Details

analyze28.0ms (0.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
50%	50%	0.1%	2
50%	50%	0.1%	3
50%	25%	25.1%	4
50%	25%	25.1%	5
50%	12.5%	37.6%	6
50%	12.5%	37.6%	7
50%	6.2%	43.8%	8
50%	6.2%	43.8%	9
50%	3.1%	46.9%	10
50%	3.1%	46.9%	11
50%	1.6%	48.5%	12
50%	1.6%	48.5%	13
50%	0.8%	49.3%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample892.0ms (27.4%)

Infinites

7% of outputs are infinite.

Results

731.0ms	8256×	body	128	valid
14.0ms	124×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify185.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

1205×	`fma-neg_binary64`
900×	`fma-def_binary64`
326×	`associate-/l*_binary64`
318×	`cancel-sign-sub-inv_binary64`
290×	`distribute-rgt-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	28	18
2	68	18
3	145	16
4	257	16
5	411	16
6	861	16
7	1371	16
8	2386	16
9	2493	16
10	2675	16
11	2607	16
12	2581	16
13	2581	16
14	3531	16
15	3364	16
16	3364	16
17	3364	16
18	3364	16
19	3171	16

prune4.0ms (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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.4b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))

Compiler

Compiled 85 to 66 computations (22.4% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
✓	0.2b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
✓	0.3b	(*.f64 3 (sqrt.f64 x))
✓	0.5b	(/.f64 1 (*.f64 x 9))

series47.0ms (1.4%)

Counts

4 → 48

Calls

4 calls:

30.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
10.0ms	(*.f64 3 (sqrt.f64 x))
5.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
2.0ms	(/.f64 1 (*.f64 x 9))

rewrite33.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
37×	`add-sqr-sqrt_binary64`
30×	`prod-diff_binary64`
29×	`add-cube-cbrt_binary64`
22×	`add-exp-log_binary64`

Counts

4 → 140

Calls

4 calls:

11.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
5.0ms	(*.f64 3 (sqrt.f64 x))
4.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
3.0ms	(/.f64 1 (*.f64 x 9))

simplify76.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

625×	`times-frac_binary64`
456×	`distribute-rgt-in_binary64`
422×	`distribute-lft-in_binary64`
305×	`fma-def_binary64`
290×	`associate-/l*_binary64`

Counts

188 → 171

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	2841
1	412	2251
2	1241	2225
3	5098	2225

prune178.0ms (5.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	163	8	171
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	165	8	173

Error

0.0b

Counts

173 → 8

Alt Table

Status	Error	Program
	0.8b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
▶	0.3b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
	0.4b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y)))
	0.6b	(.f64 (.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	1.3b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 3 (sqrt.f64 x))) (cbrt.f64 (.f64 3 (sqrt.f64 x)))) (cbrt.f64 (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.6b	(.f64 (.f64 (.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.6b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	33.0b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (sqrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))) (sqrt.f64 (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))

Compiler

Compiled 4211 to 3174 computations (24.6% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 3 y -3)
✓	0.1b	(sqrt.f64 (/.f64 1 x))
✓	0.1b	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
✓	0.4b	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

series44.0ms (1.4%)

Counts

4 → 24

Calls

4 calls:

28.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))
10.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
5.0ms	(sqrt.f64 (/.f64 1 x))
1.0ms	(fma.f64 3 y -3)

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
29×	`sqrt-prod_binary64`
22×	`times-frac_binary64`
22×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`

Counts

4 → 87

Calls

4 calls:

7.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
2.0ms	(sqrt.f64 (/.f64 1 x))
0.0ms	(fma.f64 3 y -3)
0.0ms	(fma.f64 (sqrt.f64 x) (fma.f64 3 y -3) (*.f64 1/3 (sqrt.f64 (/.f64 1 x))))

simplify72.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

853×	`associate-+l+_binary64`
393×	`distribute-lft-in_binary64`
393×	`distribute-rgt-in_binary64`
288×	`associate-l_binary64`
263×	`distribute-rgt-out_binary64`

Counts

111 → 116

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	102	1378
1	155	1248
2	265	1247
3	574	1247
4	2181	1247
5	5373	1247

prune142.0ms (4.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	117	7	124

Error

0.0b

Counts

124 → 7

Alt Table

Status	Error	Program
	0.4b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y)))
	0.6b	(.f64 (.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	1.3b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 3 (sqrt.f64 x))) (cbrt.f64 (.f64 3 (sqrt.f64 x)))) (cbrt.f64 (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
▶	0.3b	(fma.f64 (sqrt.f64 x) (-.f64 (.f64 3 y) 3) (.f64 1/3 (sqrt.f64 (/.f64 1 x))))
	0.8b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.6b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	33.0b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (sqrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))) (sqrt.f64 (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))

Compiler

Compiled 2462 to 1794 computations (27.1% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 3 y) 3)
	0.1b	(sqrt.f64 (/.f64 1 x))
✓	0.1b	(fma.f64 (sqrt.f64 x) (-.f64 (.f64 3 y) 3) (.f64 1/3 (sqrt.f64 (/.f64 1 x))))
	0.4b	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

series27.0ms (0.8%)

Counts

2 → 15

Calls

2 calls:

26.0ms	(fma.f64 (sqrt.f64 x) (-.f64 (.f64 3 y) 3) (.f64 1/3 (sqrt.f64 (/.f64 1 x))))
2.0ms	(-.f64 (*.f64 3 y) 3)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`
3×	`cancel-sign-sub-inv_binary64`

Counts

2 → 30

Calls

2 calls:

3.0ms	(-.f64 (*.f64 3 y) 3)
0.0ms	(fma.f64 (sqrt.f64 x) (-.f64 (.f64 3 y) 3) (.f64 1/3 (sqrt.f64 (/.f64 1 x))))

simplify49.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

858×	`associate-+l+_binary64`
394×	`distribute-rgt-in_binary64`
392×	`distribute-lft-in_binary64`
275×	`distribute-rgt-out_binary64`
269×	`associate-l_binary64`

Counts

45 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	698
1	145	574
2	276	571
3	649	569
4	2267	569
5	5399	569

prune138.0ms (4.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	136	7	143

Error

0.0b

Counts

143 → 7

Alt Table

Status	Error	Program
▶	0.4b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y)))
	0.6b	(.f64 (.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	1.3b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 3 (sqrt.f64 x))) (cbrt.f64 (.f64 3 (sqrt.f64 x)))) (cbrt.f64 (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
✓	0.3b	(fma.f64 (sqrt.f64 x) (-.f64 (.f64 3 y) 3) (.f64 1/3 (sqrt.f64 (/.f64 1 x))))
	0.8b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.6b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	33.0b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (sqrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))) (sqrt.f64 (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))

Compiler

Compiled 2975 to 2218 computations (25.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 (/.f64 1/9 x) 1) y)
✓	0.2b	(*.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y))
✓	0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y)))
✓	0.4b	(/.f64 1/9 x)

series61.0ms (1.9%)

Counts

4 → 48

Calls

4 calls:

30.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y)))
24.0ms	(*.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y))
5.0ms	(+.f64 (-.f64 (/.f64 1/9 x) 1) y)
2.0ms	(/.f64 1/9 x)

rewrite53.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-sqr-sqrt_binary64`
66×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64`
43×	`associate-+l+_binary64`
39×	`prod-diff_binary64`

Counts

4 → 155

Calls

4 calls:

15.0ms	(*.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y))
13.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y)))
11.0ms	(+.f64 (-.f64 (/.f64 1/9 x) 1) y)
2.0ms	(/.f64 1/9 x)

simplify74.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

922×	`distribute-rgt-in_binary64`
905×	`distribute-lft-in_binary64`
285×	`fma-def_binary64`
119×	`associate-l_binary64`
117×	`associate-r_binary64`

Counts

203 → 220

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	2465
1	382	2234
2	1227	2200
3	5247	2200

prune219.0ms (6.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	219	1	220
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	219	8	227

Error

Counts

227 → 8

Alt Table

Status	Error	Program
✓	0.4b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y)))
	0.6b	(.f64 (.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	1.3b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 3 (sqrt.f64 x))) (cbrt.f64 (.f64 3 (sqrt.f64 x)))) (cbrt.f64 (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.5b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y))))
✓	0.3b	(fma.f64 (sqrt.f64 x) (-.f64 (.f64 3 y) 3) (.f64 1/3 (sqrt.f64 (/.f64 1 x))))
	0.8b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.6b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	33.0b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (sqrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))) (sqrt.f64 (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))

Compiler

Compiled 5102 to 3758 computations (26.3% saved)

regimes734.0ms (22.6%)

Accuracy

Total 0.3b remaining (87.6%)

Threshold costs 0.3b (87.6%)

Counts

208 → 1

Compiler

Compiled 12488 to 9888 computations (20.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	19
1	20	19
2	21	19
3	19	19

end140.0ms (4.3%)

Compiler: Compiled 202 to 162 computations (19.8% saved)

Details

analyze28.0ms (0.9%)

sample892.0ms (27.4%)

simplify185.0ms (5.7%)

prune4.0ms (0.1%)

localize9.0ms (0.3%)

series47.0ms (1.4%)

rewrite33.0ms (1%)

simplify76.0ms (2.3%)

prune178.0ms (5.5%)

localize9.0ms (0.3%)

series44.0ms (1.4%)

rewrite14.0ms (0.4%)

simplify72.0ms (2.2%)

prune142.0ms (4.4%)

localize9.0ms (0.3%)

series27.0ms (0.8%)

rewrite4.0ms (0.1%)

simplify49.0ms (1.5%)

prune138.0ms (4.2%)

localize8.0ms (0.2%)

series61.0ms (1.9%)

rewrite53.0ms (1.6%)

simplify74.0ms (2.3%)

prune219.0ms (6.8%)

regimes734.0ms (22.6%)

simplify3.0ms (0.1%)

end140.0ms (4.3%)

Profiling