0.3b	(*.f64 a (pow.f64 b 2))
✓	1.3b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series39.0ms (0.6%)

Counts

4 → 0

Calls

4 calls:

13.0ms	(.f64 12 (.f64 a (pow.f64 b 2)))
12.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))
11.0ms	(*.f64 a (pow.f64 b 2))
3.0ms	(*.f64 4 (pow.f64 b 2))

rewrite39.0ms (0.6%)

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:

16.0ms	(*.f64 a (pow.f64 b 2))
6.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))
5.0ms	(.f64 12 (.f64 a (pow.f64 b 2)))
4.0ms	(*.f64 4 (pow.f64 b 2))

simplify94.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-def_binary64`
370×	`*-commutative_binary64`
304×	`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	1439
1	295	1250
2	861	1225
3	1569	1162
4	2619	1162
5	4814	1162
6	4897	1162

prune377.0ms (6.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	186	3	189

Error

Counts

189 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))))) (.f64 12 (*.f64 a (pow.f64 b 2)))) -1)
▶	0.2b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) -1)
	0.4b	(+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) -1)

Compiler

Compiled 9673 to 7426 computations (23.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2))
	0.1b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
	0.2b	(.f64 (.f64 b b) (fma.f64 a -3 1))
✓	0.4b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series40.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

25.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2))
15.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`add-exp-log_binary64`
3×	`pow1_binary64`

Counts

2 → 30

Calls

2 calls:

4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2))

simplify103.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

599×	`fma-def_binary64`
590×	`unswap-sqr_binary64`
490×	`cancel-sign-sub-inv_binary64`
404×	`associate-+l+_binary64`
319×	`exp-prod_binary64`

Counts

78 → 79

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	1914
1	236	1771
2	662	1521
3	2687	1517
4	4555	1517
5	4703	1517
6	5117	1517

prune184.0ms (3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	145	3	148

Error

Counts

148 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))))) (.f64 12 (*.f64 a (pow.f64 b 2)))) -1)
✓	0.2b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) -1)
▶	0.4b	(+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) -1)

Compiler

Compiled 4778 to 2368 computations (50.4% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f64 (.f64 b b) (fma.f64 a -3 1))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))))
✓	0.4b	(.f64 (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))))
✓	10.2b	(cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))

series604.0ms (9.8%)

Counts

3 → 72

Calls

3 calls:

409.0ms

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

157.0ms

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

37.0ms

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

rewrite27.0ms (0.4%)

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:

7.0ms

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

7.0ms

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

1.0ms

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

simplify233.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

507×	`associate-+l+_binary64`
310×	`*-commutative_binary64`
201×	`+-commutative_binary64`
185×	`associate--l+_binary64`
181×	`fma-def_binary64`

Counts

165 → 192

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	782	13856
1	2470	12464
2	4957	12460
3	5050	12460

prune1.1s (17.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	401	0	401
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	401	3	404

Error

Counts

404 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))))) (.f64 12 (*.f64 a (pow.f64 b 2)))) -1)
✓	0.2b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) -1)
✓	0.4b	(+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) (cbrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) -1)

Compiler

Compiled 41951 to 25596 computations (39% saved)

regimes1.2s (19.8%)

Accuracy

Total 0.0b remaining (45.9%)

Threshold costs 0.0b (45.9%)

Counts

191 → 1

Compiler

Compiled 30071 to 19702 computations (34.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
11×	`*-commutative_binary64`
5×	`sub-neg_binary64`
4×	`distribute-lft-neg-in_binary64`
4×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	67
1	46	67
2	53	67
3	63	67
4	70	67
5	75	67
6	77	67
7	76	67

end1.0ms (0%)

Compiler: Compiled 47 to 38 computations (19.1% saved)

sample1.2s (19.4%)

Algorithm

1×

intervals

Results

764.0ms	8000×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 231 to 156 computations (32.5% saved)

Details

analyze198.0ms (3.2%)

sample89.0ms (1.5%)

simplify68.0ms (1.1%)

prune6.0ms (0.1%)

localize16.0ms (0.3%)

series99.0ms (1.6%)

rewrite11.0ms (0.2%)

simplify128.0ms (2.1%)

prune245.0ms (4%)

localize25.0ms (0.4%)

series39.0ms (0.6%)

rewrite39.0ms (0.6%)

simplify94.0ms (1.5%)

prune377.0ms (6.1%)

localize15.0ms (0.2%)

series40.0ms (0.6%)

rewrite6.0ms (0.1%)

simplify103.0ms (1.7%)

prune184.0ms (3%)

localize18.0ms (0.3%)

series604.0ms (9.8%)

rewrite27.0ms (0.4%)

simplify233.0ms (3.8%)

prune1.1s (17.4%)

regimes1.2s (19.8%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.2s (19.4%)

Profiling