Details

analyze182.0ms (2.7%)

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)

sample1.3s (19.6%)

Results

1.2s	8256×	body	128	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify59.0ms (0.9%)

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 (0.1%)

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 3 a))))) 1)
▶	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))

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 3 a))))) 1)

▶

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))

Compiler

Compiled 166 to 104 computations (37.3% saved)

localize13.0ms (0.2%)

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)))
✓	1.0b	(.f64 (.f64 b b) (+.f64 a 3))

series89.0ms (1.3%)

Counts

4 → 96

Calls

4 calls:

37.0ms	(+.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))
32.0ms	(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))

rewrite17.0ms (0.3%)

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:

8.0ms	(.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)))

simplify82.0ms (1.2%)

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

prune186.0ms (2.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	161	3	164

Error

Counts

164 → 3

Alt Table

Status	Error	Program
	13.4b	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))
▶	0.0b	(+.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4)) -1)
	13.3b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))

Compiler

Compiled 4986 to 2915 computations (41.5% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series95.0ms (1.4%)

Counts

4 → 96

Calls

4 calls:

37.0ms	(fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4))
37.0ms	(+.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4)) -1)
13.0ms	(-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3))
8.0ms	(.f64 (+.f64 3 a) (.f64 b b))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
36×	`prod-diff_binary64`
31×	`add-cube-cbrt_binary64`
13×	`cube-prod_binary64`

Counts

4 → 123

Calls

4 calls:

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

simplify156.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

750×	`fma-neg_binary64`
642×	`distribute-rgt-in_binary64`
535×	`cancel-sign-sub-inv_binary64`
249×	`unswap-sqr_binary64`
173×	`distribute-rgt-out_binary64`

Counts

219 → 209

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	255	5599
1	546	5141
2	2015	4716
3	4904	4699
4	5196	4699

prune289.0ms (4.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	208	1	209
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	209	3	212

Error

Counts

212 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4)) -1)
	13.4b	(+.f64 (fma.f64 4 (.f64 a a) (.f64 (pow.f64 a 3) (-.f64 a 4))) -1)
▶	13.3b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))

Compiler

Compiled 7565 to 4560 computations (39.7% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1))
	1.0b	(.f64 (+.f64 3 a) (.f64 b b))
✓	3.4b	(-.f64 (pow.f64 (hypot.f64 a b) 8) (.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))
✓	12.4b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))

series621.0ms (9.2%)

Counts

3 → 72

Calls

3 calls:

530.0ms

(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (*.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))

50.0ms

(-.f64 (pow.f64 (hypot.f64 a b) 8) (*.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))

40.0ms

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

rewrite43.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`add-sqr-sqrt_binary64`
48×	`difference-of-squares_binary64`
42×	`times-frac_binary64`
40×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`

Counts

3 → 136

Calls

3 calls:

9.0ms

(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (*.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))

4.0ms

(-.f64 (pow.f64 (hypot.f64 a b) 8) (*.f64 (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (*.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))

3.0ms

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

simplify423.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

559×	`times-frac_binary64`
338×	`+-commutative_binary64`
297×	`fma-def_binary64`
293×	`associate-+r+_binary64`
198×	`*-commutative_binary64`

Counts

208 → 310

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	997	26410
1	3221	25576
2	4998	25576
3	4949	25576

prune1.6s (23.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	436	0	436
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	436	3	439

Error

Counts

439 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4)) -1)
▶	13.4b	(+.f64 (fma.f64 4 (.f64 a a) (.f64 (pow.f64 a 3) (-.f64 a 4))) -1)
✓	13.3b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))

Compiler

Compiled 48160 to 30997 computations (35.6% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series7.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(fma.f64 4 (.f64 a a) (.f64 (pow.f64 a 3) (-.f64 a 4)))
3.0ms	(*.f64 (pow.f64 a 3) (-.f64 a 4))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 73

Calls

2 calls:

9.0ms	(*.f64 (pow.f64 a 3) (-.f64 a 4))
0.0ms	(fma.f64 4 (.f64 a a) (.f64 (pow.f64 a 3) (-.f64 a 4)))

simplify85.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

658×	`exp-prod_binary64`
634×	`fma-neg_binary64`
509×	`unswap-sqr_binary64`
356×	`fma-def_binary64`
355×	`*-commutative_binary64`

Counts

97 → 108

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	136	1504
1	233	1217
2	869	1201
3	2217	1177
4	4197	1177
5	5194	1177

prune122.0ms (1.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	108	3	111

Error

Counts

111 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 (pow.f64 (hypot.f64 a b) 4)) -1)
✓	13.4b	(+.f64 (fma.f64 4 (.f64 a a) (.f64 (pow.f64 a 3) (-.f64 a 4))) -1)
✓	13.3b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (*.f64 b b))) (pow.f64 a 3)) 4 -1)))

Compiler

Compiled 2608 to 1851 computations (29% saved)

regimes1.2s (17.7%)

Accuracy

Total 0.0b remaining (66.3%)

Threshold costs 0.0b (66.3%)

Counts

173 → 1

Compiler

Compiled 28363 to 19716 computations (30.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-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	15	30
1	19	30
2	23	30
3	25	30
4	26	30
5	26	30

end101.0ms (1.5%)

Compiler: Compiled 154 to 103 computations (33.1% saved)

Details

analyze182.0ms (2.7%)

sample1.3s (19.6%)

simplify59.0ms (0.9%)

prune5.0ms (0.1%)

localize13.0ms (0.2%)

series89.0ms (1.3%)

rewrite17.0ms (0.3%)

simplify82.0ms (1.2%)

prune186.0ms (2.8%)

localize16.0ms (0.2%)

series95.0ms (1.4%)

rewrite23.0ms (0.3%)

simplify156.0ms (2.3%)

prune289.0ms (4.3%)

localize19.0ms (0.3%)

series621.0ms (9.2%)

rewrite43.0ms (0.6%)

simplify423.0ms (6.3%)

prune1.6s (23.3%)

localize8.0ms (0.1%)

series7.0ms (0.1%)

rewrite14.0ms (0.2%)

simplify85.0ms (1.3%)

prune122.0ms (1.8%)

regimes1.2s (17.7%)

simplify3.0ms (0%)

end101.0ms (1.5%)

Profiling