Details

analyze64.0ms (2.8%)

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)

sample15.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms

256×

body

128

valid

Compiler

Compiled 30 to 24 computations (20% saved)

simplify46.0ms (2%)

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

prune9.0ms (0.4%)

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 x (-.f64 -12 (.f64 x -9))))
	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))

Compiler

Compiled 58 to 46 computations (20.7% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 -12 (*.f64 x -9))
0.1b	(.f64 x (-.f64 -12 (.f64 x -9)))

rewrite54.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 36

Calls

2 calls:

6.0ms	(.f64 x (-.f64 -12 (.f64 x -9)))
3.0ms	(-.f64 -12 (*.f64 x -9))

Compiler

Compiled 558 to 442 computations (20.8% saved)

series26.0ms (1.1%)

Error

0.0b

Counts

2 → 12

Calls

2 calls:

11.0ms	(.f64 x (-.f64 -12 (.f64 x -9)))
8.0ms	(-.f64 -12 (*.f64 x -9))

Compiler

Compiled 221 to 180 computations (18.6% saved)

simplify85.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

534×	`distribute-neg-out_binary64`
458×	`unsub-neg_binary64`
333×	`associate-l_binary64`
327×	`neg-sub0_binary64`
317×	`neg-mul-1_binary64`

Counts

48 → 41

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	71	587
1	158	515
2	461	512
3	1439	512
4	2671	512
5	4913	512
6	4888	512

prune38.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	39	2	41
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	39	4	43

Error

0.0b

Counts

43 → 4

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 3 (+.f64 (.f64 -12 x) (.f64 9 (*.f64 x x))))
	6.9b	(+.f64 3 (/.f64 (.f64 x (-.f64 144 (.f64 x (.f64 x 81)))) (+.f64 -12 (.f64 x -9))))
✓	0.1b	(+.f64 3 (.f64 x (-.f64 -12 (.f64 x -9))))
	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))

Compiler

Compiled 495 to 388 computations (21.6% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

rewrite44.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 30

Calls

2 calls:

6.0ms	(.f64 9 (.f64 x x))
4.0ms	(+.f64 (.f64 -12 x) (.f64 9 (*.f64 x x)))

Compiler

Compiled 511 to 339 computations (33.7% saved)

series22.0ms (0.9%)

Error

0.0b

Counts

2 → 9

Calls

2 calls:

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

Compiler

Compiled 201 to 168 computations (16.4% saved)

simplify76.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

452×	`associate-l_binary64`
395×	`distribute-rgt-in_binary64`
395×	`distribute-rgt-out_binary64`
357×	`distribute-lft-in_binary64`
353×	`associate-r_binary64`

Counts

39 → 25

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	490
1	170	415
2	484	397
3	1761	394
4	4697	394
5	5060	394

prune22.0ms (1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	25	0	25
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	25	4	29

Error

0.0b

Counts

29 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 3 (+.f64 (.f64 -12 x) (.f64 9 (*.f64 x x))))
	6.9b	(+.f64 3 (/.f64 (.f64 x (-.f64 144 (.f64 x (.f64 x 81)))) (+.f64 -12 (.f64 x -9))))
✓	0.1b	(+.f64 3 (.f64 x (-.f64 -12 (.f64 x -9))))
▶	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))

Compiler

Compiled 318 to 244 computations (23.3% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4)) 1)
0.0b	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))
0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
0.2b	(.f64 (.f64 x 3) x)

rewrite114.0ms (4.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-log-exp_binary64`
11×	`add-exp-log_binary64`
11×	`pow1_binary64`

Counts

4 → 69

Calls

4 calls:

11.0ms	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
8.0ms	(+.f64 (-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4)) 1)
5.0ms	(.f64 (.f64 x 3) x)
5.0ms	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))

Compiler

Compiled 1436 to 1108 computations (22.8% saved)

series70.0ms (3%)

Error

0.0b

Counts

4 → 27

Calls

4 calls:

17.0ms	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
15.0ms	(+.f64 (-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4)) 1)
14.0ms	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))
7.0ms	(.f64 (.f64 x 3) x)

Compiler

Compiled 559 to 476 computations (14.8% saved)

simplify106.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

336×	`distribute-rgt-in_binary64`
330×	`distribute-lft-in_binary64`
273×	`*-commutative_binary64`
259×	`+-commutative_binary64`
206×	`cancel-sign-sub-inv_binary64`

Counts

96 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	1593
1	316	1284
2	882	1257
3	2378	1255
4	4545	1255
5	4951	1255

prune78.0ms (3.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	1	1
Picked	0	1	1
Done	1	1	2
Total	81	4	85

Error

Counts

85 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 3 (+.f64 (.f64 -12 x) (.f64 9 (*.f64 x x))))
	6.9b	(+.f64 3 (/.f64 (.f64 x (-.f64 144 (.f64 x (.f64 x 81)))) (+.f64 -12 (.f64 x -9))))
✓	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
▶	0.2b	(.f64 (.f64 3 (sqrt.f64 (+.f64 (.f64 x (+.f64 -4 (.f64 3 x))) 1))) (sqrt.f64 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4)) 1)))

Compiler

Compiled 1053 to 835 computations (20.7% saved)

localize18.0ms (0.8%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 x (+.f64 -4 (.f64 3 x)))
0.1b	(.f64 (.f64 3 (sqrt.f64 (+.f64 (.f64 x (+.f64 -4 (.f64 3 x))) 1))) (sqrt.f64 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4)) 1)))
0.1b	(.f64 3 (sqrt.f64 (+.f64 (.f64 x (+.f64 -4 (*.f64 3 x))) 1)))
0.2b	(.f64 (.f64 x 3) x)

rewrite189.0ms (8.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

19×	`associate-r_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`
18×	`pow1_binary64`

Counts

4 → 94

Calls

4 calls:

23.0ms	(.f64 (.f64 3 (sqrt.f64 (+.f64 (.f64 x (+.f64 -4 (.f64 3 x))) 1))) (sqrt.f64 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4)) 1)))
10.0ms	(.f64 3 (sqrt.f64 (+.f64 (.f64 x (+.f64 -4 (*.f64 3 x))) 1)))
7.0ms	(.f64 x (+.f64 -4 (.f64 3 x)))
5.0ms	(.f64 (.f64 x 3) x)

Compiler

Compiled 3261 to 2610 computations (20% saved)

series99.0ms (4.3%)

Error

Counts

4 → 30

Calls

4 calls:

29.0ms	(.f64 3 (sqrt.f64 (+.f64 (.f64 x (+.f64 -4 (*.f64 3 x))) 1)))
17.0ms	(.f64 (.f64 3 (sqrt.f64 (+.f64 (.f64 x (+.f64 -4 (.f64 3 x))) 1))) (sqrt.f64 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4)) 1)))
14.0ms	(.f64 x (+.f64 -4 (.f64 3 x)))
10.0ms	(.f64 (.f64 x 3) x)

Compiler

Compiled 1470 to 1238 computations (15.8% saved)

simplify143.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

549×	`distribute-rgt-in_binary64`
518×	`distribute-lft-in_binary64`
313×	`associate-l_binary64`
255×	`cancel-sign-sub-inv_binary64`
230×	`associate-r_binary64`

Counts

124 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	234	3073
1	606	2520
2	1770	2309
3	4663	2307
4	4997	2307
5	4898	2307

prune104.0ms (4.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	100	4	104

Error

Counts

104 → 4

Alt Table

Status	Error	Program
	0.1b	(+.f64 3 (+.f64 (.f64 -12 x) (.f64 9 (*.f64 x x))))
	6.9b	(+.f64 3 (/.f64 (.f64 x (-.f64 144 (.f64 x (.f64 x 81)))) (+.f64 -12 (.f64 x -9))))
	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
	0.2b	(.f64 (.f64 3 (sqrt.f64 (+.f64 (.f64 x (+.f64 -4 (.f64 3 x))) 1))) (sqrt.f64 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4)) 1)))

Compiler

Compiled 2180 to 1747 computations (19.9% saved)

regimes327.0ms (14.2%)

Accuracy

Total 0.1b remaining (77.1%)

Threshold costs 0.1b (77.1%)

Compiler

Compiled 3928 to 3177 computations (19.1% saved)

simplify5.0ms (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)

sample535.0ms (23.1%)

Algorithm

1×

intervals

Results

262.0ms

8000×

body

128

valid

Compiler

Compiled 96 to 76 computations (20.8% 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

analyze64.0ms (2.8%)

sample15.0ms (0.7%)

simplify46.0ms (2%)

prune9.0ms (0.4%)

localize6.0ms (0.3%)

rewrite54.0ms (2.4%)

series26.0ms (1.1%)

simplify85.0ms (3.7%)

prune38.0ms (1.6%)

localize7.0ms (0.3%)

rewrite44.0ms (1.9%)

series22.0ms (0.9%)

simplify76.0ms (3.3%)

prune22.0ms (1%)

localize9.0ms (0.4%)

rewrite114.0ms (4.9%)

series70.0ms (3%)

simplify106.0ms (4.6%)

prune78.0ms (3.4%)

localize18.0ms (0.8%)

rewrite189.0ms (8.2%)

series99.0ms (4.3%)

simplify143.0ms (6.2%)

prune104.0ms (4.5%)

regimes327.0ms (14.2%)

simplify5.0ms (0.2%)

end1.0ms (0%)

sample535.0ms (23.1%)

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