Details

analyze504.0ms (21.5%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
18.7%	81.1%	0.1%	7
21.8%	78%	0.1%	8
43.7%	56.2%	0.1%	9
54.6%	39%	6.4%	10
58.5%	35.1%	6.4%	11
67.3%	26.3%	6.4%	12
71.7%	18.8%	9.5%	13
74.1%	16.4%	9.5%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample24.0ms (1%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 24 to 18 computations (25% saved)

simplify18.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

56×	`cancel-sign-sub-inv_binary64`
36×	`distribute-rgt-neg-in_binary64`
30×	`sub-neg_binary64`
20×	`distribute-lft-neg-in_binary64`
19×	`distribute-rgt-in_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	17	10
2	43	10
3	82	10
4	94	10
5	129	10
6	151	10
7	172	10
8	244	10
9	248	10
10	254	10
11	209	10

prune1.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 x (.f64 (.f64 y 4) z))

Compiler

Compiled 20 to 14 computations (30% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

0.0b	(-.f64 x (.f64 (.f64 y 4) z))

rewrite9.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

3×	`add-log-exp_binary64`
1×	`cancel-sign-sub-inv_binary64`
1×	`flip--_binary64`
1×	`sub-neg_binary64`
1×	`*-un-lft-identity_binary64`

Counts

1 → 12

Calls

1 calls:

2.0ms

(-.f64 x (*.f64 (*.f64 y 4) z))

Compiler

Compiled 190 to 123 computations (35.3% saved)

series25.0ms (1.1%)

Error

0.0b

Counts

1 → 18

Calls

1 calls:

22.0ms

(-.f64 x (*.f64 (*.f64 y 4) z))

Compiler

Compiled 252 to 177 computations (29.8% saved)

simplify65.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

534×	`neg-mul-1_binary64`
468×	`associate-l_binary64`
419×	`unsub-neg_binary64`
359×	`associate-r_binary64`
355×	`distribute-rgt-neg-in_binary64`

Counts

30 → 19

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	348
1	100	324
2	366	324
3	1527	324
4	3280	324
5	4589	324
6	4973	324

prune8.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	17	2	19
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	17	3	20

Error

Counts

20 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x (.f64 (.f64 y 4) z))
	38.2b	(/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 (.f64 y 16) (.f64 z z)))) (+.f64 x (.f64 (*.f64 y z) 4)))
▶	1.3b	(.f64 (.f64 (cbrt.f64 (+.f64 (.f64 -4 (.f64 y z)) x)) (cbrt.f64 (+.f64 (.f64 -4 (.f64 y z)) x))) (cbrt.f64 (+.f64 (.f64 -4 (.f64 y z)) x)))

Compiler

Compiled 254 to 149 computations (41.3% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (cbrt.f64 (+.f64 (.f64 -4 (.f64 y z)) x)) (cbrt.f64 (+.f64 (.f64 -4 (*.f64 y z)) x)))
0.5b	(cbrt.f64 (+.f64 (.f64 -4 (.f64 y z)) x))
0.5b	(cbrt.f64 (+.f64 (.f64 -4 (.f64 y z)) x))
0.5b	(cbrt.f64 (+.f64 (.f64 -4 (.f64 y z)) x))

rewrite134.0ms (5.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
18×	`cbrt-div_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`

Counts

4 → 87

Calls

4 calls:

14.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 -4 (.f64 y z)) x)) (cbrt.f64 (+.f64 (.f64 -4 (*.f64 y z)) x)))
5.0ms	(cbrt.f64 (+.f64 (.f64 -4 (.f64 y z)) x))
4.0ms	(cbrt.f64 (+.f64 (.f64 -4 (.f64 y z)) x))
4.0ms	(cbrt.f64 (+.f64 (.f64 -4 (.f64 y z)) x))

Compiler

Compiled 3222 to 1814 computations (43.7% saved)

series275.0ms (11.7%)

Error

Counts

4 → 60

Calls

4 calls:

115.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 -4 (.f64 y z)) x)) (cbrt.f64 (+.f64 (.f64 -4 (*.f64 y z)) x)))
44.0ms	(cbrt.f64 (+.f64 (.f64 -4 (.f64 y z)) x))
44.0ms	(cbrt.f64 (+.f64 (.f64 -4 (.f64 y z)) x))
41.0ms	(cbrt.f64 (+.f64 (.f64 -4 (.f64 y z)) x))

Compiler

Compiled 5682 to 4133 computations (27.3% saved)

simplify183.0ms (7.8%)

Algorithm

1×	egg-herbie

Rules

257×	`times-frac_binary64`
228×	`exp-sum_binary64`
227×	`associate-/l*_binary64`
215×	`distribute-rgt-neg-in_binary64`
212×	`distribute-lft-neg-in_binary64`

Counts

147 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	3877
1	518	3709
2	1559	3435
3	4261	3182
4	4921	3182
5	5000	3182

prune61.0ms (2.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	134	3	137

Error

Counts

137 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x (.f64 (.f64 y 4) z))
▶	38.2b	(/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 (.f64 y 16) (.f64 z z)))) (+.f64 x (.f64 (*.f64 y z) 4)))
✓	1.3b	(.f64 (.f64 (cbrt.f64 (+.f64 (.f64 -4 (.f64 y z)) x)) (cbrt.f64 (+.f64 (.f64 -4 (.f64 y z)) x))) (cbrt.f64 (+.f64 (.f64 -4 (.f64 y z)) x)))

Compiler

Compiled 3196 to 1809 computations (43.4% saved)

localize13.0ms (0.6%)

Local error

Found 4 expressions with local error:

3.5b	(-.f64 (.f64 x x) (.f64 y (.f64 (.f64 y 16) (*.f64 z z))))
3.5b	(.f64 y (.f64 (.f64 y 16) (.f64 z z)))
9.7b	(.f64 (.f64 y 16) (*.f64 z z))
27.4b	(/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 (.f64 y 16) (.f64 z z)))) (+.f64 x (.f64 (*.f64 y z) 4)))

rewrite117.0ms (5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

36×	`add-cbrt-cube_binary64`
36×	`add-exp-log_binary64`
34×	`pow1_binary64`
21×	`cbrt-unprod_binary64`
21×	`prod-exp_binary64`

Counts

4 → 93

Calls

4 calls:

7.0ms	(.f64 y (.f64 (.f64 y 16) (.f64 z z)))
7.0ms	(.f64 (.f64 y 16) (*.f64 z z))
6.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 (.f64 y 16) (.f64 z z)))) (+.f64 x (.f64 (*.f64 y z) 4)))
3.0ms	(-.f64 (.f64 x x) (.f64 y (.f64 (.f64 y 16) (*.f64 z z))))

Compiler

Compiled 2851 to 1316 computations (53.8% saved)

series123.0ms (5.3%)

Error

Counts

4 → 48

Calls

4 calls:

48.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 (.f64 y 16) (.f64 z z)))) (+.f64 x (.f64 (*.f64 y z) 4)))
42.0ms	(-.f64 (.f64 x x) (.f64 y (.f64 (.f64 y 16) (*.f64 z z))))
16.0ms	(.f64 y (.f64 (.f64 y 16) (.f64 z z)))
14.0ms	(.f64 (.f64 y 16) (*.f64 z z))

Compiler

Compiled 1507 to 1067 computations (29.2% saved)

simplify121.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

390×	`associate-/l*_binary64`
368×	`exp-prod_binary64`
280×	`distribute-rgt-neg-in_binary64`
276×	`associate-r_binary64`
261×	`associate-l_binary64`

Counts

141 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	163	3158
1	440	2883
2	1682	2850
3	4524	2848
4	5028	2848

prune31.0ms (1.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	119	3	122

Error

Counts

122 → 3

Alt Table

Status	Error	Program
	0.0b	(-.f64 x (.f64 (.f64 y 4) z))
	38.2b	(/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 (.f64 y 16) (.f64 z z)))) (+.f64 x (.f64 (*.f64 y z) 4)))
	1.3b	(.f64 (.f64 (cbrt.f64 (+.f64 (.f64 -4 (.f64 y z)) x)) (cbrt.f64 (+.f64 (.f64 -4 (.f64 y z)) x))) (cbrt.f64 (+.f64 (.f64 -4 (.f64 y z)) x)))

Compiler

Compiled 1831 to 786 computations (57.1% saved)

regimes95.0ms (4.1%)

Accuracy

Total 0.0b remaining (86.1%)

Threshold costs 0.0b (86.1%)

Compiler

Compiled 1728 to 1194 computations (30.9% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`distribute-rgt-neg-in_binary64`
4×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	15	10
2	32	10
3	40	10
4	46	10
5	48	10
6	47	10

end6.0ms (0.2%)

Remove: (sort y z)
Compiler: Compiled 30 to 21 computations (30% saved)

sample511.0ms (21.8%)

Algorithm

1×

intervals

Results

224.0ms	8000×	body	128	valid
8.0ms	317×	body	128	invalid

Compiler

Compiled 87 to 58 computations (33.3% saved)

Iter	Nodes	Cost
0	8	10
1	17	10
2	43	10
3	82	10
4	94	10
5	129	10
6	151	10
7	172	10
8	244	10
9	248	10
10	254	10
11	209	10

Iter	Nodes	Cost
0	8	10
1	17	10
2	43	10
3	82	10
4	94	10
5	129	10
6	151	10
7	172	10
8	244	10
9	248	10
10	254	10
11	209	10

Details

analyze504.0ms (21.5%)

sample24.0ms (1%)

simplify18.0ms (0.8%)

prune1.0ms (0.1%)

localize6.0ms (0.3%)

rewrite9.0ms (0.4%)

series25.0ms (1.1%)

simplify65.0ms (2.8%)

prune8.0ms (0.3%)

localize10.0ms (0.4%)

rewrite134.0ms (5.7%)

series275.0ms (11.7%)

simplify183.0ms (7.8%)

prune61.0ms (2.6%)

localize13.0ms (0.6%)

rewrite117.0ms (5%)

series123.0ms (5.3%)

simplify121.0ms (5.2%)

prune31.0ms (1.3%)

regimes95.0ms (4.1%)

simplify5.0ms (0.2%)

end6.0ms (0.2%)

sample511.0ms (21.8%)

Profiling

Iter	Nodes	Cost
0	8	10
1	17	10
2	43	10
3	82	10
4	94	10
5	129	10
6	151	10
7	172	10
8	244	10
9	248	10
10	254	10
11	209	10