Details

analyze104.0ms (2.2%)

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
12.5%	87.4%	0.1%	5
46.8%	53.1%	0.1%	6
70.2%	29.7%	0.1%	7
76.5%	23.4%	0.1%	8
83.5%	16.4%	0.1%	9
87%	12.9%	0.1%	10
91.1%	8.8%	0.1%	11
93.2%	6.7%	0.1%	12
95.4%	4.5%	0.1%	13
96.5%	3.4%	0.1%	14

Compiler

Compiled 20 to 10 computations (50% saved)

sample935.0ms (20.1%)

Symmetry

(sort x y)

Results

813.0ms

8256×

body

128

valid

Compiler

Compiled 59 to 29 computations (50.8% saved)

simplify141.0ms (3%)

Algorithm

1×	egg-herbie

Rules

985×	`associate-/l*_binary64`
659×	`distribute-lft-out_binary64`
601×	`*-commutative_binary64`
469×	`distribute-rgt-out_binary64`
356×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	39	25
2	135	23
3	474	23
4	1536	23
5	2122	23
6	2589	23
7	2567	23
8	2620	23
9	2677	23
10	2770	23
11	3956	23
12	4088	23
13	4454	23
14	4983	23
15	4968	23
16	4961	23

prune3.0ms (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

21.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	21.0b	(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
	21.1b	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))

Compiler

Compiled 109 to 47 computations (56.9% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))
✓	0.0b	(pow.f64 (+.f64 x y) 3)
✓	20.9b	(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

series89.0ms (1.9%)

Counts

3 → 72

Calls

3 calls:

69.0ms	(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
11.0ms	(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))
8.0ms	(pow.f64 (+.f64 x y) 3)

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 62

Calls

3 calls:

3.0ms	(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
3.0ms	(pow.f64 (+.f64 x y) 3)
0.0ms	(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))

simplify147.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

326×	`fma-def_binary64`
301×	`times-frac_binary64`
297×	`associate-+r+_binary64`
257×	`associate-/l*_binary64`
223×	`+-commutative_binary64`

Counts

134 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	347	4819
1	1047	4272
2	4702	4260
3	4981	4260
4	4996	4260
5	4981	4260

prune187.0ms (4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	156	6	162
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	157	7	164

Error

3.4b

Counts

164 → 7

Alt Table

Status	Error	Program
	12.0b	(/.f64 x (/.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)) y))
	21.1b	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
▶	11.7b	(*.f64 (/.f64 x 1) (/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
	35.3b	(*.f64 (/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))))
	33.5b	(*.f64 (/.f64 x (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (/.f64 y (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
	44.5b	(-.f64 (/.f64 x (.f64 y y)) (fma.f64 3 (/.f64 (.f64 x x) (pow.f64 y 3)) (/.f64 x (pow.f64 y 3))))
	38.6b	(/.f64 y (pow.f64 x 2))

Compiler

Compiled 5941 to 3142 computations (47.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))
	0.0b	(pow.f64 (+.f64 x y) 3)
✓	4.2b	(*.f64 (/.f64 x 1) (/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
✓	9.7b	(/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

series136.0ms (2.9%)

Counts

2 → 48

Calls

2 calls:

70.0ms	(*.f64 (/.f64 x 1) (/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
66.0ms	(/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
26×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`
21×	`add-exp-log_binary64`

Counts

2 → 85

Calls

2 calls:

9.0ms	(*.f64 (/.f64 x 1) (/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
2.0ms	(/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

simplify100.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

428×	`times-frac_binary64`
391×	`associate-/l*_binary64`
391×	`fma-def_binary64`
316×	`associate-/r*_binary64`
246×	`associate-r_binary64`

Counts

133 → 207

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	486	7311
1	1473	6634
2	4981	6634

prune356.0ms (7.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	295	2	297
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	295	9	304

Error

3.4b

Counts

304 → 9

Alt Table

Status	Error	Program
▶	12.0b	(/.f64 x (/.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)) y))
	21.1b	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
	12.0b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 (/.f64 y (fma.f64 (+.f64 y x) (+.f64 y x) (pow.f64 (+.f64 y x) 3))) (cbrt.f64 x)))
✓	11.7b	(*.f64 (/.f64 x 1) (/.f64 y (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))))
	35.3b	(*.f64 (/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))))
	33.5b	(*.f64 (/.f64 x (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (/.f64 y (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
	44.5b	(-.f64 (/.f64 x (.f64 y y)) (fma.f64 3 (/.f64 (.f64 x x) (pow.f64 y 3)) (/.f64 x (pow.f64 y 3))))
	38.6b	(/.f64 y (pow.f64 x 2))
	35.9b	(.f64 (/.f64 x 1) (.f64 (/.f64 1 (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2)))))

Compiler

Compiled 12058 to 6647 computations (44.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))
	0.0b	(pow.f64 (+.f64 x y) 3)
✓	4.5b	(/.f64 x (/.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)) y))
✓	9.4b	(/.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)) y)

series92.0ms (2%)

Counts

2 → 48

Calls

2 calls:

77.0ms	(/.f64 x (/.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)) y))
14.0ms	(/.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)) y)

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 101

Calls

2 calls:

4.0ms	(/.f64 x (/.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)) y))
2.0ms	(/.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)) y)

simplify136.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

303×	`associate-+r+_binary64`
279×	`times-frac_binary64`
257×	`associate-/l*_binary64`
254×	`fma-def_binary64`
225×	`+-commutative_binary64`

Counts

149 → 241

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	413	7037
1	1139	6463
2	4768	6436
3	4985	6436

prune402.0ms (8.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	324	7	331
Fresh	2	5	7
Picked	1	0	1
Done	1	0	1
Total	328	12	340

Error

3.3b

Counts

340 → 12

Alt Table

Status	Error	Program
	35.3b	(*.f64 (/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))))
▶	11.7b	(*.f64 (/.f64 x (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) y)
	35.6b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 (cbrt.f64 x) (/.f64 (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2)) y)))
	33.5b	(*.f64 (/.f64 x (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (/.f64 y (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
	34.0b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) (*.f64 (cbrt.f64 y) (cbrt.f64 y)))) (/.f64 (cbrt.f64 x) (/.f64 (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) (cbrt.f64 y))))
	12.3b	(/.f64 1 (/.f64 (/.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)) y) x))
	32.5b	(/.f64 x (fma.f64 3 (.f64 y x) (+.f64 y (fma.f64 y y (.f64 2 x)))))
	35.9b	(.f64 (/.f64 x 1) (.f64 (/.f64 1 (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2)))))
	35.4b	(*.f64 (/.f64 1 (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 x (/.f64 (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2)) y)))
	32.9b	(/.f64 x (fma.f64 3 (*.f64 y x) (fma.f64 y y y)))
	38.6b	(/.f64 y (pow.f64 x 2))
	21.1b	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))

Compiler

Compiled 11537 to 5310 computations (54% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))
	0.0b	(pow.f64 (+.f64 x y) 3)
✓	4.9b	(*.f64 (/.f64 x (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) y)
✓	9.0b	(/.f64 x (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

series137.0ms (3%)

Counts

2 → 48

Calls

2 calls:

74.0ms	(*.f64 (/.f64 x (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) y)
63.0ms	(/.f64 x (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
19×	`times-frac_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
13×	`associate-l_binary64`

Counts

2 → 63

Calls

2 calls:

4.0ms	(*.f64 (/.f64 x (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) y)
2.0ms	(/.f64 x (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

simplify94.0ms (2%)

Algorithm

1×	egg-herbie

Rules

390×	`fma-def_binary64`
380×	`times-frac_binary64`
330×	`associate-/l*_binary64`
281×	`associate-/r*_binary64`
209×	`associate-r_binary64`

Counts

111 → 154

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	460	6573
1	1429	6005
2	5051	6005

prune312.0ms (6.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	242	2	244
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	242	14	256

Error

3.3b

Counts

256 → 14

Alt Table

Status	Error	Program
	35.3b	(*.f64 (/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))))
✓	11.7b	(*.f64 (/.f64 x (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) y)
	35.6b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 (cbrt.f64 x) (/.f64 (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2)) y)))
	33.5b	(*.f64 (/.f64 x (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (/.f64 y (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
	34.0b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) (*.f64 (cbrt.f64 y) (cbrt.f64 y)))) (/.f64 (cbrt.f64 x) (/.f64 (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))) (cbrt.f64 y))))
	12.3b	(/.f64 1 (/.f64 (/.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)) y) x))
	32.5b	(/.f64 x (fma.f64 3 (.f64 y x) (+.f64 y (fma.f64 y y (.f64 2 x)))))
	35.9b	(.f64 (/.f64 x 1) (.f64 (/.f64 1 (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2)))))
	35.4b	(*.f64 (/.f64 1 (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 x (/.f64 (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2)) y)))
	32.9b	(/.f64 x (fma.f64 3 (*.f64 y x) (fma.f64 y y y)))
	38.7b	(.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2))) (/.f64 (cbrt.f64 x) (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2)))) y)
	38.6b	(*.f64 (/.f64 1 (pow.f64 x 2)) y)
	38.6b	(/.f64 y (pow.f64 x 2))
	21.1b	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))

Compiler

Compiled 10094 to 5572 computations (44.8% saved)

regimes758.0ms (16.3%)

Accuracy

Total 2.3b remaining (33.5%)

Threshold costs 0b (0%)

Counts

166 → 3

Compiler

Compiled 11057 to 5777 computations (47.8% saved)

bsearch53.0ms (1.1%)

Steps

Iters	Range		Point
9	-4.350290783309419e-155	-4.485550809646211e-163	-4.557595512962212e-163
8	-6.095470218273884e+103	-2.8777946570337284e+100	-5.870948528129125e+102

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	79
1	31	79
2	30	79

end381.0ms (8.2%)

Compiler: Compiled 552 to 274 computations (50.4% saved)

Details

analyze104.0ms (2.2%)

sample935.0ms (20.1%)

simplify141.0ms (3%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series89.0ms (1.9%)

rewrite9.0ms (0.2%)

simplify147.0ms (3.2%)

prune187.0ms (4%)

localize8.0ms (0.2%)

series136.0ms (2.9%)

rewrite19.0ms (0.4%)

simplify100.0ms (2.1%)

prune356.0ms (7.7%)

localize11.0ms (0.2%)

series92.0ms (2%)

rewrite15.0ms (0.3%)

simplify136.0ms (2.9%)

prune402.0ms (8.6%)

localize7.0ms (0.1%)

series137.0ms (3%)

rewrite10.0ms (0.2%)

simplify94.0ms (2%)

prune312.0ms (6.7%)

regimes758.0ms (16.3%)

bsearch53.0ms (1.1%)

simplify3.0ms (0.1%)

end381.0ms (8.2%)

Profiling