Details

analyze480.0ms (11.8%)

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 (0.5%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	32×	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

prune8.0ms (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
▶	1.5b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z)))
	4.9b	(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 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
0.0b	(/.f64 (+.f64 x 4) y)
2.8b	(*.f64 (/.f64 x y) z)

rewrite109.0ms (2.7%)

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-l_binary64`

Counts

3 → 79

Calls

3 calls:

10.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
7.0ms	(*.f64 (/.f64 x y) z)
6.0ms	(/.f64 (+.f64 x 4) y)

Compiler

Compiled 1437 to 693 computations (51.8% saved)

series112.0ms (2.8%)

Error

0.0b

Counts

3 → 33

Calls

3 calls:

53.0ms	(-.f64 (/.f64 (+.f64 x 4) y) (*.f64 (/.f64 x y) z))
25.0ms	(*.f64 (/.f64 x y) z)
20.0ms	(/.f64 (+.f64 x 4) y)

Compiler

Compiled 1070 to 689 computations (35.6% saved)

simplify101.0ms (2.5%)

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

prune58.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	58	7	65

Error

Counts

65 → 7

Alt Table

Status	Error	Program
▶	1.5b	(fabs.f64 (-.f64 (+.f64 (/.f64 4 y) (/.f64 x y)) (*.f64 (/.f64 x y) z)))
	32.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 x y)) (.f64 z (sqrt.f64 (/.f64 x y))))))
	2.4b	(fabs.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (+.f64 x 4)) (cbrt.f64 (+.f64 x 4))) (/.f64 (cbrt.f64 (+.f64 x 4)) y)) (*.f64 (/.f64 x y) z)))
	2.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
	6.0b	(fabs.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (+.f64 x 4) (.f64 x z)) y)) (cbrt.f64 (/.f64 (-.f64 (+.f64 x 4) (.f64 x z)) y))) (cbrt.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))))
	4.9b	(fabs.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))
	1.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 z (cbrt.f64 (/.f64 x y))))))

Compiler

Compiled 1083 to 567 computations (47.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (/.f64 4 y) (/.f64 x y))
0.0b	(-.f64 (+.f64 (/.f64 4 y) (/.f64 x y)) (*.f64 (/.f64 x y) z))
2.8b	(*.f64 (/.f64 x y) z)

rewrite114.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

21×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64` `associate-l_binary64`
10×	`add-log-exp_binary64`

Counts

3 → 66

Calls

3 calls:

20.0ms	(-.f64 (+.f64 (/.f64 4 y) (/.f64 x y)) (*.f64 (/.f64 x y) z))
14.0ms	(+.f64 (/.f64 4 y) (/.f64 x y))
7.0ms	(*.f64 (/.f64 x y) z)

Compiler

Compiled 1477 to 621 computations (58% saved)

series118.0ms (2.9%)

Error

Counts

3 → 33

Calls

3 calls:

53.0ms	(-.f64 (+.f64 (/.f64 4 y) (/.f64 x y)) (*.f64 (/.f64 x y) z))
28.0ms	(*.f64 (/.f64 x y) z)
23.0ms	(+.f64 (/.f64 4 y) (/.f64 x y))

Compiler

Compiled 1108 to 707 computations (36.2% saved)

simplify83.0ms (2%)

Algorithm

1×	egg-herbie

Rules

770×	`times-frac_binary64`
372×	`associate-*l/_binary64`
327×	`distribute-rgt-in_binary64`
305×	`distribute-lft-in_binary64`
303×	`associate-*r/_binary64`

Counts

99 → 63

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	152	1465
1	393	1354
2	1232	1297
3	3856	1297
4	4951	1297

prune57.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	64	6	70

Error

Counts

70 → 6

Alt Table

Status	Error	Program
	32.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 x y)) (.f64 z (sqrt.f64 (/.f64 x y))))))
	2.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
	6.0b	(fabs.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (+.f64 x 4) (.f64 x z)) y)) (cbrt.f64 (/.f64 (-.f64 (+.f64 x 4) (.f64 x z)) y))) (cbrt.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))))
	4.9b	(fabs.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))
	1.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 z (cbrt.f64 (/.f64 x y))))))
▶	1.6b	(fabs.f64 (-.f64 (.f64 (/.f64 1 y) (+.f64 x 4)) (.f64 (/.f64 x y) z)))

Compiler

Compiled 1206 to 584 computations (51.6% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 (/.f64 1 y) (+.f64 x 4)) (.f64 (/.f64 x y) z))
0.1b	(*.f64 (/.f64 1 y) (+.f64 x 4))
2.8b	(*.f64 (/.f64 x y) z)

rewrite130.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

31×	`add-sqr-sqrt_binary64`
26×	`associate-l_binary64`
22×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`

Counts

3 → 94

Calls

3 calls:

10.0ms	(*.f64 (/.f64 1 y) (+.f64 x 4))
9.0ms	(-.f64 (.f64 (/.f64 1 y) (+.f64 x 4)) (.f64 (/.f64 x y) z))
7.0ms	(*.f64 (/.f64 x y) z)

Compiler

Compiled 2017 to 1123 computations (44.3% saved)

series110.0ms (2.7%)

Error

Counts

3 → 33

Calls

3 calls:

52.0ms	(-.f64 (.f64 (/.f64 1 y) (+.f64 x 4)) (.f64 (/.f64 x y) z))
28.0ms	(*.f64 (/.f64 x y) z)
18.0ms	(*.f64 (/.f64 1 y) (+.f64 x 4))

Compiler

Compiled 1108 to 727 computations (34.4% saved)

simplify97.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

624×	`distribute-rgt-in_binary64`
602×	`distribute-lft-in_binary64`
304×	`associate-/l*_binary64`
187×	`cancel-sign-sub-inv_binary64`
174×	`associate-l_binary64`

Counts

127 → 96

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	197	1584
1	537	1527
2	1668	1494
3	4992	1494
4	4958	1494

prune77.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	96	6	102

Error

Counts

102 → 6

Alt Table

Status	Error	Program
	32.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 x y)) (.f64 z (sqrt.f64 (/.f64 x y))))))
	2.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
	6.0b	(fabs.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (+.f64 x 4) (.f64 x z)) y)) (cbrt.f64 (/.f64 (-.f64 (+.f64 x 4) (.f64 x z)) y))) (cbrt.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))))
	4.9b	(fabs.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))
▶	1.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 z (cbrt.f64 (/.f64 x y))))))
✓	1.6b	(fabs.f64 (-.f64 (.f64 (/.f64 1 y) (+.f64 x 4)) (.f64 (/.f64 x y) z)))

Compiler

Compiled 1581 to 849 computations (46.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y)))
9.6b	(cbrt.f64 (/.f64 x y))
9.6b	(cbrt.f64 (/.f64 x y))
9.6b	(cbrt.f64 (/.f64 x y))

rewrite193.0ms (4.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

103×	`cbrt-prod_binary64`
81×	`add-sqr-sqrt_binary64`
69×	`times-frac_binary64`
57×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
16×	`swap-sqr_binary64` `associate-l_binary64` `associate-r_binary64`

Counts

4 → 144

Calls

4 calls:

15.0ms	(*.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y)))
2.0ms	(cbrt.f64 (/.f64 x y))
2.0ms	(cbrt.f64 (/.f64 x y))
2.0ms	(cbrt.f64 (/.f64 x y))

Compiler

Compiled 4323 to 1286 computations (70.3% saved)

series218.0ms (5.4%)

Error

Counts

4 → 24

Calls

4 calls:

59.0ms	(*.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y)))
47.0ms	(cbrt.f64 (/.f64 x y))
45.0ms	(cbrt.f64 (/.f64 x y))
43.0ms	(cbrt.f64 (/.f64 x y))

Compiler

Compiled 2238 to 1478 computations (34% saved)

simplify207.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

701×	`log-div_binary64`
419×	`associate-/l*_binary64`
328×	`associate-/r*_binary64`
310×	`exp-prod_binary64`
284×	`associate-l_binary64`

Counts

168 → 123

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	184	3152
1	332	2995
2	756	2845
3	1896	2467
4	4457	2323
5	4780	2319
6	4863	2319
7	5397	2319

prune92.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	123	6	129

Error

Counts

129 → 6

Alt Table

Status	Error	Program
	32.1b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (sqrt.f64 (/.f64 x y)) (.f64 z (sqrt.f64 (/.f64 x y))))))
	2.9b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (*.f64 x (/.f64 z y))))
	6.0b	(fabs.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (+.f64 x 4) (.f64 x z)) y)) (cbrt.f64 (/.f64 (-.f64 (+.f64 x 4) (.f64 x z)) y))) (cbrt.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))))
	4.9b	(fabs.f64 (/.f64 (-.f64 (+.f64 x 4) (*.f64 x z)) y))
	1.8b	(fabs.f64 (-.f64 (/.f64 (+.f64 x 4) y) (.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 z (cbrt.f64 (/.f64 x y))))))
	1.6b	(fabs.f64 (-.f64 (.f64 (/.f64 1 y) (+.f64 x 4)) (.f64 (/.f64 x y) z)))

Compiler

Compiled 2456 to 963 computations (60.8% saved)

regimes633.0ms (15.6%)

Accuracy

Total 0.2b remaining (92.4%)

Threshold costs 0.2b (92.4%)

Compiler

Compiled 7132 to 4651 computations (34.8% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 15 to 10 computations (33.3% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

19×	`+-commutative_binary64`
17×	`sub-neg_binary64`
14×	`*-commutative_binary64`
11×	`neg-mul-1_binary64` `neg-sub0_binary64`
6×	`cancel-sign-sub-inv_binary64` `distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	65
1	50	65
2	73	65
3	98	65
4	125	65
5	138	65
6	142	65
7	143	65
8	140	65

end4.0ms (0.1%)

Compiler: Compiled 46 to 27 computations (41.3% saved)

sample927.0ms (22.9%)

Algorithm

1×

intervals

Results

451.0ms	8000×	body	128	valid
45.0ms	1240×	body	128	invalid

Compiler

Compiled 193 to 119 computations (38.3% 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

analyze480.0ms (11.8%)

sample21.0ms (0.5%)

simplify55.0ms (1.4%)

prune8.0ms (0.2%)

localize9.0ms (0.2%)

rewrite109.0ms (2.7%)

series112.0ms (2.8%)

simplify101.0ms (2.5%)

prune58.0ms (1.4%)

localize8.0ms (0.2%)

rewrite114.0ms (2.8%)

series118.0ms (2.9%)

simplify83.0ms (2%)

prune57.0ms (1.4%)

localize10.0ms (0.2%)

rewrite130.0ms (3.2%)

series110.0ms (2.7%)

simplify97.0ms (2.4%)

prune77.0ms (1.9%)

localize13.0ms (0.3%)

rewrite193.0ms (4.8%)

series218.0ms (5.4%)

simplify207.0ms (5.1%)

prune92.0ms (2.3%)

regimes633.0ms (15.6%)

bsearch4.0ms (0.1%)

simplify7.0ms (0.2%)

end4.0ms (0.1%)

sample927.0ms (22.9%)

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