Details

analyze191.0ms (5%)

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)

sample1.4s (36.8%)

Results

1.3s	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 101 to 65 computations (35.6% saved)

simplify63.0ms (1.7%)

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

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
	0.2b	(-.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)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.0b	(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))
✓	0.0b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
✓	0.5b	(.f64 (.f64 b b) (fma.f64 a -3 1))

series103.0ms (2.7%)

Counts

4 → 96

Calls

4 calls:

40.0ms	(pow.f64 (hypot.f64 a b) 4)
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))
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))

rewrite9.0ms (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:

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

simplify122.0ms (3.2%)

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

prune159.0ms (4.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	137	3	140
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	138	4	142

Error

Counts

142 → 4

Alt Table

Status	Error	Program
	10.3b	(+.f64 (*.f64 (pow.f64 a 3) (+.f64 4 a)) -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 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))) -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)
	13.8b	(+.f64 (cbrt.f64 (pow.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)) 3)) -1)

Compiler

Compiled 4092 to 2262 computations (44.7% saved)

localize17.0ms (0.4%)

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 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)))
	0.0b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
✓	0.3b	(pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))
	0.5b	(.f64 (.f64 b b) (fma.f64 a -3 1))

series75.0ms (2%)

Counts

2 → 48

Calls

2 calls:

38.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)))
37.0ms	(pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`unpow-prod-down_binary64`
6×	`pow-unpow_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 39

Calls

2 calls:

3.0ms	(pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))
0.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)))

simplify98.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

637×	`fma-neg_binary64`
598×	`fma-def_binary64`
490×	`cancel-sign-sub-inv_binary64`
402×	`associate-+l+_binary64`
273×	`distribute-lft-out_binary64`

Counts

87 → 87

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	112	2078
1	273	1827
2	726	1634
3	2823	1611
4	4642	1585
5	4906	1585

prune174.0ms (4.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	153	4	157

Error

Counts

157 → 4

Alt Table

Status	Error	Program
▶	10.3b	(+.f64 (*.f64 (pow.f64 a 3) (+.f64 4 a)) -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 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))) -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)
	13.8b	(+.f64 (cbrt.f64 (pow.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)) 3)) -1)

Compiler

Compiled 4833 to 2820 computations (41.7% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (pow.f64 a 3) (+.f64 4 a))

series11.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(*.f64 (pow.f64 a 3) (+.f64 4 a))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-l_binary64`
12×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
6×	`add-exp-log_binary64`
5×	`add-cube-cbrt_binary64`

Counts

1 → 38

Calls

1 calls:

7.0ms

(*.f64 (pow.f64 a 3) (+.f64 4 a))

simplify63.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

971×	`fma-def_binary64`
348×	`sqr-pow_binary64`
340×	`*-commutative_binary64`
308×	`associate-+l+_binary64`
297×	`associate-+r+_binary64`

Counts

50 → 47

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	623
1	178	591
2	818	591
3	2091	567
4	4420	567
5	5174	567

prune59.0ms (1.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	47	4	51

Error

Counts

51 → 4

Alt Table

Status	Error	Program
✓	10.3b	(+.f64 (*.f64 (pow.f64 a 3) (+.f64 4 a)) -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 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))) -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)
▶	13.8b	(+.f64 (cbrt.f64 (pow.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)) 3)) -1)

Compiler

Compiled 827 to 625 computations (24.4% saved)

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b)))
✓	0.2b	(pow.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)) 3)
✓	0.5b	(.f64 (fma.f64 a -3 1) (.f64 b b))
✓	33.3b	(cbrt.f64 (pow.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)) 3))

series223.0ms (5.8%)

Counts

4 → 96

Calls

4 calls:

160.0ms	(pow.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)) 3)
40.0ms	(cbrt.f64 (pow.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)) 3))
13.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b)))
10.0ms	(.f64 (fma.f64 a -3 1) (.f64 b b))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
12×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
10×	`add-cbrt-cube_binary64`

Counts

4 → 79

Calls

4 calls:

4.0ms	(.f64 (fma.f64 a -3 1) (.f64 b b))
2.0ms	(cbrt.f64 (pow.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)) 3))
2.0ms	(pow.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)) 3)
0.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b)))

simplify155.0ms (4%)

Algorithm

1×	egg-herbie

Rules

548×	`fma-def_binary64`
496×	`associate-+r+_binary64`
323×	`associate-+l+_binary64`
314×	`+-commutative_binary64`
298×	`associate-r_binary64`

Counts

175 → 182

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	363	6307
1	1116	5502
2	4457	5478
3	4929	5478
4	4954	5478

prune251.0ms (6.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	182	4	186

Error

Counts

186 → 4

Alt Table

Status	Error	Program
✓	10.3b	(+.f64 (*.f64 (pow.f64 a 3) (+.f64 4 a)) -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 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))) -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)
✓	13.8b	(+.f64 (cbrt.f64 (pow.f64 (fma.f64 (fma.f64 a (fma.f64 a a a) (.f64 (fma.f64 a -3 1) (.f64 b b))) 4 (pow.f64 (hypot.f64 a b) 4)) 3)) -1)

Compiler

Compiled 7444 to 4751 computations (36.2% saved)

regimes475.0ms (12.4%)

Accuracy

Total 0.0b remaining (64.4%)

Threshold costs 0.0b (64.4%)

Counts

85 → 1

Compiler

Compiled 9325 to 6799 computations (27.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	14	25
2	14	25

end102.0ms (2.7%)

Compiler: Compiled 132 to 89 computations (32.6% saved)

Details

analyze191.0ms (5%)

sample1.4s (36.8%)

simplify63.0ms (1.7%)

prune5.0ms (0.1%)

localize13.0ms (0.4%)

series103.0ms (2.7%)

rewrite9.0ms (0.2%)

simplify122.0ms (3.2%)

prune159.0ms (4.2%)

localize17.0ms (0.4%)

series75.0ms (2%)

rewrite5.0ms (0.1%)

simplify98.0ms (2.6%)

prune174.0ms (4.6%)

localize5.0ms (0.1%)

series11.0ms (0.3%)

rewrite9.0ms (0.2%)

simplify63.0ms (1.6%)

prune59.0ms (1.5%)

localize20.0ms (0.5%)

series223.0ms (5.8%)

rewrite12.0ms (0.3%)

simplify155.0ms (4%)

prune251.0ms (6.6%)

regimes475.0ms (12.4%)

simplify2.0ms (0.1%)

end102.0ms (2.7%)

Profiling