Details

analyze173.0ms (3.7%)

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)

sample1.4s (29.3%)

Results

1.3s	8256×	body	128	valid
1.0ms	7×	body	128	invalid

Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify60.0ms (1.3%)

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)

localize18.0ms (0.4%)

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	(pow.f64 (hypot.f64 a b) 4)
✓	0.1b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	1.3b	(.f64 (.f64 b b) (+.f64 a 3))

series101.0ms (2.1%)

Counts

4 → 96

Calls

4 calls:

40.0ms	(pow.f64 (hypot.f64 a b) 4)
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))
13.0ms	(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 (0.4%)

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:

6.0ms	(.f64 (.f64 b b) (+.f64 a 3))
6.0ms	(+.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)))

simplify85.0ms (1.8%)

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

prune258.0ms (5.5%)

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

0.0b

Counts

164 → 3

Alt Table

Status	Error	Program
	2.0b	(expm1.f64 (log1p.f64 (+.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	(+.f64 (+.f64 (fma.f64 2 (.f64 a (.f64 a (.f64 b b))) (pow.f64 b 4)) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
	0.1b	(+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 (.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))

Compiler

Compiled 5000 to 2923 computations (41.5% saved)

localize19.0ms (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)))
✓	0.1b	(.f64 a (.f64 a (*.f64 b b)))
✓	1.2b	(.f64 a (.f64 b b))
	1.3b	(.f64 (.f64 b b) (+.f64 a 3))

series21.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(.f64 a (.f64 a (*.f64 b b)))
8.0ms	(.f64 a (.f64 b b))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

2 → 44

Calls

2 calls:

7.0ms	(.f64 a (.f64 a (*.f64 b b)))
4.0ms	(.f64 a (.f64 b b))

simplify74.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

593×	`associate-l_binary64`
566×	`fma-def_binary64`
511×	`unswap-sqr_binary64`
413×	`*-commutative_binary64`
369×	`associate-r_binary64`

Counts

92 → 51

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	57	979
1	125	850
2	375	826
3	1084	808
4	2147	797
5	3407	797
6	4998	797

prune170.0ms (3.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	124	3	127

Error

0.0b

Counts

127 → 3

Alt Table

Status	Error	Program
	2.0b	(expm1.f64 (log1p.f64 (+.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	(+.f64 (+.f64 (fma.f64 2 (.f64 a (.f64 a (.f64 b b))) (pow.f64 b 4)) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
▶	0.1b	(+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 (.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))

Compiler

Compiled 4989 to 2637 computations (47.1% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series33.0ms (0.7%)

Counts

4 → 60

Calls

4 calls:

22.0ms	(.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (*.f64 2 a)))))
4.0ms	(.f64 a (+.f64 4 (.f64 2 a)))
3.0ms	(*.f64 (pow.f64 a 3) (-.f64 a 4))
3.0ms	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
25×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
16×	`associate-l_binary64`

Counts

4 → 126

Calls

4 calls:

10.0ms	(*.f64 (pow.f64 a 3) (-.f64 a 4))
9.0ms	(.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (*.f64 2 a)))))
4.0ms	(.f64 a (+.f64 4 (.f64 2 a)))
0.0ms	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))

simplify120.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

480×	`associate-l_binary64`
455×	`fma-neg_binary64`
439×	`associate-r_binary64`
393×	`exp-prod_binary64`
239×	`cancel-sign-sub-inv_binary64`

Counts

186 → 217

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	275	3597
1	700	2721
2	3127	2717
3	4515	2687
4	4898	2687

prune297.0ms (6.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	217	3	220

Error

0.0b

Counts

220 → 3

Alt Table

Status	Error	Program
▶	2.0b	(expm1.f64 (log1p.f64 (+.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	(+.f64 (+.f64 (fma.f64 2 (.f64 a (.f64 a (.f64 b b))) (pow.f64 b 4)) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
✓	0.1b	(+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 (.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))

Compiler

Compiled 9134 to 5808 computations (36.4% saved)

localize18.0ms (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)))
	1.3b	(.f64 (.f64 b b) (+.f64 a 3))
✓	2.0b	(expm1.f64 (log1p.f64 (+.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))))
✓	2.7b	(log1p.f64 (+.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)))

series141.0ms (3%)

Counts

2 → 48

Calls

2 calls:

100.0ms

(log1p.f64 (+.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)))

40.0ms

(expm1.f64 (log1p.f64 (+.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))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

1.0ms

(log1p.f64 (+.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

(expm1.f64 (log1p.f64 (+.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))))

simplify98.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

398×	`cancel-sign-sub-inv_binary64`
356×	`fma-def_binary64`
329×	`associate-+r+_binary64`
311×	`sub-neg_binary64`
271×	`fma-neg_binary64`

Counts

70 → 100

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	321	4209
1	1009	4010
2	3980	3990
3	5258	3990

prune235.0ms (5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	173	3	176

Error

0.0b

Counts

176 → 3

Alt Table

Status	Error	Program
✓	2.0b	(expm1.f64 (log1p.f64 (+.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	(+.f64 (+.f64 (fma.f64 2 (.f64 a (.f64 a (.f64 b b))) (pow.f64 b 4)) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
✓	0.1b	(+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 (.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))

Compiler

Compiled 7544 to 5010 computations (33.6% saved)

regimes1.2s (25.8%)

Accuracy

Total 0.0b remaining (60.3%)

Threshold costs 0.0b (60.3%)

Counts

202 → 1

Compiler

Compiled 27583 to 19381 computations (29.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`*-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	22	49
1	32	49
2	35	49
3	37	49
4	38	49
5	37	49

end111.0ms (2.3%)

Compiler: Compiled 169 to 111 computations (34.3% saved)

Details

analyze173.0ms (3.7%)

sample1.4s (29.3%)

simplify60.0ms (1.3%)

prune5.0ms (0.1%)

localize18.0ms (0.4%)

series101.0ms (2.1%)

rewrite17.0ms (0.4%)

simplify85.0ms (1.8%)

prune258.0ms (5.5%)

localize19.0ms (0.4%)

series21.0ms (0.4%)

rewrite14.0ms (0.3%)

simplify74.0ms (1.6%)

prune170.0ms (3.6%)

localize18.0ms (0.4%)

series33.0ms (0.7%)

rewrite32.0ms (0.7%)

simplify120.0ms (2.5%)

prune297.0ms (6.3%)

localize18.0ms (0.4%)

series141.0ms (3%)

rewrite2.0ms (0%)

simplify98.0ms (2.1%)

prune235.0ms (5%)

regimes1.2s (25.8%)

simplify3.0ms (0.1%)

end111.0ms (2.3%)

Profiling