Details

analyze45.0ms (2.6%)

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 11 to 9 computations (18.2% saved)

sample14.0ms (0.8%)

Algorithm

1×

intervals

Results

6.0ms	234×	body	128	valid
1.0ms	15×	body	1024	valid
0.0ms	6×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 22 to 18 computations (18.2% saved)

simplify31.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

127×	`cancel-sign-sub-inv_binary64`
85×	`distribute-rgt-in_binary64`
63×	`associate-l_binary64`
60×	`distribute-lft-in_binary64`
55×	`associate-r_binary64`

Counts

1 → 1

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	40	10
3	87	10
4	146	10
5	195	10
6	244	10
7	379	10
8	367	10
9	426	10
10	533	10
11	530	10
12	524	10
13	524	10
14	405	10

prune4.0ms (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

0.2b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	0.2b	(.f64 x (+.f64 6 (.f64 x -9)))
	0.2b	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)

Compiler

Compiled 44 to 34 computations (22.7% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 6 (*.f64 x -9))
0.1b	(.f64 x (+.f64 6 (.f64 x -9)))

rewrite47.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

6×	`add-sqr-sqrt_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
3×	`associate-l_binary64` `associate-r_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `*-commutative_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

2 → 33

Calls

2 calls:

10.0ms	(.f64 x (+.f64 6 (.f64 x -9)))
3.0ms	(+.f64 6 (*.f64 x -9))

Compiler

Compiled 459 to 353 computations (23.1% saved)

series28.0ms (1.6%)

Error

0.1b

Counts

2 → 12

Calls

2 calls:

14.0ms	(.f64 x (+.f64 6 (.f64 x -9)))
8.0ms	(+.f64 6 (*.f64 x -9))

Compiler

Compiled 173 to 132 computations (23.7% saved)

simplify77.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

717×	`unsub-neg_binary64`
301×	`distribute-neg-out_binary64`
263×	`times-frac_binary64` `*-commutative_binary64`
256×	`neg-mul-1_binary64`
252×	`neg-sub0_binary64`

Counts

45 → 37

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	542
1	181	485
2	558	482
3	1375	482
4	2540	482
5	4648	482
6	5199	482

prune37.0ms (2.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	31	6	37
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	32	7	39

Error

0.0b

Counts

39 → 7

Alt Table

Status	Error	Program
	12.0b	(.f64 (.f64 x (sqrt.f64 (-.f64 6 (.f64 x 9)))) (sqrt.f64 (+.f64 6 (.f64 x -9))))
	0.2b	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)
	9.7b	(.f64 x (cbrt.f64 (pow.f64 (-.f64 6 (.f64 x 9)) 3)))
	32.9b	(.f64 (sqrt.f64 x) (.f64 (-.f64 6 (*.f64 x 9)) (sqrt.f64 x)))
	1.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (-.f64 6 (.f64 x 9)) (cbrt.f64 x)))
	9.3b	(/.f64 (.f64 x (-.f64 36 (.f64 x (.f64 x 81)))) (-.f64 6 (.f64 x -9)))
▶	0.2b	(+.f64 (.f64 6 x) (.f64 (*.f64 x x) -9))

Compiler

Compiled 525 to 392 computations (25.3% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 6 x) (.f64 (*.f64 x x) -9))
0.2b	(.f64 (.f64 x x) -9)

rewrite35.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

7×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
3×	`pow-prod-down_binary64` `prod-exp_binary64` `add-cube-cbrt_binary64` `cbrt-unprod_binary64` `-un-lft-identity_binary64` `associate-r*_binary64`
1×	`unswap-sqr_binary64` `associate-l_binary64` `*-commutative_binary64` `sum-log_binary64` `flip3-+_binary64` `flip-+_binary64` `+-commutative_binary64`

Counts

2 → 30

Calls

2 calls:

5.0ms	(.f64 (.f64 x x) -9)
4.0ms	(+.f64 (.f64 6 x) (.f64 (*.f64 x x) -9))

Compiler

Compiled 468 to 292 computations (37.6% saved)

series22.0ms (1.3%)

Error

0.0b

Counts

2 → 9

Calls

2 calls:

12.0ms	(+.f64 (.f64 6 x) (.f64 (*.f64 x x) -9))
7.0ms	(.f64 (.f64 x x) -9)

Compiler

Compiled 163 to 130 computations (20.2% saved)

simplify86.0ms (5%)

Algorithm

1×	egg-herbie

Rules

879×	`unsub-neg_binary64`
588×	`times-frac_binary64`
285×	`*-commutative_binary64`
257×	`distribute-rgt-in_binary64`
235×	`distribute-lft-out_binary64`

Counts

39 → 31

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	498
1	180	423
2	558	405
3	1324	405
4	3466	405
5	4284	405
6	5178	405

prune24.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	31	7	38

Error

0.0b

Counts

38 → 7

Alt Table

Status	Error	Program
	12.0b	(.f64 (.f64 x (sqrt.f64 (-.f64 6 (.f64 x 9)))) (sqrt.f64 (+.f64 6 (.f64 x -9))))
▶	0.2b	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)
	9.7b	(.f64 x (cbrt.f64 (pow.f64 (-.f64 6 (.f64 x 9)) 3)))
	32.9b	(.f64 (sqrt.f64 x) (.f64 (-.f64 6 (*.f64 x 9)) (sqrt.f64 x)))
	1.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (-.f64 6 (.f64 x 9)) (cbrt.f64 x)))
	9.3b	(/.f64 (.f64 x (-.f64 36 (.f64 x (.f64 x 81)))) (-.f64 6 (.f64 x -9)))
✓	0.2b	(+.f64 (.f64 6 x) (.f64 (*.f64 x x) -9))

Compiler

Compiled 427 to 302 computations (29.3% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 2 (*.f64 x 3))
0.1b	(.f64 3 (-.f64 2 (.f64 x 3)))
0.1b	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)

rewrite70.0ms (4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

10×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64` `-un-lft-identity_binary64` `associate-r*_binary64`
5×	`add-log-exp_binary64`
4×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `associate-l*_binary64`

Counts

3 → 56

Calls

3 calls:

7.0ms	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)
5.0ms	(.f64 3 (-.f64 2 (.f64 x 3)))
3.0ms	(-.f64 2 (*.f64 x 3))

Compiler

Compiled 880 to 716 computations (18.6% saved)

series35.0ms (2%)

Error

0.0b

Counts

3 → 18

Calls

3 calls:

12.0ms	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)
9.0ms	(.f64 3 (-.f64 2 (.f64 x 3)))
8.0ms	(-.f64 2 (*.f64 x 3))

Compiler

Compiled 273 to 211 computations (22.7% saved)

simplify88.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

391×	`*-commutative_binary64`
244×	`unsub-neg_binary64`
243×	`distribute-rgt-neg-out_binary64`
242×	`distribute-lft-neg-out_binary64`
213×	`exp-prod_binary64`

Counts

74 → 56

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	942
1	225	732
2	632	726
3	1597	726
4	2406	726
5	4613	726
6	4882	726

prune44.0ms (2.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	55	8	63

Error

Counts

63 → 8

Alt Table

Status	Error	Program
	12.0b	(.f64 (.f64 x (sqrt.f64 (-.f64 6 (.f64 x 9)))) (sqrt.f64 (+.f64 6 (.f64 x -9))))
✓	0.2b	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)
	9.7b	(.f64 x (cbrt.f64 (pow.f64 (-.f64 6 (.f64 x 9)) 3)))
	32.9b	(.f64 (sqrt.f64 x) (.f64 (-.f64 6 (*.f64 x 9)) (sqrt.f64 x)))
	1.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (-.f64 6 (.f64 x 9)) (cbrt.f64 x)))
	9.3b	(/.f64 (.f64 x (-.f64 36 (.f64 x (.f64 x 81)))) (-.f64 6 (.f64 x -9)))
▶	0.2b	(.f64 3 (.f64 x (-.f64 2 (*.f64 x 3))))
✓	0.2b	(+.f64 (.f64 6 x) (.f64 (*.f64 x x) -9))

Compiler

Compiled 614 to 469 computations (23.6% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 2 (*.f64 x 3))
0.1b	(.f64 x (-.f64 2 (.f64 x 3)))
0.1b	(.f64 3 (.f64 x (-.f64 2 (*.f64 x 3))))

rewrite75.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

10×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`sub-neg_binary64` `cancel-sign-sub-inv_binary64`
6×	`add-cube-cbrt_binary64` `-un-lft-identity_binary64` `associate-r/_binary64` `associate-l_binary64`
5×	`add-log-exp_binary64`

Counts

3 → 64

Calls

3 calls:

7.0ms	(.f64 3 (.f64 x (-.f64 2 (*.f64 x 3))))
5.0ms	(.f64 x (-.f64 2 (.f64 x 3)))
3.0ms	(-.f64 2 (*.f64 x 3))

Compiler

Compiled 981 to 777 computations (20.8% saved)

series41.0ms (2.4%)

Error

Counts

3 → 18

Calls

3 calls:

14.0ms	(.f64 3 (.f64 x (-.f64 2 (*.f64 x 3))))
11.0ms	(.f64 x (-.f64 2 (.f64 x 3)))
8.0ms	(-.f64 2 (*.f64 x 3))

Compiler

Compiled 314 to 254 computations (19.1% saved)

simplify117.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

339×	`unsub-neg_binary64`
268×	`unswap-sqr_binary64`
261×	`distribute-rgt-neg-out_binary64`
246×	`neg-mul-1_binary64`
242×	`neg-sub0_binary64`

Counts

82 → 62

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	110	1094
1	224	893
2	679	893
3	1703	893
4	2818	893
5	4955	893
6	4994	893
7	4907	893

prune40.0ms (2.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	62	8	70

Error

Counts

70 → 8

Alt Table

Status	Error	Program
	12.0b	(.f64 (.f64 x (sqrt.f64 (-.f64 6 (.f64 x 9)))) (sqrt.f64 (+.f64 6 (.f64 x -9))))
	0.2b	(.f64 (.f64 3 (-.f64 2 (*.f64 x 3))) x)
	9.7b	(.f64 x (cbrt.f64 (pow.f64 (-.f64 6 (.f64 x 9)) 3)))
	1.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (-.f64 6 (.f64 x 9)) (cbrt.f64 x)))
	9.3b	(/.f64 (.f64 x (-.f64 36 (.f64 x (.f64 x 81)))) (-.f64 6 (.f64 x -9)))
	0.2b	(.f64 3 (.f64 x (-.f64 2 (*.f64 x 3))))
	0.2b	(+.f64 (.f64 6 x) (.f64 (*.f64 x x) -9))
	0.7b	(.f64 (sqrt.f64 3) (.f64 x (.f64 (-.f64 2 (.f64 x 3)) (sqrt.f64 3))))

Compiler

Compiled 541 to 409 computations (24.4% saved)

regimes187.0ms (10.8%)

Accuracy

Total 0.2b remaining (89.3%)

Threshold costs 0.2b (89.3%)

Compiler

Compiled 1906 to 1470 computations (22.9% saved)

simplify5.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`sub-neg_binary64` `+-commutative_binary64`
2×	`neg-mul-1_binary64` `neg-sub0_binary64` `cancel-sign-sub-inv_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	17	13
2	25	13
3	29	13
4	32	13
5	33	13
6	32	13

end1.0ms (0%)

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

sample563.0ms (32.4%)

Algorithm

1×

intervals

Results

184.0ms	7202×	body	128	valid
49.0ms	453×	body	1024	valid
16.0ms	249×	body	512	valid
4.0ms	96×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 124 to 96 computations (22.6% saved)

Iter	Nodes	Cost
0	8	13
1	18	13
2	40	10
3	87	10
4	146	10
5	195	10
6	244	10
7	379	10
8	367	10
9	426	10
10	533	10
11	530	10
12	524	10
13	524	10
14	405	10

Iter	Nodes	Cost
0	8	13
1	18	13
2	40	10
3	87	10
4	146	10
5	195	10
6	244	10
7	379	10
8	367	10
9	426	10
10	533	10
11	530	10
12	524	10
13	524	10
14	405	10

Details

analyze45.0ms (2.6%)

sample14.0ms (0.8%)

simplify31.0ms (1.8%)

prune4.0ms (0.2%)

localize5.0ms (0.3%)

rewrite47.0ms (2.7%)

series28.0ms (1.6%)

simplify77.0ms (4.4%)

prune37.0ms (2.1%)

localize6.0ms (0.3%)

rewrite35.0ms (2%)

series22.0ms (1.3%)

simplify86.0ms (5%)

prune24.0ms (1.4%)

localize6.0ms (0.3%)

rewrite70.0ms (4%)

series35.0ms (2%)

simplify88.0ms (5.1%)

prune44.0ms (2.5%)

localize6.0ms (0.3%)

rewrite75.0ms (4.3%)

series41.0ms (2.4%)

simplify117.0ms (6.7%)

prune40.0ms (2.3%)

regimes187.0ms (10.8%)

simplify5.0ms (0.3%)

end1.0ms (0%)

sample563.0ms (32.4%)

Profiling

Iter	Nodes	Cost
0	8	13
1	18	13
2	40	10
3	87	10
4	146	10
5	195	10
6	244	10
7	379	10
8	367	10
9	426	10
10	533	10
11	530	10
12	524	10
13	524	10
14	405	10