Details

analyze101.0ms (2.4%)

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)

sample31.0ms (0.7%)

Algorithm

1×

intervals

Results

10.0ms	53×	body	1024	valid
5.0ms	132×	body	128	valid
5.0ms	40×	body	512	valid
2.0ms	9×	body	2048	valid
2.0ms	22×	body	256	valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify80.0ms (1.9%)

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

31.6b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	31.6b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b	(/.f64 x (+.f64 x 1))
5.6b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite214.0ms (5%)

Algorithm

1×	rewrite-expression-head

Error

30.8b

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:

34.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
4.0ms	(/.f64 x (+.f64 x 1))

Compiler

Compiled 2467 to 1786 computations (27.6% saved)

series58.0ms (1.4%)

Error

0.1b

Counts

3 → 36

Calls

3 calls:

13.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
10.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
9.0ms	(/.f64 x (+.f64 x 1))

Compiler

Compiled 930 to 740 computations (20.4% saved)

simplify147.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

566×	`times-frac_binary64`
367×	`distribute-rgt-in_binary64`
282×	`div-sub_binary64`
255×	`distribute-lft-in_binary64`
229×	`cancel-sign-sub-inv_binary64`

Counts

183 → 171

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	253	3952
1	691	3853
2	2209	3408
3	4385	3400
4	5095	3400

prune74.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	167	4	171
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	167	5	172

Error

0.0b

Counts

172 → 5

Alt Table

Status	Error	Program
	31.6b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (/.f64 (-.f64 x 1) (+.f64 1 x))))
	33.3b	(-.f64 (/.f64 x (+.f64 x 1)) (.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (/.f64 (sqrt.f64 (+.f64 1 x)) (cbrt.f64 (-.f64 x 1)))))
✓	31.6b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
	60.7b	(*.f64 (+.f64 (sqrt.f64 (/.f64 x (+.f64 1 x))) (sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 x 1)))) (-.f64 (sqrt.f64 (/.f64 x (+.f64 1 x))) (sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 x 1)))))
▶	29.4b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))

Compiler

Compiled 2117 to 1500 computations (29.1% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 1 (pow.f64 x 4))
0.9b	(/.f64 3 (pow.f64 x 3))
6.6b	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
7.8b	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))

rewrite241.0ms (5.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

93×	`*-un-lft-identity_binary64`
88×	`times-frac_binary64`
75×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`
35×	`unpow-prod-down_binary64`

Counts

4 → 199

Calls

4 calls:

42.0ms	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
19.0ms	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
4.0ms	(/.f64 3 (pow.f64 x 3))
4.0ms	(/.f64 1 (pow.f64 x 4))

Compiler

Compiled 5549 to 4080 computations (26.5% saved)

series43.0ms (1%)

Error

0.0b

Counts

4 → 22

Calls

4 calls:

12.0ms	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
11.0ms	(-.f64 (-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 4)))
7.0ms	(/.f64 1 (pow.f64 x 4))
7.0ms	(/.f64 3 (pow.f64 x 3))

Compiler

Compiled 783 to 636 computations (18.8% saved)

simplify204.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

585×	`cancel-sign-sub-inv_binary64`
196×	`log-prod_binary64`
188×	`associate-l_binary64`
179×	`associate-r_binary64`
172×	`associate-/r*_binary64`

Counts

221 → 185

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	290	4776
1	718	4496
2	2642	4439
3	4629	4380
4	4962	4380
5	4929	4380

prune71.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	183	2	185
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	184	6	190

Error

0.0b

Counts

190 → 6

Alt Table

Status	Error	Program
	31.6b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (/.f64 (-.f64 x 1) (+.f64 1 x))))
	33.3b	(-.f64 (/.f64 x (+.f64 x 1)) (.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (/.f64 (sqrt.f64 (+.f64 1 x)) (cbrt.f64 (-.f64 x 1)))))
✓	31.6b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
	60.7b	(*.f64 (+.f64 (sqrt.f64 (/.f64 x (+.f64 1 x))) (sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 x 1)))) (-.f64 (sqrt.f64 (/.f64 x (+.f64 1 x))) (sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 x 1)))))
▶	29.4b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x)))))
	47.2b	(cbrt.f64 (pow.f64 (+.f64 (/.f64 -1 (pow.f64 x 4)) (-.f64 (/.f64 -3 x) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x))))) 3))

Compiler

Compiled 2390 to 1725 computations (27.8% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 1 (pow.f64 x 4))
0.9b	(/.f64 3 (pow.f64 x 3))
6.2b	(+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x))))
6.6b	(+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x)))

rewrite189.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

61×	`*-un-lft-identity_binary64`
59×	`times-frac_binary64`
45×	`add-sqr-sqrt_binary64`
45×	`add-cube-cbrt_binary64`
24×	`unpow-prod-down_binary64`

Counts

4 → 155

Calls

4 calls:

32.0ms	(+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x))))
19.0ms	(+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x)))
4.0ms	(/.f64 3 (pow.f64 x 3))
4.0ms	(/.f64 1 (pow.f64 x 4))

Compiler

Compiled 3940 to 2889 computations (26.7% saved)

series47.0ms (1.1%)

Error

0.0b

Counts

4 → 19

Calls

4 calls:

14.0ms	(+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x)))
12.0ms	(+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x))))
8.0ms	(/.f64 1 (pow.f64 x 4))
7.0ms	(/.f64 3 (pow.f64 x 3))

Compiler

Compiled 746 to 600 computations (19.6% saved)

simplify166.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

409×	`unswap-sqr_binary64`
386×	`associate-/l/_binary64`
354×	`log-prod_binary64`
300×	`distribute-rgt-in_binary64`
259×	`distribute-lft-in_binary64`

Counts

174 → 115

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	209	3126
1	449	2980
2	1622	2872
3	4481	2816
4	4867	2816
5	5064	2816

prune46.0ms (1.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	115	6	121

Error

0.0b

Counts

121 → 6

Alt Table

Status	Error	Program
▶	31.6b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (/.f64 (-.f64 x 1) (+.f64 1 x))))
	33.3b	(-.f64 (/.f64 x (+.f64 x 1)) (.f64 (/.f64 (sqrt.f64 (+.f64 1 x)) (.f64 (cbrt.f64 (-.f64 x 1)) (cbrt.f64 (-.f64 x 1)))) (/.f64 (sqrt.f64 (+.f64 1 x)) (cbrt.f64 (-.f64 x 1)))))
✓	31.6b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
	60.7b	(*.f64 (+.f64 (sqrt.f64 (/.f64 x (+.f64 1 x))) (sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 x 1)))) (-.f64 (sqrt.f64 (/.f64 x (+.f64 1 x))) (sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 x 1)))))
✓	29.4b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x)))))
	47.2b	(cbrt.f64 (pow.f64 (+.f64 (/.f64 -1 (pow.f64 x 4)) (-.f64 (/.f64 -3 x) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x))))) 3))

Compiler

Compiled 1543 to 1122 computations (27.3% saved)

localize10.0ms (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)))
5.6b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (/.f64 (-.f64 x 1) (+.f64 1 x))))

rewrite422.0ms (9.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

461×	`times-frac_binary64`
417×	`*-un-lft-identity_binary64`
345×	`add-sqr-sqrt_binary64`
180×	`add-cube-cbrt_binary64`
107×	`cancel-sign-sub-inv_binary64`

Counts

4 → 382

Calls

4 calls:

81.0ms	(-.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))
4.0ms	(/.f64 x (+.f64 x 1))

Compiler

Compiled 7506 to 5803 computations (22.7% saved)

series65.0ms (1.5%)

Error

0.0b

Counts

4 → 48

Calls

4 calls:

13.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (/.f64 (-.f64 x 1) (+.f64 1 x))))
13.0ms	(/.f64 x (+.f64 x 1))
10.0ms	(/.f64 (-.f64 x 1) (+.f64 1 x))
10.0ms	(/.f64 1 (/.f64 (-.f64 x 1) (+.f64 1 x)))

Compiler

Compiled 1348 to 1088 computations (19.3% saved)

simplify310.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

791×	`times-frac_binary64`
346×	`cancel-sign-sub-inv_binary64`
304×	`div-sub_binary64`
253×	`sub-neg_binary64`
132×	`distribute-neg-frac_binary64`

Counts

430 → 415

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	348	10503
1	882	9509
2	2717	9209
3	4378	9122
4	4993	9122

prune122.0ms (2.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	414	1	415
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	415	6	421

Error

0.0b

Counts

421 → 6

Alt Table

Status	Error	Program
✓	31.6b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (/.f64 (-.f64 x 1) (+.f64 1 x))))
✓	31.6b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
	60.7b	(*.f64 (+.f64 (sqrt.f64 (/.f64 x (+.f64 1 x))) (sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 x 1)))) (-.f64 (sqrt.f64 (/.f64 x (+.f64 1 x))) (sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 x 1)))))
	31.6b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (+.f64 x -1) (+.f64 1 x)) 3))))
✓	29.4b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x)))))
	47.2b	(cbrt.f64 (pow.f64 (+.f64 (/.f64 -1 (pow.f64 x 4)) (-.f64 (/.f64 -3 x) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (*.f64 x x))))) 3))

Compiler

Compiled 3695 to 2692 computations (27.1% saved)

regimes362.0ms (8.5%)

Accuracy

Total 0.0b remaining (24.1%)

Threshold costs 0.0b (24.1%)

Compiler

Compiled 4930 to 3714 computations (24.7% saved)

bsearch33.0ms (0.8%)

Steps

Iters	Range		Point
7	701.9903369533564	42665.44518182745	2080.752977890011
9	-9137325406.650663	-32.73708442621197	-2313.321495409526

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

14×	`+-commutative_binary64`
11×	`sub-neg_binary64`
10×	`*-commutative_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	73
1	49	73
2	65	73
3	84	73
4	102	73
5	109	73
6	111	73
7	108	73

end1.0ms (0%)

Compiler: Compiled 50 to 37 computations (26% saved)

sample1.2s (27.6%)

Algorithm

1×

intervals

Results

393.0ms	1983×	body	1024	valid
246.0ms	4273×	body	128	valid
123.0ms	1031×	body	512	valid
45.0ms	507×	body	256	valid
40.0ms	206×	body	2048	valid

Compiler

Compiled 194 to 147 computations (24.2% 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

analyze101.0ms (2.4%)

sample31.0ms (0.7%)

simplify80.0ms (1.9%)

prune2.0ms (0%)

localize7.0ms (0.2%)

rewrite214.0ms (5%)

series58.0ms (1.4%)

simplify147.0ms (3.5%)

prune74.0ms (1.7%)

localize13.0ms (0.3%)

rewrite241.0ms (5.7%)

series43.0ms (1%)

simplify204.0ms (4.8%)

prune71.0ms (1.7%)

localize13.0ms (0.3%)

rewrite189.0ms (4.4%)

series47.0ms (1.1%)

simplify166.0ms (3.9%)

prune46.0ms (1.1%)

localize10.0ms (0.2%)

rewrite422.0ms (9.9%)

series65.0ms (1.5%)

simplify310.0ms (7.3%)

prune122.0ms (2.9%)

regimes362.0ms (8.5%)

bsearch33.0ms (0.8%)

simplify7.0ms (0.2%)

end1.0ms (0%)

sample1.2s (27.6%)

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