Details

analyze167.0ms (3.1%)

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 (24.2%)

Results

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

Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify58.0ms (1.1%)

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)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	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	(hypot.f64 a b)
✓	0.1b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	0.4b	(.f64 (.f64 b b) (+.f64 a 3))

series107.0ms (2%)

Counts

4 → 96

Calls

4 calls:

50.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
38.0ms	(+.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))
11.0ms	(hypot.f64 a b)
8.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite14.0ms (0.2%)

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)

simplify84.0ms (1.5%)

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

prune175.0ms (3.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	171	3	174

Error

Counts

174 → 3

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))
	13.1b	(/.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 5459 to 3235 computations (40.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series47.0ms (0.9%)

Counts

4 → 84

Calls

4 calls:

16.0ms	(.f64 (.f64 b b) (+.f64 3 a))
15.0ms	(+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (.f64 b b) (+.f64 3 a)))
13.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
3.0ms	(.f64 (.f64 a a) (-.f64 1 a))

rewrite45.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64`
41×	`add-sqr-sqrt_binary64`
36×	`prod-diff_binary64`
36×	`add-cube-cbrt_binary64`
28×	`distribute-lft-in_binary64`

Counts

4 → 144

Calls

4 calls:

14.0ms	(+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (.f64 b b) (+.f64 3 a)))
11.0ms	(.f64 (.f64 a a) (-.f64 1 a))
6.0ms	(.f64 (.f64 b b) (+.f64 3 a))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify125.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

522×	`fma-neg_binary64`
433×	`associate-l_binary64`
332×	`associate-r_binary64`
297×	`exp-prod_binary64`
271×	`cancel-sign-sub-inv_binary64`

Counts

228 → 241

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	249	3731
1	593	3518
2	2645	3152
3	4505	3144
4	4945	3144

prune371.0ms (6.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	241	0	241
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	241	3	244

Error

Counts

244 → 3

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))
▶	13.1b	(/.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 9582 to 4744 computations (50.5% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.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))
✓	0.4b	(.f64 (+.f64 3 a) (.f64 b b))
✓	3.8b	(-.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)))
✓	12.2b	(/.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)))

series647.0ms (11.8%)

Counts

4 → 96

Calls

4 calls:

546.0ms	(/.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)))
41.0ms	(.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))
9.0ms	(.f64 (+.f64 3 a) (.f64 b b))

rewrite51.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`add-sqr-sqrt_binary64`
48×	`difference-of-squares_binary64`
44×	`*-un-lft-identity_binary64`
42×	`times-frac_binary64`
28×	`add-cube-cbrt_binary64`

Counts

4 → 160

Calls

4 calls:

10.0ms	(/.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)))
6.0ms	(.f64 (+.f64 3 a) (.f64 b b))
4.0ms	(.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))
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)))

simplify377.0ms (6.9%)

Algorithm

1×	egg-herbie

Rules

583×	`times-frac_binary64`
342×	`+-commutative_binary64`
298×	`fma-def_binary64`
294×	`associate-+r+_binary64`
210×	`*-commutative_binary64`

Counts

256 → 353

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1037	26974
1	3319	26095
2	4986	26095

prune1.1s (20.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	439	0	439
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	439	3	442

Error

Counts

442 → 3

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))
✓	13.1b	(/.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 48363 to 31082 computations (35.7% saved)

regimes569.0ms (10.4%)

Accuracy

Total 0.0b remaining (60.2%)

Threshold costs 0.0b (60.2%)

Counts

85 → 1

Compiler

Compiled 16611 to 11273 computations (32.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-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	17	33
1	24	33
2	27	33
3	29	33
4	30	33
5	29	33

end105.0ms (1.9%)

Compiler: Compiled 173 to 112 computations (35.3% saved)

Details

analyze167.0ms (3.1%)

sample1.3s (24.2%)

simplify58.0ms (1.1%)

prune5.0ms (0.1%)

localize17.0ms (0.3%)

series107.0ms (2%)

rewrite14.0ms (0.2%)

simplify84.0ms (1.5%)

prune175.0ms (3.2%)

localize14.0ms (0.2%)

series47.0ms (0.9%)

rewrite45.0ms (0.8%)

simplify125.0ms (2.3%)

prune371.0ms (6.8%)

localize21.0ms (0.4%)

series647.0ms (11.8%)

rewrite51.0ms (0.9%)

simplify377.0ms (6.9%)

prune1.1s (20.8%)

regimes569.0ms (10.4%)

simplify3.0ms (0.1%)

end105.0ms (1.9%)

Profiling