Details

analyze512.0ms (12.9%)

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)

sample25.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
2.0ms	40×	body	128	invalid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify55.0ms (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

prune5.0ms (0.1%)

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
▶	1.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	2.9b	(fabs.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))

Compiler

Compiled 69 to 47 computations (31.9% saved)

localize9.0ms (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))
4.2b	(*.f64 (/.f64 x y) z)

rewrite105.0ms (2.7%)

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))
7.0ms	(*.f64 (/.f64 x y) z)
5.0ms	(/.f64 (+.f64 x 4) y)

Compiler

Compiled 1437 to 693 computations (51.8% saved)

series120.0ms (3%)

Error

0.0b

Counts

3 → 33

Calls

3 calls:

56.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
29.0ms	(*.f64 (/.f64 x y) z)
21.0ms	(/.f64 (+.f64 x 4) y)

Compiler

Compiled 1070 to 689 computations (35.6% saved)

simplify111.0ms (2.8%)

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

prune57.0ms (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
	32.6b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 (-.f64 (+.f64 x 4) (.f64 x z)) y)) (sqrt.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))))
	28.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 (.f64 x z) y)) (sqrt.f64 (/.f64 (*.f64 x z) y)))))
	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 x z) y)) (cbrt.f64 (/.f64 (.f64 x z) y))) (cbrt.f64 (/.f64 (*.f64 x z) y)))))
✓	1.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	2.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
▶	2.8b	(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))))))
	2.9b	(fabs.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))

Compiler

Compiled 1050 to 537 computations (48.9% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)
2.3b	(*.f64 z (/.f64 x (cbrt.f64 y)))
4.3b	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 z (/.f64 x (cbrt.f64 y))))

rewrite178.0ms (4.5%)

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:

18.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 z (/.f64 x (cbrt.f64 y))))
9.0ms	(*.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)

series163.0ms (4.1%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

77.0ms	(*.f64 z (/.f64 x (cbrt.f64 y)))
38.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (*.f64 z (/.f64 x (cbrt.f64 y))))
18.0ms	(cbrt.f64 y)
17.0ms	(cbrt.f64 y)

Compiler

Compiled 1279 to 878 computations (31.4% saved)

simplify113.0ms (2.9%)

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

prune70.0ms (1.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	97	7	104

Error

0.0b

Counts

104 → 7

Alt Table

Status	Error	Program
	32.6b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 (-.f64 (+.f64 x 4) (.f64 x z)) y)) (sqrt.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))))
	28.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 (.f64 x z) y)) (sqrt.f64 (/.f64 (*.f64 x z) y)))))
	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 x z) y)) (cbrt.f64 (/.f64 (.f64 x z) y))) (cbrt.f64 (/.f64 (*.f64 x z) y)))))
✓	1.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
▶	2.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
✓	2.8b	(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))))))
	2.9b	(fabs.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))

Compiler

Compiled 1305 to 665 computations (49% saved)

localize9.0ms (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)))
5.7b	(*.f64 x (/.f64 z y))

rewrite128.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

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:

10.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y)))
7.0ms	(*.f64 x (/.f64 z y))
5.0ms	(/.f64 (+.f64 x 4) y)

Compiler

Compiled 1437 to 693 computations (51.8% saved)

series124.0ms (3.1%)

Error

0.0b

Counts

3 → 33

Calls

3 calls:

57.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y)))
29.0ms	(*.f64 x (/.f64 z y))
22.0ms	(/.f64 (+.f64 x 4) y)

Compiler

Compiled 1070 to 697 computations (34.9% saved)

simplify111.0ms (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 (1.2%)

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
	32.6b	(fabs.f64 (.f64 (sqrt.f64 (/.f64 (-.f64 (+.f64 x 4) (.f64 x z)) y)) (sqrt.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))))
	28.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 (.f64 x z) y)) (sqrt.f64 (/.f64 (*.f64 x z) y)))))
	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 x z) y)) (cbrt.f64 (/.f64 (.f64 x z) y))) (cbrt.f64 (/.f64 (*.f64 x z) y)))))
✓	1.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
✓	2.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
✓	2.8b	(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))))))
▶	2.9b	(fabs.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))

Compiler

Compiled 853 to 445 computations (47.8% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (+.f64 x 4) (*.f64 x z))
2.7b	(/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y)

rewrite72.0ms (1.8%)

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:

8.0ms	(/.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)

series78.0ms (2%)

Error

0.0b

Counts

2 → 27

Calls

2 calls:

43.0ms	(/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y)
23.0ms	(-.f64 (+.f64 x 4) (*.f64 x z))

Compiler

Compiled 701 to 481 computations (31.4% saved)

simplify96.0ms (2.4%)

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

prune50.0ms (1.3%)

Pruning

8 alts after pruning (4 fresh and 4 done)

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

Error

Counts

69 → 8

Alt Table

Status	Error	Program
	33.4b	(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 y)) (/.f64 (+.f64 4 (-.f64 x (.f64 x z))) (sqrt.f64 y))))
	28.4b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 (.f64 x z) y)) (sqrt.f64 (/.f64 (*.f64 x z) y)))))
	3.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 x z) y)) (cbrt.f64 (/.f64 (.f64 x z) y))) (cbrt.f64 (/.f64 (*.f64 x z) y)))))
	2.9b	(fabs.f64 (/.f64 1 (/.f64 y (+.f64 4 (-.f64 x (*.f64 x z))))))
	1.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	2.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
	2.8b	(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))))))
	2.9b	(fabs.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))

Compiler

Compiled 843 to 421 computations (50.1% saved)

regimes829.0ms (20.9%)

Accuracy

Total 0.3b remaining (96.3%)

Threshold costs 0.3b (96.3%)

Compiler

Compiled 9539 to 6156 computations (35.5% saved)

bsearch21.0ms (0.5%)

Steps

Iters	Range		Point
8	1.4721712473542654e-69	1.7889168920915399e-65	4.6080437301362304e-68
1	-4.4017670332432275e-33	-2.9816116476497484e-36	-1.160409340095365e-34

Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

17×	`+-commutative_binary64`
15×	`sub-neg_binary64`
14×	`*-commutative_binary64`
10×	`neg-mul-1_binary64` `neg-sub0_binary64`
8×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	69
1	59	69
2	87	69
3	113	69
4	136	69
5	145	69
6	147	69
7	142	69

end1.0ms (0%)

Compiler: Compiled 49 to 33 computations (32.7% saved)

sample848.0ms (21.4%)

Algorithm

1×

intervals

Results

320.0ms	8000×	body	128	valid
49.0ms	1186×	body	128	invalid

Compiler

Compiled 222 to 140 computations (36.9% 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

analyze512.0ms (12.9%)

sample25.0ms (0.6%)

simplify55.0ms (1.4%)

prune5.0ms (0.1%)

localize9.0ms (0.2%)

rewrite105.0ms (2.7%)

series120.0ms (3%)

simplify111.0ms (2.8%)

prune57.0ms (1.4%)

localize16.0ms (0.4%)

rewrite178.0ms (4.5%)

series163.0ms (4.1%)

simplify113.0ms (2.9%)

prune70.0ms (1.8%)

localize9.0ms (0.2%)

rewrite128.0ms (3.2%)

series124.0ms (3.1%)

simplify111.0ms (2.8%)

prune49.0ms (1.2%)

localize7.0ms (0.2%)

rewrite72.0ms (1.8%)

series78.0ms (2%)

simplify96.0ms (2.4%)

prune50.0ms (1.3%)

regimes829.0ms (20.9%)

bsearch21.0ms (0.5%)

simplify7.0ms (0.2%)

end1.0ms (0%)

sample848.0ms (21.4%)

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