Details

analyze871.0ms (26.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
12.5%	87.3%	0.2%	7
18.7%	81.1%	0.2%	8
46.8%	53%	0.2%	9
47.6%	52.2%	0.2%	10
48.3%	51.5%	0.2%	11
54.2%	45.6%	0.2%	12
67.6%	32.2%	0.2%	13
68.2%	31.6%	0.2%	14

Compiler

Compiled 18 to 14 computations (22.2% saved)

sample37.0ms (1.1%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
2.0ms	38×	body	128	invalid

Compiler

Compiled 39 to 31 computations (20.5% saved)

simplify25.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

113×	`cancel-sign-sub-inv_binary64`
62×	`sub-neg_binary64`
58×	`unsub-neg_binary64`
50×	`distribute-rgt-neg-in_binary64`
39×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	16
1	26	16
2	47	16
3	88	16
4	164	16
5	257	16
6	348	16
7	437	16
8	494	16
9	491	16
10	417	16

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (-.f64 (.f64 1/8 x) (/.f64 (.f64 y z) 2)) t)

Compiler

Compiled 45 to 33 computations (26.7% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (*.f64 y z) 2)
0.0b	(-.f64 (.f64 1/8 x) (/.f64 (.f64 y z) 2))
0.0b	(+.f64 (-.f64 (.f64 1/8 x) (/.f64 (.f64 y z) 2)) t)

rewrite61.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

14×	`cancel-sign-sub-inv_binary64`
11×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`

Counts

3 → 61

Calls

3 calls:

6.0ms	(+.f64 (-.f64 (.f64 1/8 x) (/.f64 (.f64 y z) 2)) t)
5.0ms	(/.f64 (*.f64 y z) 2)
4.0ms	(-.f64 (.f64 1/8 x) (/.f64 (.f64 y z) 2))

Compiler

Compiled 1135 to 711 computations (37.4% saved)

series83.0ms (2.5%)

Error

0.0b

Counts

3 → 48

Calls

3 calls:

37.0ms	(+.f64 (-.f64 (.f64 1/8 x) (/.f64 (.f64 y z) 2)) t)
26.0ms	(-.f64 (.f64 1/8 x) (/.f64 (.f64 y z) 2))
11.0ms	(/.f64 (*.f64 y z) 2)

Compiler

Compiled 1071 to 780 computations (27.2% saved)

simplify116.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

411×	`associate-l_binary64`
354×	`associate-r_binary64`
318×	`distribute-neg-frac_binary64`
287×	`associate-/l*_binary64`
243×	`associate-*l/_binary64`

Counts

109 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	1394
1	331	1361
2	885	1346
3	3483	1345
4	4707	1345
5	4996	1345
6	4902	1345

prune28.0ms (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	3	82

Error

Counts

82 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (-.f64 (.f64 1/8 x) (/.f64 (.f64 y z) 2)) t)
▶	0.4b	(+.f64 (-.f64 (.f64 1/8 x) (.f64 (.f64 (cbrt.f64 (.f64 1/2 (.f64 y z))) (cbrt.f64 (.f64 1/2 (.f64 y z)))) (cbrt.f64 (.f64 1/2 (*.f64 y z))))) t)
	32.0b	(+.f64 (.f64 (sqrt.f64 (+.f64 (.f64 1/8 x) (.f64 (.f64 y z) -1/2))) (sqrt.f64 (+.f64 (.f64 1/8 x) (.f64 (*.f64 y z) -1/2)))) t)

Compiler

Compiled 712 to 446 computations (37.4% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (.f64 1/2 (.f64 y z))) (cbrt.f64 (.f64 1/2 (*.f64 y z))))
8.8b	(cbrt.f64 (.f64 1/2 (.f64 y z)))
8.8b	(cbrt.f64 (.f64 1/2 (.f64 y z)))
8.8b	(cbrt.f64 (.f64 1/2 (.f64 y z)))

rewrite89.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

11×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`pow1/3_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`

Counts

4 → 58

Calls

4 calls:

7.0ms	(cbrt.f64 (.f64 1/2 (.f64 y z)))
5.0ms	(.f64 (cbrt.f64 (.f64 1/2 (.f64 y z))) (cbrt.f64 (.f64 1/2 (*.f64 y z))))
3.0ms	(cbrt.f64 (.f64 1/2 (.f64 y z)))
3.0ms	(cbrt.f64 (.f64 1/2 (.f64 y z)))

Compiler

Compiled 1742 to 1047 computations (39.9% saved)

series195.0ms (5.9%)

Error

Counts

4 → 24

Calls

4 calls:

54.0ms	(.f64 (cbrt.f64 (.f64 1/2 (.f64 y z))) (cbrt.f64 (.f64 1/2 (*.f64 y z))))
43.0ms	(cbrt.f64 (.f64 1/2 (.f64 y z)))
41.0ms	(cbrt.f64 (.f64 1/2 (.f64 y z)))
38.0ms	(cbrt.f64 (.f64 1/2 (.f64 y z)))

Compiler

Compiled 2413 to 1806 computations (25.2% saved)

simplify141.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

442×	`exp-sum_binary64`
428×	`exp-prod_binary64`
374×	`associate-l_binary64`
329×	`exp-diff_binary64`
297×	`div-exp_binary64`

Counts

82 → 69

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	114	1343
1	240	1295
2	495	1152
3	1674	1032
4	3722	908
5	4790	890
6	4559	890
7	4868	890
8	5364	890

prune38.0ms (1.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	69	3	72

Error

Counts

72 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (-.f64 (.f64 1/8 x) (/.f64 (.f64 y z) 2)) t)
✓	0.4b	(+.f64 (-.f64 (.f64 1/8 x) (.f64 (.f64 (cbrt.f64 (.f64 1/2 (.f64 y z))) (cbrt.f64 (.f64 1/2 (.f64 y z)))) (cbrt.f64 (.f64 1/2 (*.f64 y z))))) t)
▶	32.0b	(+.f64 (.f64 (sqrt.f64 (+.f64 (.f64 1/8 x) (.f64 (.f64 y z) -1/2))) (sqrt.f64 (+.f64 (.f64 1/8 x) (.f64 (*.f64 y z) -1/2)))) t)

Compiler

Compiled 1191 to 737 computations (38.1% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 1/8 x) (.f64 (*.f64 y z) -1/2))
0.0b	(sqrt.f64 (+.f64 (.f64 1/8 x) (.f64 (*.f64 y z) -1/2)))
0.0b	(sqrt.f64 (+.f64 (.f64 1/8 x) (.f64 (*.f64 y z) -1/2)))
0.3b	(.f64 (sqrt.f64 (+.f64 (.f64 1/8 x) (.f64 (.f64 y z) -1/2))) (sqrt.f64 (+.f64 (.f64 1/8 x) (.f64 (*.f64 y z) -1/2))))

rewrite110.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

32×	`add-sqr-sqrt_binary64`
24×	`sqrt-prod_binary64`
21×	`pow1_binary64`
16×	`sqrt-div_binary64`
14×	`*-un-lft-identity_binary64`

Counts

4 → 100

Calls

4 calls:

10.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 1/8 x) (.f64 (.f64 y z) -1/2))) (sqrt.f64 (+.f64 (.f64 1/8 x) (.f64 (*.f64 y z) -1/2))))
4.0ms	(+.f64 (.f64 1/8 x) (.f64 (*.f64 y z) -1/2))
3.0ms	(sqrt.f64 (+.f64 (.f64 1/8 x) (.f64 (*.f64 y z) -1/2)))
3.0ms	(sqrt.f64 (+.f64 (.f64 1/8 x) (.f64 (*.f64 y z) -1/2)))

Compiler

Compiled 3097 to 1981 computations (36% saved)

series119.0ms (3.6%)

Error

Counts

4 → 59

Calls

4 calls:

30.0ms	(+.f64 (.f64 1/8 x) (.f64 (*.f64 y z) -1/2))
28.0ms	(sqrt.f64 (+.f64 (.f64 1/8 x) (.f64 (*.f64 y z) -1/2)))
28.0ms	(sqrt.f64 (+.f64 (.f64 1/8 x) (.f64 (*.f64 y z) -1/2)))
26.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 1/8 x) (.f64 (.f64 y z) -1/2))) (sqrt.f64 (+.f64 (.f64 1/8 x) (.f64 (*.f64 y z) -1/2))))

Compiler

Compiled 2693 to 1937 computations (28.1% saved)

simplify144.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

450×	`distribute-rgt-neg-in_binary64`
409×	`neg-sub0_binary64`
390×	`neg-mul-1_binary64`
356×	`distribute-lft-neg-in_binary64`
324×	`*-commutative_binary64`

Counts

159 → 116

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	110	2946
1	242	2785
2	902	2727
3	2230	2629
4	4079	2629
5	4945	2629

prune52.0ms (1.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	116	3	119

Error

Counts

119 → 3

Alt Table

Status	Error	Program
	0.0b	(+.f64 (-.f64 (.f64 1/8 x) (/.f64 (.f64 y z) 2)) t)
	0.4b	(+.f64 (-.f64 (.f64 1/8 x) (.f64 (.f64 (cbrt.f64 (.f64 1/2 (.f64 y z))) (cbrt.f64 (.f64 1/2 (.f64 y z)))) (cbrt.f64 (.f64 1/2 (*.f64 y z))))) t)
	32.0b	(+.f64 (.f64 (sqrt.f64 (+.f64 (.f64 1/8 x) (.f64 (.f64 y z) -1/2))) (sqrt.f64 (+.f64 (.f64 1/8 x) (.f64 (*.f64 y z) -1/2)))) t)

Compiler

Compiled 1791 to 1140 computations (36.3% saved)

regimes320.0ms (9.6%)

Accuracy

Total 0.0b remaining (3.5%)

Threshold costs 0.0b (3.5%)

Compiler

Compiled 5571 to 4086 computations (26.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
6×	`*-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	17	16
2	24	16
3	34	16
4	41	16
5	46	16
6	48	16
7	48	16

end6.0ms (0.2%)

Remove: (sort y z)
Compiler: Compiled 45 to 33 computations (26.7% saved)

sample859.0ms (25.8%)

Algorithm

1×

intervals

Results

418.0ms	7997×	body	128	valid
61.0ms	1229×	body	128	invalid
0.0ms	3×	body	1024	valid

Compiler

Compiled 109 to 79 computations (27.5% saved)

Iter	Nodes	Cost
0	15	16
1	26	16
2	47	16
3	88	16
4	164	16
5	257	16
6	348	16
7	437	16
8	494	16
9	491	16
10	417	16

Iter	Nodes	Cost
0	15	16
1	26	16
2	47	16
3	88	16
4	164	16
5	257	16
6	348	16
7	437	16
8	494	16
9	491	16
10	417	16

Details

analyze871.0ms (26.1%)

sample37.0ms (1.1%)

simplify25.0ms (0.7%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

rewrite61.0ms (1.8%)

series83.0ms (2.5%)

simplify116.0ms (3.5%)

prune28.0ms (0.8%)

localize12.0ms (0.4%)

rewrite89.0ms (2.7%)

series195.0ms (5.9%)

simplify141.0ms (4.2%)

prune38.0ms (1.1%)

localize12.0ms (0.4%)

rewrite110.0ms (3.3%)

series119.0ms (3.6%)

simplify144.0ms (4.3%)

prune52.0ms (1.6%)

regimes320.0ms (9.6%)

simplify4.0ms (0.1%)

end6.0ms (0.2%)

sample859.0ms (25.8%)

Profiling

Iter	Nodes	Cost
0	15	16
1	26	16
2	47	16
3	88	16
4	164	16
5	257	16
6	348	16
7	437	16
8	494	16
9	491	16
10	417	16