Details

analyze83.0ms (2.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
62.5%	12.5%	25%	5
68.7%	6.2%	25%	6
71.8%	3.1%	25%	7
73.4%	1.6%	25%	8
74.2%	0.8%	25%	9
74.6%	0.4%	25%	10
74.8%	0.2%	25%	11
74.9%	0.1%	25%	12
74.9%	0%	25.1%	13
74.9%	0%	25.1%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample30.0ms (0.9%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 30 to 24 computations (20% saved)

simplify63.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

154×	`cancel-sign-sub-inv_binary64`
107×	`distribute-rgt-in_binary64`
92×	`sub-neg_binary64`
83×	`associate-r_binary64`
81×	`associate-l_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	31	16
2	61	16
3	133	13
4	211	13
5	284	13
6	435	13
7	627	13
8	733	13
9	745	13
10	766	13
11	752	13
12	752	13
13	617	13

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

0.0b

Counts

2 → 2

Alt Table

Status	Error	Program
	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
▶	0.1b	(+.f64 3 (.f64 x (-.f64 -12 (.f64 x -9))))

Compiler

Compiled 58 to 46 computations (20.7% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 3 (.f64 x (-.f64 -12 (.f64 x -9))))
0.1b	(.f64 x (-.f64 -12 (.f64 x -9)))

rewrite87.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

6×	`add-sqr-sqrt_binary64`
4×	`associate-+r+_binary64`
4×	`distribute-lft-in_binary64`
4×	`cancel-sign-sub-inv_binary64`
4×	`distribute-rgt-in_binary64`

Counts

2 → 39

Calls

2 calls:

10.0ms	(.f64 x (-.f64 -12 (.f64 x -9)))
5.0ms	(+.f64 3 (.f64 x (-.f64 -12 (.f64 x -9))))

Compiler

Compiled 635 to 498 computations (21.6% saved)

series54.0ms (1.6%)

Error

0.0b

Counts

2 → 15

Calls

2 calls:

23.0ms	(+.f64 3 (.f64 x (-.f64 -12 (.f64 x -9))))
18.0ms	(.f64 x (-.f64 -12 (.f64 x -9)))

Compiler

Compiled 261 to 217 computations (16.9% saved)

simplify108.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

418×	`associate-l_binary64`
380×	`associate-+l+_binary64`
357×	`neg-mul-1_binary64`
340×	`associate-r_binary64`
330×	`cancel-sign-sub-inv_binary64`

Counts

54 → 34

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	87	754
1	211	697
2	591	697
3	2277	697
4	4467	697
5	5053	697

prune73.0ms (2.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	31	3	34
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	32	4	36

Error

0.0b

Counts

36 → 4

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 3 (+.f64 (.f64 -12 x) (.f64 9 (*.f64 x x))))
✓	0.1b	(+.f64 3 (.f64 x (-.f64 -12 (.f64 x -9))))
	0.4b	(+.f64 3 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (-.f64 -12 (.f64 x -9)) (cbrt.f64 x))))
	7.8b	(+.f64 3 (/.f64 (+.f64 (.f64 x 144) (.f64 (pow.f64 x 3) -81)) (+.f64 -12 (*.f64 x -9))))

Compiler

Compiled 389 to 295 computations (24.2% saved)

localize13.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 3 (+.f64 (.f64 -12 x) (.f64 9 (*.f64 x x))))
0.0b	(+.f64 (.f64 -12 x) (.f64 9 (*.f64 x x)))
0.2b	(.f64 9 (.f64 x x))

rewrite107.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

10×	`add-log-exp_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
6×	`*-un-lft-identity_binary64`

Counts

3 → 44

Calls

3 calls:

10.0ms	(+.f64 3 (+.f64 (.f64 -12 x) (.f64 9 (*.f64 x x))))
8.0ms	(.f64 9 (.f64 x x))
6.0ms	(+.f64 (.f64 -12 x) (.f64 9 (*.f64 x x)))

Compiler

Compiled 799 to 535 computations (33% saved)

series56.0ms (1.6%)

Error

0.0b

Counts

3 → 18

Calls

3 calls:

22.0ms	(+.f64 3 (+.f64 (.f64 -12 x) (.f64 9 (*.f64 x x))))
18.0ms	(+.f64 (.f64 -12 x) (.f64 9 (*.f64 x x)))
9.0ms	(.f64 9 (.f64 x x))

Compiler

Compiled 344 to 286 computations (16.9% saved)

simplify128.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

536×	`associate-l_binary64`
470×	`distribute-rgt-out_binary64`
434×	`associate-r_binary64`
319×	`distribute-rgt-neg-in_binary64`
264×	`distribute-lft-neg-in_binary64`

Counts

62 → 43

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	943
1	246	787
2	736	769
3	2876	766
4	4943	766
5	4900	766

prune54.0ms (1.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	42	5	47

Error

Counts

47 → 5

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 3 (+.f64 (.f64 -12 x) (.f64 9 (*.f64 x x))))
✓	0.1b	(+.f64 3 (.f64 x (-.f64 -12 (.f64 x -9))))
▶	0.1b	(+.f64 3 (+.f64 (.f64 -12 x) (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (*.f64 x x) (cbrt.f64 9)))))
	0.4b	(+.f64 3 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (-.f64 -12 (.f64 x -9)) (cbrt.f64 x))))
	7.8b	(+.f64 3 (/.f64 (+.f64 (.f64 x 144) (.f64 (pow.f64 x 3) -81)) (+.f64 -12 (*.f64 x -9))))

Compiler

Compiled 530 to 412 computations (22.3% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 3 (+.f64 (.f64 -12 x) (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (*.f64 x x) (cbrt.f64 9)))))
0.0b	(+.f64 (.f64 -12 x) (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (*.f64 x x) (cbrt.f64 9))))
0.1b	(.f64 (.f64 x x) (cbrt.f64 9))
0.2b	(.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (.f64 x x) (cbrt.f64 9)))

rewrite268.0ms (7.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

30×	`add-exp-log_binary64`
30×	`pow1_binary64`
18×	`cbrt-unprod_binary64`
18×	`add-cbrt-cube_binary64`
18×	`prod-exp_binary64`

Counts

4 → 76

Calls

4 calls:

19.0ms	(.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (.f64 x x) (cbrt.f64 9)))
11.0ms	(.f64 (.f64 x x) (cbrt.f64 9))
11.0ms	(+.f64 3 (+.f64 (.f64 -12 x) (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (*.f64 x x) (cbrt.f64 9)))))
7.0ms	(+.f64 (.f64 -12 x) (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (*.f64 x x) (cbrt.f64 9))))

Compiler

Compiled 1925 to 1489 computations (22.6% saved)

series123.0ms (3.6%)

Error

Counts

4 → 21

Calls

4 calls:

39.0ms	(+.f64 3 (+.f64 (.f64 -12 x) (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (*.f64 x x) (cbrt.f64 9)))))
31.0ms	(+.f64 (.f64 -12 x) (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (*.f64 x x) (cbrt.f64 9))))
22.0ms	(.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (.f64 x x) (cbrt.f64 9)))
16.0ms	(.f64 (.f64 x x) (cbrt.f64 9))

Compiler

Compiled 566 to 494 computations (12.7% saved)

simplify161.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

493×	`distribute-rgt-neg-in_binary64`
420×	`*-commutative_binary64`
298×	`distribute-rgt-in_binary64`
265×	`distribute-lft-in_binary64`
259×	`cancel-sign-sub-inv_binary64`

Counts

97 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	1399
1	333	1291
2	1191	1129
3	3181	1129
4	4728	1129
5	5287	1129

prune75.0ms (2.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	78	5	83

Error

Counts

83 → 5

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 3 (+.f64 (.f64 -12 x) (.f64 9 (*.f64 x x))))
✓	0.1b	(+.f64 3 (.f64 x (-.f64 -12 (.f64 x -9))))
✓	0.1b	(+.f64 3 (+.f64 (.f64 -12 x) (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (*.f64 x x) (cbrt.f64 9)))))
▶	0.4b	(+.f64 3 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (-.f64 -12 (.f64 x -9)) (cbrt.f64 x))))
	7.8b	(+.f64 3 (/.f64 (+.f64 (.f64 x 144) (.f64 (pow.f64 x 3) -81)) (+.f64 -12 (*.f64 x -9))))

Compiler

Compiled 788 to 610 computations (22.6% saved)

localize20.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite132.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`

Counts

4 → 73

Calls

4 calls:

10.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

Compiler

Compiled 1420 to 695 computations (51.1% saved)

series143.0ms (4.2%)

Error

Counts

4 → 12

Calls

4 calls:

32.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
25.0ms	(cbrt.f64 x)
24.0ms	(cbrt.f64 x)
23.0ms	(cbrt.f64 x)

Compiler

Compiled 621 to 469 computations (24.5% saved)

simplify146.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

428×	`neg-mul-1_binary64`
414×	`unswap-sqr_binary64`
407×	`neg-sub0_binary64`
369×	`log-prod_binary64`
357×	`*-commutative_binary64`

Counts

85 → 64

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	82	887
1	153	711
2	583	697
3	1058	683
4	2620	559
5	4079	559
6	4768	559
7	4868	559

prune44.0ms (1.3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	64	5	69

Error

Counts

69 → 5

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 3 (+.f64 (.f64 -12 x) (.f64 9 (*.f64 x x))))
✓	0.1b	(+.f64 3 (.f64 x (-.f64 -12 (.f64 x -9))))
✓	0.1b	(+.f64 3 (+.f64 (.f64 -12 x) (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (*.f64 x x) (cbrt.f64 9)))))
✓	0.4b	(+.f64 3 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (-.f64 -12 (.f64 x -9)) (cbrt.f64 x))))
	7.8b	(+.f64 3 (/.f64 (+.f64 (.f64 x 144) (.f64 (pow.f64 x 3) -81)) (+.f64 -12 (*.f64 x -9))))

Compiler

Compiled 598 to 395 computations (33.9% saved)

regimes367.0ms (10.7%)

Accuracy

Total 0.1b remaining (88%)

Threshold costs 0.1b (88%)

Compiler

Compiled 3008 to 2369 computations (21.2% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-rgt-neg-in_binary64`
2×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	17	13
2	28	13
3	32	13
4	34	13
5	33	13

end1.0ms (0%)

Compiler: Compiled 10 to 8 computations (20% saved)

sample1.1s (31.1%)

Algorithm

1×

intervals

Results

621.0ms	8000×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 102 to 80 computations (21.6% saved)

Iter	Nodes	Cost
0	11	19
1	31	16
2	61	16
3	133	13
4	211	13
5	284	13
6	435	13
7	627	13
8	733	13
9	745	13
10	766	13
11	752	13
12	752	13
13	617	13

Iter	Nodes	Cost
0	11	19
1	31	16
2	61	16
3	133	13
4	211	13
5	284	13
6	435	13
7	627	13
8	733	13
9	745	13
10	766	13
11	752	13
12	752	13
13	617	13

Details

analyze83.0ms (2.4%)

sample30.0ms (0.9%)

simplify63.0ms (1.8%)

prune5.0ms (0.2%)

localize10.0ms (0.3%)

rewrite87.0ms (2.5%)

series54.0ms (1.6%)

simplify108.0ms (3.1%)

prune73.0ms (2.1%)

localize13.0ms (0.4%)

rewrite107.0ms (3.1%)

series56.0ms (1.6%)

simplify128.0ms (3.7%)

prune54.0ms (1.6%)

localize18.0ms (0.5%)

rewrite268.0ms (7.8%)

series123.0ms (3.6%)

simplify161.0ms (4.7%)

prune75.0ms (2.2%)

localize20.0ms (0.6%)

rewrite132.0ms (3.8%)

series143.0ms (4.2%)

simplify146.0ms (4.2%)

prune44.0ms (1.3%)

regimes367.0ms (10.7%)

simplify7.0ms (0.2%)

end1.0ms (0%)

sample1.1s (31.1%)

Profiling

Iter	Nodes	Cost
0	11	19
1	31	16
2	61	16
3	133	13
4	211	13
5	284	13
6	435	13
7	627	13
8	733	13
9	745	13
10	766	13
11	752	13
12	752	13
13	617	13