Details

analyze488.0ms (14.4%)

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
0%	99.9%	0.1%	5
21.8%	78%	0.1%	6
26.5%	73.3%	0.1%	7
32%	67.9%	0.1%	8
46.4%	52.7%	0.9%	9
50.9%	47.2%	1.9%	10
54.3%	43.3%	2.4%	11
62.1%	32.5%	5.4%	12
64.3%	28.1%	7.6%	13
66.3%	24.6%	9.2%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample21.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	29×	body	128	invalid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify54.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

225×	`cancel-sign-sub-inv_binary64`
222×	`distribute-rgt-in_binary64`
163×	`distribute-lft-in_binary64`
129×	`unsub-neg_binary64`
111×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	22	18
2	41	18
3	68	18
4	114	18
5	187	18
6	250	18
7	390	18
8	769	15
9	855	15
10	914	15
11	879	15
12	864	15
13	864	15
14	761	15

prune5.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

2 → 2

Alt Table

Status	Error	Program
	2.3b	(fabs.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))
▶	0.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 69 to 47 computations (31.9% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
2.5b	(*.f64 (/.f64 x y) z)

rewrite75.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

15×	`add-sqr-sqrt_binary64`
13×	`associate-l_binary64`
10×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64` `times-frac_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64` `add-log-exp_binary64`

Counts

2 → 46

Calls

2 calls:

13.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
6.0ms	(*.f64 (/.f64 x y) z)

Compiler

Compiled 885 to 409 computations (53.8% saved)

series85.0ms (2.5%)

Error

0.0b

Counts

2 → 24

Calls

2 calls:

51.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
25.0ms	(*.f64 (/.f64 x y) z)

Compiler

Compiled 763 to 508 computations (33.4% saved)

simplify85.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

641×	`distribute-rgt-in_binary64`
353×	`associate-l_binary64`
317×	`distribute-rgt-neg-in_binary64`
309×	`associate-*l/_binary64`
292×	`distribute-lft-neg-in_binary64`

Counts

70 → 50

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	116	935
1	292	875
2	818	869
3	2698	839
4	4861	839
5	4949	839

prune47.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	45	5	50
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	46	6	52

Error

0.0b

Counts

52 → 6

Alt Table

Status	Error	Program
	2.3b	(fabs.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))
	29.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 x y)) (.f64 z (sqrt.f64 (/.f64 x y))))))
	31.3b	(fabs.f64 (/.f64 (.f64 y (-.f64 (+.f64 x 4) (.f64 x z))) (*.f64 y y)))
	25.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 (.f64 x z) y)) (sqrt.f64 (/.f64 (*.f64 x z) y)))))
	3.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
▶	1.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 z (/.f64 x (cbrt.f64 y))))))

Compiler

Compiled 864 to 447 computations (48.3% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)
1.1b	(*.f64 z (/.f64 x (cbrt.f64 y)))
3.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 z (/.f64 x (cbrt.f64 y))))

rewrite156.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

87×	`add-exp-log_binary64`
46×	`prod-exp_binary64`
35×	`add-cbrt-cube_binary64`
30×	`add-sqr-sqrt_binary64`
23×	`times-frac_binary64` `associate-r_binary64`

Counts

4 → 115

Calls

4 calls:

15.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 z (/.f64 x (cbrt.f64 y))))
12.0ms	(*.f64 z (/.f64 x (cbrt.f64 y)))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)

Compiler

Compiled 3149 to 1233 computations (60.8% saved)

series144.0ms (4.3%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

69.0ms	(*.f64 z (/.f64 x (cbrt.f64 y)))
32.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 z (/.f64 x (cbrt.f64 y))))
17.0ms	(cbrt.f64 y)
16.0ms	(cbrt.f64 y)

Compiler

Compiled 1279 to 878 computations (31.4% saved)

simplify108.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

605×	`associate-/r*_binary64`
403×	`*-commutative_binary64`
346×	`log-div_binary64`
298×	`log-prod_binary64`
275×	`associate-/l/_binary64`

Counts

139 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	169	2288
1	380	1337
2	1494	1322
3	3189	1322
4	4687	1322
5	5000	1322

prune56.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	97	6	103

Error

0.0b

Counts

103 → 6

Alt Table

Status	Error	Program
▶	2.3b	(fabs.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))
	29.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 x y)) (.f64 z (sqrt.f64 (/.f64 x y))))))
	31.3b	(fabs.f64 (/.f64 (.f64 y (-.f64 (+.f64 x 4) (.f64 x z))) (*.f64 y y)))
	25.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 (.f64 x z) y)) (sqrt.f64 (/.f64 (*.f64 x z) y)))))
	3.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
✓	1.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 z (/.f64 x (cbrt.f64 y))))))

Compiler

Compiled 1256 to 643 computations (48.8% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (+.f64 x 4) (*.f64 x z))
2.2b	(/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y)

rewrite63.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

10×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-/l_binary64` `associate-/r_binary64`

Counts

2 → 44

Calls

2 calls:

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

Compiler

Compiled 854 to 460 computations (46.1% saved)

series66.0ms (1.9%)

Error

0.0b

Counts

2 → 27

Calls

2 calls:

36.0ms	(/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y)
20.0ms	(-.f64 (+.f64 x 4) (*.f64 x z))

Compiler

Compiled 701 to 481 computations (31.4% saved)

simplify85.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

377×	`neg-mul-1_binary64`
278×	`div-sub_binary64`
277×	`distribute-rgt-in_binary64`
267×	`distribute-lft-in_binary64`
238×	`associate-/l/_binary64`

Counts

71 → 62

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	1245
1	261	1168
2	750	1138
3	2409	1108
4	4308	1108
5	4948	1108

prune44.0ms (1.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	63	5	68

Error

Counts

68 → 5

Alt Table

Status	Error	Program
▶	2.4b	(fabs.f64 (/.f64 1 (/.f64 y (+.f64 4 (-.f64 x (*.f64 x z))))))
✓	2.3b	(fabs.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))
	25.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 (.f64 x z) y)) (sqrt.f64 (/.f64 (*.f64 x z) y)))))
	3.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
✓	1.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 z (/.f64 x (cbrt.f64 y))))))

Compiler

Compiled 832 to 418 computations (49.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 x (*.f64 x z))
0.1b	(/.f64 1 (/.f64 y (+.f64 4 (-.f64 x (*.f64 x z)))))
2.2b	(/.f64 y (+.f64 4 (-.f64 x (*.f64 x z))))

rewrite154.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

114×	`times-frac_binary64`
95×	`*-un-lft-identity_binary64`
63×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
22×	`associate-/r*_binary64`
16×	`add-exp-log_binary64` `distribute-lft-out_binary64`

Counts

3 → 141

Calls

3 calls:

9.0ms	(/.f64 1 (/.f64 y (+.f64 4 (-.f64 x (*.f64 x z)))))
6.0ms	(/.f64 y (+.f64 4 (-.f64 x (*.f64 x z))))
3.0ms	(-.f64 x (*.f64 x z))

Compiler

Compiled 3072 to 1609 computations (47.6% saved)

series173.0ms (5.1%)

Error

Counts

3 → 51

Calls

3 calls:

72.0ms	(/.f64 y (+.f64 4 (-.f64 x (*.f64 x z))))
39.0ms	(/.f64 1 (/.f64 y (+.f64 4 (-.f64 x (*.f64 x z)))))
19.0ms	(-.f64 x (*.f64 x z))

Compiler

Compiled 2611 to 1884 computations (27.8% saved)

simplify138.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

928×	`times-frac_binary64`
316×	`cancel-sign-sub-inv_binary64`
151×	`associate-l_binary64` `associate-r_binary64`
145×	`unswap-sqr_binary64` `associate-/r*_binary64`
141×	`sub-neg_binary64`

Counts

192 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	5009
1	804	4715
2	2987	4643
3	5023	4643

prune98.0ms (2.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	169	5	174

Error

Counts

174 → 5

Alt Table

Status	Error	Program
	2.4b	(fabs.f64 (/.f64 1 (/.f64 y (+.f64 4 (-.f64 x (*.f64 x z))))))
	2.3b	(fabs.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))
	25.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 (.f64 x z) y)) (sqrt.f64 (/.f64 (*.f64 x z) y)))))
	3.6b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
	1.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 z (/.f64 x (cbrt.f64 y))))))

Compiler

Compiled 2323 to 1258 computations (45.8% saved)

regimes431.0ms (12.8%)

Accuracy

Total 0.6b remaining (94.7%)

Threshold costs 0.6b (94.7%)

Compiler

Compiled 5892 to 3796 computations (35.6% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
12×	`sub-neg_binary64` `*-commutative_binary64`
10×	`neg-mul-1_binary64` `neg-sub0_binary64`
5×	`distribute-rgt-neg-in_binary64`
4×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	42
1	27	42
2	41	42
3	63	42
4	85	42
5	99	42
6	105	42
7	106	42
8	105	42

end1.0ms (0%)

Compiler: Compiled 29 to 16 computations (44.8% saved)

sample761.0ms (22.5%)

Algorithm

1×

intervals

Results

312.0ms	8000×	body	128	valid
45.0ms	1235×	body	128	invalid

Compiler

Compiled 138 to 87 computations (37% saved)

Iter	Nodes	Cost
0	11	18
1	22	18
2	41	18
3	68	18
4	114	18
5	187	18
6	250	18
7	390	18
8	769	15
9	855	15
10	914	15
11	879	15
12	864	15
13	864	15
14	761	15

Iter	Nodes	Cost
0	11	18
1	22	18
2	41	18
3	68	18
4	114	18
5	187	18
6	250	18
7	390	18
8	769	15
9	855	15
10	914	15
11	879	15
12	864	15
13	864	15
14	761	15

Details

analyze488.0ms (14.4%)

sample21.0ms (0.6%)

simplify54.0ms (1.6%)

prune5.0ms (0.2%)

localize8.0ms (0.3%)

rewrite75.0ms (2.2%)

series85.0ms (2.5%)

simplify85.0ms (2.5%)

prune47.0ms (1.4%)

localize14.0ms (0.4%)

rewrite156.0ms (4.6%)

series144.0ms (4.3%)

simplify108.0ms (3.2%)

prune56.0ms (1.7%)

localize7.0ms (0.2%)

rewrite63.0ms (1.9%)

series66.0ms (1.9%)

simplify85.0ms (2.5%)

prune44.0ms (1.3%)

localize8.0ms (0.2%)

rewrite154.0ms (4.6%)

series173.0ms (5.1%)

simplify138.0ms (4.1%)

prune98.0ms (2.9%)

regimes431.0ms (12.8%)

simplify5.0ms (0.2%)

end1.0ms (0%)

sample761.0ms (22.5%)

Profiling

Iter	Nodes	Cost
0	11	18
1	22	18
2	41	18
3	68	18
4	114	18
5	187	18
6	250	18
7	390	18
8	769	15
9	855	15
10	914	15
11	879	15
12	864	15
13	864	15
14	761	15