Details

analyze98.0ms (2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample24.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	83×	body	1024	valid
4.0ms	124×	body	128	valid
2.0ms	28×	body	512	valid
1.0ms	18×	body	256	valid
0.0ms	3×	body	2048	valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify84.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

335×	`div-sub_binary64`
178×	`associate-/l*_binary64`
162×	`sub-neg_binary64`
146×	`times-frac_binary64`
139×	`cancel-sign-sub-inv_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	33	19
4	55	19
5	85	19
6	165	19
7	242	19
8	538	19
9	578	19
10	658	19
11	835	19
12	780	19
13	770	19
14	764	19
15	766	19
16	768	19
17	770	19
18	770	19
19	681	19

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

32.0b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	32.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b	(/.f64 x (+.f64 x 1))
2.9b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite263.0ms (5.3%)

Algorithm

1×	rewrite-expression-head

Error

31.5b

Rules

148×	`*-un-lft-identity_binary64`
88×	`times-frac_binary64`
85×	`add-sqr-sqrt_binary64`
37×	`add-cube-cbrt_binary64`
34×	`cancel-sign-sub-inv_binary64`

Counts

3 → 147

Calls

3 calls:

45.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
8.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
6.0ms	(/.f64 x (+.f64 x 1))

Compiler

Compiled 2467 to 1786 computations (27.6% saved)

series62.0ms (1.3%)

Error

0.0b

Counts

3 → 36

Calls

3 calls:

16.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
12.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
11.0ms	(/.f64 x (+.f64 x 1))

Compiler

Compiled 930 to 740 computations (20.4% saved)

simplify145.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

566×	`times-frac_binary64`
534×	`associate-/l*_binary64`
331×	`distribute-rgt-in_binary64`
237×	`distribute-lft-in_binary64`
170×	`associate-/l/_binary64`

Counts

183 → 166

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	3709
1	635	3606
2	1963	3158
3	4525	3142
4	4949	3142

prune120.0ms (2.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	161	5	166
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	162	5	167

Error

0.0b

Counts

167 → 5

Alt Table

Status	Error	Program
	34.6b	(+.f64 1 (*.f64 x (+.f64 3 x)))
	32.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (/.f64 (+.f64 x -1) (+.f64 1 x))))
	32.0b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)) (+.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (/.f64 (+.f64 x (.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
	32.6b	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (-.f64 -1 x) (pow.f64 (cbrt.f64 (+.f64 x -1)) 3)))
▶	29.1b	(-.f64 (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))) (/.f64 3 (pow.f64 x 3)))

Compiler

Compiled 2107 to 1490 computations (29.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x)))
0.3b	(/.f64 3 (pow.f64 x 3))
0.5b	(/.f64 1 (*.f64 x x))
7.2b	(-.f64 (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))) (/.f64 3 (pow.f64 x 3)))

rewrite229.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

95×	`times-frac_binary64`
83×	`add-sqr-sqrt_binary64`
72×	`*-un-lft-identity_binary64`
57×	`add-cube-cbrt_binary64`
54×	`cancel-sign-sub-inv_binary64`

Counts

4 → 198

Calls

4 calls:

44.0ms	(-.f64 (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))) (/.f64 3 (pow.f64 x 3)))
11.0ms	(-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x)))
5.0ms	(/.f64 3 (pow.f64 x 3))
5.0ms	(/.f64 1 (*.f64 x x))

Compiler

Compiled 3962 to 2795 computations (29.5% saved)

series46.0ms (0.9%)

Error

0.0b

Counts

4 → 19

Calls

4 calls:

14.0ms	(-.f64 (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))) (/.f64 3 (pow.f64 x 3)))
11.0ms	(-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x)))
7.0ms	(/.f64 3 (pow.f64 x 3))
7.0ms	(/.f64 1 (*.f64 x x))

Compiler

Compiled 586 to 478 computations (18.4% saved)

simplify177.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

440×	`unswap-sqr_binary64`
300×	`log-prod_binary64`
266×	`cancel-sign-sub-inv_binary64`
250×	`associate-/r*_binary64`
246×	`distribute-neg-frac_binary64`

Counts

217 → 178

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	279	3198
1	656	3040
2	2553	3019
3	4542	2947
4	4650	2947
5	4942	2947

prune64.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	177	6	183

Error

0.0b

Counts

183 → 6

Alt Table

Status	Error	Program
	34.6b	(+.f64 1 (*.f64 x (+.f64 3 x)))
▶	32.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (/.f64 (+.f64 x -1) (+.f64 1 x))))
	32.0b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)) (+.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (/.f64 (+.f64 x (.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
	32.6b	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (-.f64 -1 x) (pow.f64 (cbrt.f64 (+.f64 x -1)) 3)))
	53.5b	(-.f64 (/.f64 (-.f64 (pow.f64 (/.f64 -3 x) 3) (/.f64 1 (pow.f64 x 6))) (+.f64 (/.f64 (/.f64 9 x) x) (+.f64 (/.f64 -3 (pow.f64 x 3)) (pow.f64 (/.f64 1 x) 4)))) (/.f64 3 (pow.f64 x 3)))
✓	29.1b	(-.f64 (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))) (/.f64 3 (pow.f64 x 3)))

Compiler

Compiled 1678 to 1202 computations (28.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 x -1) (+.f64 1 x))
0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 1 (/.f64 (+.f64 x -1) (+.f64 1 x)))
2.9b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (/.f64 (+.f64 x -1) (+.f64 1 x))))

rewrite418.0ms (8.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

349×	`times-frac_binary64`
320×	`*-un-lft-identity_binary64`
214×	`add-sqr-sqrt_binary64`
148×	`add-cube-cbrt_binary64`
83×	`cancel-sign-sub-inv_binary64`

Counts

4 → 315

Calls

4 calls:

86.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (/.f64 (+.f64 x -1) (+.f64 1 x))))
12.0ms	(/.f64 1 (/.f64 (+.f64 x -1) (+.f64 1 x)))
7.0ms	(/.f64 (+.f64 x -1) (+.f64 1 x))
5.0ms	(/.f64 x (+.f64 x 1))

Compiler

Compiled 6673 to 5174 computations (22.5% saved)

series78.0ms (1.6%)

Error

0.0b

Counts

4 → 48

Calls

4 calls:

16.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (/.f64 (+.f64 x -1) (+.f64 1 x))))
12.0ms	(/.f64 (+.f64 x -1) (+.f64 1 x))
12.0ms	(/.f64 x (+.f64 x 1))
12.0ms	(/.f64 1 (/.f64 (+.f64 x -1) (+.f64 1 x)))

Compiler

Compiled 1348 to 1088 computations (19.3% saved)

simplify317.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

476×	`distribute-rgt-in_binary64`
395×	`distribute-lft-in_binary64`
217×	`cancel-sign-sub-inv_binary64`
178×	`div-sub_binary64`
165×	`sub-neg_binary64`

Counts

363 → 319

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	321	8128
1	818	7341
2	2438	7083
3	4731	6936
4	4995	6936
5	4944	6936

prune144.0ms (2.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	318	1	319
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	319	6	325

Error

0.0b

Counts

325 → 6

Alt Table

Status	Error	Program
✓	32.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (/.f64 (+.f64 x -1) (+.f64 1 x))))
▶	32.0b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)) (+.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (/.f64 (+.f64 x (.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
	32.6b	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (-.f64 -1 x) (pow.f64 (cbrt.f64 (+.f64 x -1)) 3)))
	53.5b	(-.f64 (/.f64 (-.f64 (pow.f64 (/.f64 -3 x) 3) (/.f64 1 (pow.f64 x 6))) (+.f64 (/.f64 (/.f64 9 x) x) (+.f64 (/.f64 -3 (pow.f64 x 3)) (pow.f64 (/.f64 1 x) 4)))) (/.f64 3 (pow.f64 x 3)))
	34.8b	(+.f64 (+.f64 1 (.f64 x (+.f64 3 x))) (.f64 3 (pow.f64 x 3)))
✓	29.1b	(-.f64 (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))) (/.f64 3 (pow.f64 x 3)))

Compiler

Compiled 3279 to 2379 computations (27.4% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 x (*.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))
0.0b	(pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)
0.1b	(pow.f64 (/.f64 x (+.f64 1 x)) 3)
2.9b	(-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3))

rewrite486.0ms (9.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

351×	`*-un-lft-identity_binary64`
207×	`times-frac_binary64`
177×	`add-sqr-sqrt_binary64`
130×	`cube-prod_binary64`
130×	`unpow-prod-down_binary64`

Counts

4 → 311

Calls

4 calls:

123.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3))
10.0ms	(pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)
8.0ms	(/.f64 (+.f64 x (*.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))
7.0ms	(pow.f64 (/.f64 x (+.f64 1 x)) 3)

Compiler

Compiled 9696 to 7172 computations (26% saved)

series130.0ms (2.6%)

Error

0.0b

Counts

4 → 47

Calls

4 calls:

26.0ms	(-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3))
22.0ms	(pow.f64 (/.f64 x (+.f64 1 x)) 3)
20.0ms	(pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)
20.0ms	(/.f64 (+.f64 x (*.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))

Compiler

Compiled 3675 to 2770 computations (24.6% saved)

simplify261.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

334×	`associate-r_binary64`
273×	`associate-l_binary64`
187×	`log-prod_binary64`
185×	`associate-*r/_binary64`
185×	`associate-*l/_binary64`

Counts

358 → 240

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	432	10101
1	1265	9464
2	4771	9464
3	5190	9464

prune162.0ms (3.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	240	0	240
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	240	6	246

Error

0.0b

Counts

246 → 6

Alt Table

Status	Error	Program
	32.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (/.f64 (+.f64 x -1) (+.f64 1 x))))
	32.0b	(/.f64 (-.f64 (pow.f64 (/.f64 x (+.f64 1 x)) 3) (pow.f64 (/.f64 (+.f64 1 x) (+.f64 x -1)) 3)) (+.f64 (.f64 (/.f64 x (+.f64 1 x)) (/.f64 x (+.f64 1 x))) (/.f64 (+.f64 x (.f64 (+.f64 1 x) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (+.f64 x -1))))
	32.6b	(+.f64 (/.f64 x (+.f64 x 1)) (/.f64 (-.f64 -1 x) (pow.f64 (cbrt.f64 (+.f64 x -1)) 3)))
	53.5b	(-.f64 (/.f64 (-.f64 (pow.f64 (/.f64 -3 x) 3) (/.f64 1 (pow.f64 x 6))) (+.f64 (/.f64 (/.f64 9 x) x) (+.f64 (/.f64 -3 (pow.f64 x 3)) (pow.f64 (/.f64 1 x) 4)))) (/.f64 3 (pow.f64 x 3)))
	34.8b	(+.f64 (+.f64 1 (.f64 x (+.f64 3 x))) (.f64 3 (pow.f64 x 3)))
	29.1b	(-.f64 (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))) (/.f64 3 (pow.f64 x 3)))

Compiler

Compiled 5718 to 4161 computations (27.2% saved)

regimes497.0ms (10.1%)

Accuracy

Total 0.1b remaining (78.7%)

Threshold costs 0.1b (78.7%)

Compiler

Compiled 6176 to 4600 computations (25.5% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
12×	`sub-neg_binary64`
8×	`*-commutative_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	65
1	44	65
2	68	65
3	84	65
4	93	65
5	95	65
6	91	65

end1.0ms (0%)

Compiler: Compiled 45 to 34 computations (24.4% saved)

sample1.1s (22%)

Algorithm

1×

intervals

Results

227.0ms	1996×	body	1024	valid
139.0ms	4329×	body	128	valid
91.0ms	945×	body	512	valid
32.0ms	224×	body	2048	valid
29.0ms	506×	body	256	valid

Compiler

Compiled 208 to 158 computations (24% saved)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	33	19
4	55	19
5	85	19
6	165	19
7	242	19
8	538	19
9	578	19
10	658	19
11	835	19
12	780	19
13	770	19
14	764	19
15	766	19
16	768	19
17	770	19
18	770	19
19	681	19

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	33	19
4	55	19
5	85	19
6	165	19
7	242	19
8	538	19
9	578	19
10	658	19
11	835	19
12	780	19
13	770	19
14	764	19
15	766	19
16	768	19
17	770	19
18	770	19
19	681	19

Details

analyze98.0ms (2%)

sample24.0ms (0.5%)

simplify84.0ms (1.7%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite263.0ms (5.3%)

series62.0ms (1.3%)

simplify145.0ms (2.9%)

prune120.0ms (2.4%)

localize9.0ms (0.2%)

rewrite229.0ms (4.6%)

series46.0ms (0.9%)

simplify177.0ms (3.6%)

prune64.0ms (1.3%)

localize9.0ms (0.2%)

rewrite418.0ms (8.4%)

series78.0ms (1.6%)

simplify317.0ms (6.4%)

prune144.0ms (2.9%)

localize19.0ms (0.4%)

rewrite486.0ms (9.8%)

series130.0ms (2.6%)

simplify261.0ms (5.3%)

prune162.0ms (3.3%)

regimes497.0ms (10.1%)

bsearch5.0ms (0.1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.1s (22%)

Profiling

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	33	19
4	55	19
5	85	19
6	165	19
7	242	19
8	538	19
9	578	19
10	658	19
11	835	19
12	780	19
13	770	19
14	764	19
15	766	19
16	768	19
17	770	19
18	770	19
19	681	19