Details

analyze159.0ms (4.4%)

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)

sample97.0ms (2.7%)

Algorithm

1×

intervals

Results

20.0ms

256×

body

128

valid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify59.0ms (1.6%)

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

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

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))

Compiler

Compiled 104 to 66 computations (36.5% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 a b)
✓	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)))
✓	0.8b	(.f64 (.f64 b b) (+.f64 a 3))

series67.0ms (1.8%)

Counts

4 → 96

Calls

4 calls:

35.0ms	(+.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))
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))

rewrite15.0ms (0.4%)

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)

simplify79.0ms (2.2%)

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

prune180.0ms (4.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	169	3	172
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	169	4	173

Error

0.0b

Counts

173 → 4

Alt Table

Status	Error	Program
▶	0.5b	(fma.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.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))
	2.1b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) -1))
	12.2b	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -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 5415 to 3215 computations (40.6% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.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))
✓	0.4b	(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)))
	0.8b	(.f64 (.f64 b b) (+.f64 a 3))
✓	20.9b	(cbrt.f64 (pow.f64 (hypot.f64 a b) 4))

series204.0ms (5.6%)

Counts

3 → 72

Calls

3 calls:

94.0ms

(fma.f64 (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.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))

59.0ms

(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)))

51.0ms

(cbrt.f64 (pow.f64 (hypot.f64 a b) 4))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`cbrt-prod_binary64`
41×	`add-sqr-sqrt_binary64`
23×	`unpow-prod-down_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`

Counts

3 → 93

Calls

3 calls:

9.0ms

(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)))

1.0ms

(cbrt.f64 (pow.f64 (hypot.f64 a b) 4))

0.0ms

(fma.f64 (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.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))

simplify195.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

602×	`fma-neg_binary64`
469×	`associate--l+_binary64`
411×	`associate-+r+_binary64`
370×	`*-commutative_binary64`
347×	`cancel-sign-sub-inv_binary64`

Counts

165 → 189

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	240	4987
1	608	4674
2	1856	4335
3	3889	4280
4	4821	4216
5	4995	4216
6	4917	4216

prune433.0ms (11.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	309	1	310
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	310	4	314

Error

0.0b

Counts

314 → 4

Alt Table

Status	Error	Program
✓	0.5b	(fma.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.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))
▶	2.1b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) -1))
	12.2b	(fma.f64 4 (*.f64 a a) (fma.f64 (pow.f64 a 3) (+.f64 a -4) -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 13958 to 8247 computations (40.9% 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	(hypot.f64 a b)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) -1))
✓	0.8b	(.f64 (+.f64 3 a) (.f64 b b))

series81.0ms (2.2%)

Counts

3 → 72

Calls

3 calls:

37.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) -1))
36.0ms	(pow.f64 (hypot.f64 a b) 4)
8.0ms	(.f64 (+.f64 3 a) (.f64 b b))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
8×	`add-cube-cbrt_binary64`

Counts

3 → 66

Calls

3 calls:

6.0ms	(.f64 (+.f64 3 a) (.f64 b b))
4.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) -1))
2.0ms	(pow.f64 (hypot.f64 a b) 4)

simplify95.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

683×	`fma-def_binary64`
551×	`associate-l_binary64`
453×	`associate-r_binary64`
407×	`associate-+l+_binary64`
354×	`fma-neg_binary64`

Counts

138 → 126

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	142	2575
1	367	2404
2	1105	2216
3	4637	2212
4	4976	2212

prune181.0ms (5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	168	4	172

Error

0.0b

Counts

172 → 4

Alt Table

Status	Error	Program
✓	0.5b	(fma.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.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))
✓	2.1b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) -1))
▶	12.2b	(fma.f64 4 (*.f64 a a) (fma.f64 (pow.f64 a 3) (+.f64 a -4) -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 4571 to 2712 computations (40.7% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (*.f64 a a) (fma.f64 (pow.f64 a 3) (+.f64 a -4) -1))
✓	0.1b	(fma.f64 (pow.f64 a 3) (+.f64 a -4) -1)

series6.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(fma.f64 (pow.f64 a 3) (+.f64 a -4) -1)
3.0ms	(fma.f64 4 (*.f64 a a) (fma.f64 (pow.f64 a 3) (+.f64 a -4) -1))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 (pow.f64 a 3) (+.f64 a -4) -1)
0.0ms	(fma.f64 4 (*.f64 a a) (fma.f64 (pow.f64 a 3) (+.f64 a -4) -1))

simplify65.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

778×	`fma-neg_binary64`
720×	`fma-def_binary64`
515×	`exp-prod_binary64`
412×	`cancel-sign-sub-inv_binary64`
254×	`unswap-sqr_binary64`

Counts

44 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	708
1	100	599
2	244	593
3	979	550
4	2460	550
5	4802	550
6	5055	550

prune53.0ms (1.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	44	1	45
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	44	5	49

Error

Counts

49 → 5

Alt Table

Status	Error	Program
✓	0.5b	(fma.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.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))
	12.2b	(fma.f64 a (*.f64 a (fma.f64 a (+.f64 a -4) 4)) -1)
✓	2.1b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) -1))
✓	12.2b	(fma.f64 4 (*.f64 a a) (fma.f64 (pow.f64 a 3) (+.f64 a -4) -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 871 to 591 computations (32.1% saved)

regimes551.0ms (15.1%)

Accuracy

Total 0.0b remaining (47.5%)

Threshold costs 0.0b (47.5%)

Counts

100 → 1

Compiler

Compiled 12354 to 8626 computations (30.2% 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

end2.0ms (0.1%)

Compiler: Compiled 25 to 17 computations (32% saved)

sample1.0s (28.1%)

Algorithm

1×

intervals

Results

663.0ms	8000×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 172 to 115 computations (33.1% saved)

Details

analyze159.0ms (4.4%)

sample97.0ms (2.7%)

simplify59.0ms (1.6%)

prune4.0ms (0.1%)

localize13.0ms (0.4%)

series67.0ms (1.8%)

rewrite15.0ms (0.4%)

simplify79.0ms (2.2%)

prune180.0ms (4.9%)

localize18.0ms (0.5%)

series204.0ms (5.6%)

rewrite20.0ms (0.5%)

simplify195.0ms (5.4%)

prune433.0ms (11.9%)

localize13.0ms (0.4%)

series81.0ms (2.2%)

rewrite15.0ms (0.4%)

simplify95.0ms (2.6%)

prune181.0ms (5%)

localize7.0ms (0.2%)

series6.0ms (0.2%)

rewrite7.0ms (0.2%)

simplify65.0ms (1.8%)

prune53.0ms (1.4%)

regimes551.0ms (15.1%)

simplify3.0ms (0.1%)

end2.0ms (0.1%)

sample1.0s (28.1%)

Profiling