Details

analyze70.0ms (2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
37.5%	12.5%	50%	4
43.7%	6.2%	50%	5
46.9%	3.1%	50%	6
48.4%	1.6%	50%	7
49.2%	0.8%	50%	8
49.6%	0.4%	50%	9
49.8%	0.2%	50%	10
49.9%	0.1%	50%	11
49.9%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 30 to 20 computations (33.3% saved)

sample28.0ms (0.8%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 57 to 38 computations (33.3% saved)

simplify51.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-/r*_binary64`
516×	`cancel-sign-sub-inv_binary64`
510×	`distribute-rgt-in_binary64`
489×	`distribute-lft-in_binary64`
415×	`associate-/r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	39	28
2	177	19
3	904	13
4	2320	13
5	4069	13
6	5047	13

prune10.0ms (0.3%)

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

0.5b

Counts

2 → 2

Alt Table

Status	Error	Program
	46.1b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
▶	0.6b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

Compiler

Compiled 82 to 58 computations (29.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.6b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
0.8b	(/.f64 1 (*.f64 i i))

rewrite106.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

37×	`add-sqr-sqrt_binary64`
35×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`

Counts

2 → 81

Calls

2 calls:

8.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
5.0ms	(/.f64 1 (*.f64 i i))

Compiler

Compiled 1183 to 881 computations (25.5% saved)

series31.0ms (0.9%)

Error

0.0b

Counts

2 → 15

Calls

2 calls:

15.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
6.0ms	(/.f64 1 (*.f64 i i))

Compiler

Compiled 344 to 299 computations (13.1% saved)

simplify103.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

463×	`associate-/l*_binary64`
430×	`cancel-sign-sub-inv_binary64`
308×	`div-sub_binary64`
300×	`associate-/r/_binary64`
262×	`associate-/l/_binary64`

Counts

96 → 74

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	154	1565
1	300	1472
2	669	1369
3	1640	1369
4	4435	1309
5	4852	1309

prune52.0ms (1.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	73	3	76

Error

Counts

76 → 3

Alt Table

Status	Error	Program
	46.1b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
▶	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
	31.3b	(.f64 (.f64 i i) -1/4)

Compiler

Compiled 583 to 435 computations (25.4% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 2 (/.f64 1 i))
0.0b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
0.1b	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
0.1b	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

rewrite262.0ms (7.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

123×	`add-sqr-sqrt_binary64`
108×	`*-un-lft-identity_binary64`
107×	`times-frac_binary64`
55×	`add-cube-cbrt_binary64`
30×	`associate-r_binary64`

Counts

4 → 190

Calls

4 calls:

31.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
11.0ms	(-.f64 2 (/.f64 1 i))
9.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
9.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

Compiler

Compiled 4069 to 3550 computations (12.8% saved)

series80.0ms (2.3%)

Error

Counts

4 → 42

Calls

4 calls:

15.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
15.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
14.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
8.0ms	(-.f64 2 (/.f64 1 i))

Compiler

Compiled 1242 to 1067 computations (14.1% saved)

simplify165.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

589×	`associate-*l/_binary64`
538×	`associate-/l*_binary64`
290×	`associate-/l/_binary64`
209×	`times-frac_binary64`
205×	`associate-/r*_binary64`

Counts

232 → 186

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	280	4473
1	736	4143
2	2100	4019
3	4940	4019
4	4918	4019

prune153.0ms (4.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	186	3	189

Error

Counts

189 → 3

Alt Table

Status	Error	Program
	46.1b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
▶	31.2b	(+.f64 (-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4)) (*.f64 (pow.f64 i 6) -4))

Compiler

Compiled 2779 to 2354 computations (15.3% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (pow.f64 i 6) -4)
0.0b	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
0.0b	(+.f64 (-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4)) (*.f64 (pow.f64 i 6) -4))
0.2b	(.f64 (.f64 i i) -1/4)

rewrite114.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

18×	`add-sqr-sqrt_binary64`
14×	`cancel-sign-sub-inv_binary64`
14×	`add-exp-log_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

4 → 83

Calls

4 calls:

11.0ms	(+.f64 (-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4)) (*.f64 (pow.f64 i 6) -4))
7.0ms	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
6.0ms	(.f64 (.f64 i i) -1/4)
5.0ms	(*.f64 (pow.f64 i 6) -4)

Compiler

Compiled 1846 to 1288 computations (30.2% saved)

series67.0ms (1.9%)

Error

Counts

4 → 21

Calls

4 calls:

27.0ms	(+.f64 (-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4)) (*.f64 (pow.f64 i 6) -4))
14.0ms	(-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4))
8.0ms	(*.f64 (pow.f64 i 6) -4)
8.0ms	(.f64 (.f64 i i) -1/4)

Compiler

Compiled 598 to 482 computations (19.4% saved)

simplify123.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

509×	`exp-prod_binary64`
433×	`log-prod_binary64`
415×	`*-commutative_binary64`
269×	`cube-prod_binary64`
255×	`cancel-sign-sub-inv_binary64`

Counts

104 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	1506
1	389	1402
2	1279	1363
3	3596	1363
4	4694	1363
5	4983	1363

prune45.0ms (1.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	82	3	85

Error

Counts

85 → 3

Alt Table

Status	Error	Program
▶	46.1b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
✓	31.2b	(+.f64 (-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4)) (*.f64 (pow.f64 i 6) -4))

Compiler

Compiled 942 to 657 computations (30.3% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.1b

(*.f64 (*.f64 i i) (*.f64 i i))

15.8b

(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))

42.2b

(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i)))

rewrite299.0ms (8.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

302×	`add-cbrt-cube_binary64`
302×	`add-exp-log_binary64`
168×	`cbrt-unprod_binary64`
168×	`prod-exp_binary64`
114×	`pow1_binary64`

Counts

3 → 232

Calls

3 calls:

40.0ms

(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))

26.0ms

(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i)))

9.0ms

(*.f64 (*.f64 i i) (*.f64 i i))

Compiler

Compiled 8459 to 4631 computations (45.3% saved)

series44.0ms (1.2%)

Error

Counts

3 → 18

Calls

3 calls:

19.0ms

(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))

8.0ms

(*.f64 (*.f64 i i) (*.f64 i i))

7.0ms

(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i)))

Compiler

Compiled 539 to 445 computations (17.4% saved)

simplify220.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

585×	`times-frac_binary64`
294×	`associate-/l*_binary64`
285×	`log-prod_binary64`
257×	`log-div_binary64`
236×	`associate-/r*_binary64`

Counts

250 → 229

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	281	7327
1	525	3694
2	2820	3546
3	4635	3546
4	4910	3546
5	4914	3546

prune75.0ms (2.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	229	3	232

Error

Counts

232 → 3

Alt Table

Status	Error	Program
	46.1b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
	31.2b	(+.f64 (-.f64 (.f64 (.f64 i i) -1/4) (pow.f64 i 4)) (*.f64 (pow.f64 i 6) -4))

Compiler

Compiled 1463 to 980 computations (33% saved)

regimes449.0ms (12.7%)

Accuracy

Total 0.1b remaining (94.8%)

Threshold costs 0.1b (94.8%)

Compiler

Compiled 5868 to 4835 computations (17.6% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	22
1	22	22
2	28	22
3	30	22
4	31	22
5	26	22

end1.0ms (0%)

Compiler: Compiled 16 to 14 computations (12.5% saved)

sample939.0ms (26.6%)

Algorithm

1×

intervals

Results

471.0ms	8000×	body	128	valid
98.0ms	8000×	pre	128	true

Compiler

Compiled 105 to 78 computations (25.7% saved)

Details

analyze70.0ms (2%)

sample28.0ms (0.8%)

simplify51.0ms (1.5%)

prune10.0ms (0.3%)

localize6.0ms (0.2%)

rewrite106.0ms (3%)

series31.0ms (0.9%)

simplify103.0ms (2.9%)

prune52.0ms (1.5%)

localize9.0ms (0.3%)

rewrite262.0ms (7.4%)

series80.0ms (2.3%)

simplify165.0ms (4.7%)

prune153.0ms (4.3%)

localize10.0ms (0.3%)

rewrite114.0ms (3.2%)

series67.0ms (1.9%)

simplify123.0ms (3.5%)

prune45.0ms (1.3%)

localize10.0ms (0.3%)

rewrite299.0ms (8.5%)

series44.0ms (1.2%)

simplify220.0ms (6.2%)

prune75.0ms (2.1%)

regimes449.0ms (12.7%)

simplify6.0ms (0.2%)

end1.0ms (0%)

sample939.0ms (26.6%)

Profiling