Details

analyze484.0ms (13%)

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	35×	body	128	invalid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify54.0ms (1.4%)

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

prune7.0ms (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
	3.1b	(fabs.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))
▶	1.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 69 to 47 computations (31.9% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 x 4) y)
0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
2.0b	(*.f64 (/.f64 x y) z)

rewrite114.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

28×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
22×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
13×	`associate-l_binary64`

Counts

3 → 79

Calls

3 calls:

9.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
6.0ms	(*.f64 (/.f64 x y) z)
5.0ms	(/.f64 (+.f64 x 4) y)

Compiler

Compiled 1437 to 693 computations (51.8% saved)

series106.0ms (2.9%)

Error

0.0b

Counts

3 → 33

Calls

3 calls:

48.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
25.0ms	(*.f64 (/.f64 x y) z)
17.0ms	(/.f64 (+.f64 x 4) y)

Compiler

Compiled 1070 to 689 computations (35.6% saved)

simplify102.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

392×	`associate-l_binary64`
341×	`associate-*l/_binary64`
322×	`distribute-rgt-neg-in_binary64`
312×	`div-sub_binary64`
302×	`associate-r_binary64`

Counts

112 → 63

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	161	1432
1	393	1370
2	1035	1361
3	3171	1334
4	4517	1334
5	5147	1334

prune54.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	58	5	63
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	58	7	65

Error

0.0b

Counts

65 → 7

Alt Table

Status	Error	Program
	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
	32.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (sqrt.f64 y)) (.f64 z (/.f64 x (sqrt.f64 y))))))
▶	2.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 z (/.f64 (cbrt.f64 x) y)))))
	3.1b	(fabs.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))
	32.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (sqrt.f64 y)) (*.f64 z (/.f64 (cbrt.f64 x) (sqrt.f64 y))))))
	3.1b	(fabs.f64 (-.f64 (/.f64 4 y) (/.f64 (-.f64 (*.f64 x z) x) y)))
✓	1.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 1018 to 533 computations (47.6% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
1.3b	(*.f64 z (/.f64 (cbrt.f64 x) y))
4.0b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 z (/.f64 (cbrt.f64 x) y)))

rewrite179.0ms (4.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

66×	`add-exp-log_binary64`
35×	`add-cbrt-cube_binary64`
33×	`prod-exp_binary64`
30×	`add-sqr-sqrt_binary64`
23×	`associate-r_binary64`

Counts

4 → 109

Calls

4 calls:

12.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 z (/.f64 (cbrt.f64 x) y)))
9.0ms	(*.f64 z (/.f64 (cbrt.f64 x) y))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

Compiler

Compiled 3025 to 1189 computations (60.7% saved)

series130.0ms (3.5%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

58.0ms	(*.f64 z (/.f64 (cbrt.f64 x) y))
31.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 z (/.f64 (cbrt.f64 x) y)))
14.0ms	(cbrt.f64 x)
14.0ms	(cbrt.f64 x)

Compiler

Compiled 1245 to 845 computations (32.1% saved)

simplify128.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

421×	`*-commutative_binary64`
369×	`log-prod_binary64`
369×	`log-div_binary64`
320×	`associate-/r*_binary64`
319×	`associate-/l/_binary64`

Counts

133 → 95

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	162	2050
1	352	1267
2	1472	1228
3	3063	1228
4	4494	1228
5	4940	1228
6	4931	1228

prune70.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	95	7	102

Error

0.0b

Counts

102 → 7

Alt Table

Status	Error	Program
▶	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
	32.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (sqrt.f64 y)) (.f64 z (/.f64 x (sqrt.f64 y))))))
✓	2.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 z (/.f64 (cbrt.f64 x) y)))))
	3.1b	(fabs.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))
	3.1b	(fabs.f64 (-.f64 (/.f64 4 y) (/.f64 (-.f64 (*.f64 x z) x) y)))
	3.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 z y)))))
✓	1.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 1344 to 672 computations (50% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 x 4) y)
0.0b	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y)))
5.5b	(*.f64 x (/.f64 z y))

rewrite117.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

28×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
22×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`

Counts

3 → 79

Calls

3 calls:

9.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y)))
8.0ms	(/.f64 (+.f64 x 4) y)
7.0ms	(*.f64 x (/.f64 z y))

Compiler

Compiled 1437 to 693 computations (51.8% saved)

series108.0ms (2.9%)

Error

0.0b

Counts

3 → 33

Calls

3 calls:

48.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y)))
24.0ms	(*.f64 x (/.f64 z y))
18.0ms	(/.f64 (+.f64 x 4) y)

Compiler

Compiled 1070 to 697 computations (34.9% saved)

simplify103.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

466×	`div-sub_binary64`
383×	`associate-r_binary64`
317×	`associate-*r/_binary64`
300×	`associate-*l/_binary64`
298×	`distribute-rgt-neg-in_binary64`

Counts

112 → 57

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	159	1441
1	393	1409
2	1180	1379
3	3293	1350
4	4656	1346
5	5521	1346

prune49.0ms (1.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	57	7	64

Error

0.0b

Counts

64 → 7

Alt Table

Status	Error	Program
✓	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
	32.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (sqrt.f64 y)) (.f64 z (/.f64 x (sqrt.f64 y))))))
✓	2.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 z (/.f64 (cbrt.f64 x) y)))))
▶	3.1b	(fabs.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))
	3.1b	(fabs.f64 (-.f64 (/.f64 4 y) (/.f64 (-.f64 (*.f64 x z) x) y)))
	3.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 z y)))))
✓	1.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 813 to 437 computations (46.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (+.f64 x 4) (*.f64 x z))
3.0b	(/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y)

rewrite69.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_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)

series68.0ms (1.8%)

Error

0.0b

Counts

2 → 27

Calls

2 calls:

39.0ms	(/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y)
18.0ms	(-.f64 (+.f64 x 4) (*.f64 x z))

Compiler

Compiled 701 to 481 computations (31.4% saved)

simplify93.0ms (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

prune46.0ms (1.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	0	3	3
Picked	1	0	1
Done	0	3	3
Total	61	8	69

Error

0.0b

Counts

69 → 8

Alt Table

Status	Error	Program
	3.2b	(fabs.f64 (/.f64 1 (/.f64 y (+.f64 4 (-.f64 x (*.f64 x z))))))
	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
	32.2b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 1 (sqrt.f64 y)) (.f64 z (/.f64 x (sqrt.f64 y))))))
	2.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (*.f64 z (/.f64 (cbrt.f64 x) y)))))
	33.4b	(fabs.f64 (/.f64 (/.f64 (+.f64 4 (-.f64 x (*.f64 x z))) (sqrt.f64 y)) (sqrt.f64 y)))
	3.1b	(fabs.f64 (-.f64 (/.f64 4 y) (/.f64 (-.f64 (*.f64 x z) x) y)))
	3.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 z y)))))
	1.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))

Compiler

Compiled 833 to 422 computations (49.3% saved)

regimes641.0ms (17.2%)

Accuracy

Total 0.9b remaining (98.7%)

Threshold costs 0.9b (98.7%)

Compiler

Compiled 9462 to 5982 computations (36.8% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
11×	`*-commutative_binary64`
11×	`sub-neg_binary64`
9×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	42
1	27	42
2	45	42
3	64	42
4	86	42
5	97	42
6	100	42
7	99	42

end1.0ms (0%)

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

sample928.0ms (25%)

Algorithm

1×

intervals

Results

292.0ms	8000×	body	128	valid
43.0ms	1254×	body	128	invalid

Compiler

Compiled 192 to 124 computations (35.4% 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

analyze484.0ms (13%)

sample21.0ms (0.6%)

simplify54.0ms (1.4%)

prune7.0ms (0.2%)

localize8.0ms (0.2%)

rewrite114.0ms (3.1%)

series106.0ms (2.9%)

simplify102.0ms (2.7%)

prune54.0ms (1.4%)

localize17.0ms (0.5%)

rewrite179.0ms (4.8%)

series130.0ms (3.5%)

simplify128.0ms (3.4%)

prune70.0ms (1.9%)

localize8.0ms (0.2%)

rewrite117.0ms (3.2%)

series108.0ms (2.9%)

simplify103.0ms (2.8%)

prune49.0ms (1.3%)

localize7.0ms (0.2%)

rewrite69.0ms (1.9%)

series68.0ms (1.8%)

simplify93.0ms (2.5%)

prune46.0ms (1.2%)

regimes641.0ms (17.2%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample928.0ms (25%)

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