Details

analyze159.0ms (4.2%)

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%	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)

sample99.0ms (2.6%)

Algorithm

1×

intervals

Results

21.0ms

256×

body

128

valid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify58.0ms (1.5%)

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
▶	0.0b	(+.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))
	0.2b	(-.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

▶

0.0b

(+.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))

0.2b

(-.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)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 a b)
✓	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)))
✓	0.9b	(.f64 (.f64 b b) (+.f64 a 3))

series68.0ms (1.8%)

Counts

4 → 96

Calls

4 calls:

35.0ms	(pow.f64 (hypot.f64 a b) 4)
12.0ms	(hypot.f64 a b)
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))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

6.0ms	(.f64 (.f64 b b) (+.f64 a 3))
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)))
0.0ms	(hypot.f64 a b)

simplify85.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

510×	`times-frac_binary64`
492×	`fma-def_binary64`
347×	`distribute-rgt-in_binary64`
332×	`distribute-lft-in_binary64`
329×	`fma-neg_binary64`

Counts

162 → 150

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	162	2428
1	400	2268
2	1311	2221
3	4842	2221
4	4990	2221

prune171.0ms (4.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	149	3	152

Error

Counts

152 → 3

Alt Table

Status	Error	Program
	3.5b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (exp.f64 (+.f64 (log.f64 (.f64 b b)) (log.f64 (+.f64 a 3))))) -1))
	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
▶	0.0b	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))

Compiler

Compiled 4588 to 2653 computations (42.2% saved)

localize22.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2)))
	0.1b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
	0.9b	(.f64 (.f64 b b) (+.f64 a 3))
✓	1.4b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series30.0ms (0.8%)

Counts

2 → 0

Calls

2 calls:

17.0ms	(.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2)))
12.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-exp-log_binary64`
28×	`prod-exp_binary64`
23×	`add-sqr-sqrt_binary64`
16×	`unswap-sqr_binary64`
14×	`unpow-prod-down_binary64`

Counts

2 → 80

Calls

2 calls:

6.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))
5.0ms	(.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2)))

simplify74.0ms (2%)

Algorithm

1×	egg-herbie

Rules

957×	`fma-def_binary64`
325×	`*-commutative_binary64`
288×	`associate-/l*_binary64`
285×	`associate-/l/_binary64`
273×	`log-prod_binary64`

Counts

80 → 100

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	106	987
1	188	882
2	593	877
3	1121	805
4	2025	795
5	4769	795
6	4923	795

prune255.0ms (6.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

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

Error

Counts

176 → 3

Alt Table

Status	Error	Program
	3.5b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (exp.f64 (+.f64 (log.f64 (.f64 b b)) (log.f64 (+.f64 a 3))))) -1))
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
✓	0.0b	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))

Compiler

Compiled 7167 to 4683 computations (34.7% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3))
✓	0.0b	(fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b)))
	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.9b	(.f64 (+.f64 3 a) (.f64 b b))

series31.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

13.0ms	(-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3))
9.0ms	(.f64 (+.f64 3 a) (.f64 b b))
9.0ms	(fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b)))

rewrite21.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 104

Calls

3 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))
0.0ms	(fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b)))

simplify134.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

623×	`fma-neg_binary64`
509×	`distribute-rgt-in_binary64`
508×	`distribute-lft-in_binary64`
351×	`exp-prod_binary64`
267×	`cancel-sign-sub-inv_binary64`

Counts

176 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	178	3305
1	309	2999
2	1173	2771
3	4429	2763
4	4807	2763
5	4920	2763

prune224.0ms (5.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	176	3	179

Error

Counts

179 → 3

Alt Table

Status	Error	Program
▶	3.5b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (exp.f64 (+.f64 (log.f64 (.f64 b b)) (log.f64 (+.f64 a 3))))) -1))
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
✓	0.0b	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))

Compiler

Compiled 6159 to 3628 computations (41.1% saved)

localize21.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.2b	(+.f64 (log.f64 (*.f64 b b)) (log.f64 (+.f64 a 3)))
✓	3.2b	(exp.f64 (+.f64 (log.f64 (*.f64 b b)) (log.f64 (+.f64 a 3))))
✓	22.8b	(log.f64 (*.f64 b b))

series642.0ms (17%)

Counts

3 → 60

Calls

3 calls:

356.0ms	(exp.f64 (+.f64 (log.f64 (*.f64 b b)) (log.f64 (+.f64 a 3))))
260.0ms	(+.f64 (log.f64 (*.f64 b b)) (log.f64 (+.f64 a 3)))
25.0ms	(log.f64 (*.f64 b b))

rewrite21.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`pow1_binary64`
26×	`log-pow_binary64`
18×	`*-un-lft-identity_binary64`
13×	`distribute-lft-out_binary64`
9×	`fma-def_binary64`

Counts

3 → 76

Calls

3 calls:

9.0ms	(+.f64 (log.f64 (*.f64 b b)) (log.f64 (+.f64 a 3)))
6.0ms	(exp.f64 (+.f64 (log.f64 (*.f64 b b)) (log.f64 (+.f64 a 3))))
2.0ms	(log.f64 (*.f64 b b))

simplify99.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

587×	`fma-neg_binary64`
489×	`fma-def_binary64`
289×	`associate-+r+_binary64`
279×	`associate-l_binary64`
271×	`sub-neg_binary64`

Counts

136 → 132

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	159	1607
1	382	1470
2	1201	1445
3	3640	1444
4	4965	1444
5	5089	1444

prune182.0ms (4.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	166	3	169

Error

Counts

169 → 3

Alt Table

Status	Error	Program
✓	3.5b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (exp.f64 (+.f64 (log.f64 (.f64 b b)) (log.f64 (+.f64 a 3))))) -1))
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) -1))
✓	0.0b	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))

Compiler

Compiled 5354 to 3214 computations (40% saved)

regimes296.0ms (7.8%)

Accuracy

Total 0.0b remaining (11.1%)

Threshold costs 0.0b (11.1%)

Counts

53 → 1

Compiler

Compiled 7709 to 5406 computations (29.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-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	23	48
1	34	48
2	37	48
3	39	48
4	40	48
5	39	48

end1.0ms (0%)

Compiler: Compiled 35 to 25 computations (28.6% saved)

sample1.0s (26.9%)

Algorithm

1×

intervals

Results

676.0ms	8000×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 159 to 111 computations (30.2% saved)

Details

analyze159.0ms (4.2%)

sample99.0ms (2.6%)

simplify58.0ms (1.5%)

prune5.0ms (0.1%)

localize15.0ms (0.4%)

series68.0ms (1.8%)

rewrite10.0ms (0.3%)

simplify85.0ms (2.3%)

prune171.0ms (4.5%)

localize22.0ms (0.6%)

series30.0ms (0.8%)

rewrite15.0ms (0.4%)

simplify74.0ms (2%)

prune255.0ms (6.8%)

localize14.0ms (0.4%)

series31.0ms (0.8%)

rewrite21.0ms (0.6%)

simplify134.0ms (3.6%)

prune224.0ms (5.9%)

localize21.0ms (0.6%)

series642.0ms (17%)

rewrite21.0ms (0.6%)

simplify99.0ms (2.6%)

prune182.0ms (4.8%)

regimes296.0ms (7.8%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.0s (26.9%)

Profiling