Details

analyze93.0ms (2.8%)

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 (0.7%)

Algorithm

1×

intervals

Results

7.0ms	61×	body	1024	valid
4.0ms	137×	body	128	valid
3.0ms	37×	body	512	valid
2.0ms	11×	body	2048	valid
1.0ms	10×	body	256	valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify78.0ms (2.4%)

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

prune6.0ms (0.2%)

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

28.9b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	28.9b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
1.7b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite202.0ms (6.2%)

Algorithm

1×	rewrite-expression-head

Error

28.4b

Rules

130×	`*-un-lft-identity_binary64`
76×	`times-frac_binary64`
75×	`add-sqr-sqrt_binary64`
34×	`cancel-sign-sub-inv_binary64`
27×	`add-cube-cbrt_binary64`

Counts

2 → 114

Calls

2 calls:

42.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
8.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

Compiler

Compiled 1887 to 1386 computations (26.6% saved)

series40.0ms (1.2%)

Error

0.1b

Counts

2 → 20

Calls

2 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))

Compiler

Compiled 493 to 403 computations (18.3% saved)

simplify120.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

448×	`associate-/l*_binary64`
436×	`div-sub_binary64`
392×	`times-frac_binary64`
331×	`associate-l_binary64`
299×	`associate-*l/_binary64`

Counts

134 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	179	2813
1	506	2710
2	1538	2464
3	4267	2464
4	5413	2464

prune63.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	120	5	125

Error

0.1b

Counts

125 → 5

Alt Table

Status	Error	Program
✓	28.9b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
▶	28.9b	(log.f64 (exp.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))))
	32.2b	(-.f64 (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 4))))
	31.6b	(+.f64 1 (*.f64 3 x))
	30.2b	(/.f64 (-.f64 (-.f64 (.f64 x x) x) (.f64 (+.f64 1 x) (+.f64 1 x))) (+.f64 (*.f64 x x) -1))

Compiler

Compiled 1371 to 985 computations (28.2% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))))
0.0b	(/.f64 (+.f64 1 x) (+.f64 x -1))
1.7b	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
1.7b	(log.f64 (exp.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))))

rewrite310.0ms (9.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

262×	`*-un-lft-identity_binary64`
140×	`times-frac_binary64`
101×	`add-sqr-sqrt_binary64`
78×	`cancel-sign-sub-inv_binary64`
74×	`distribute-lft-out_binary64`

Counts

4 → 205

Calls

4 calls:

42.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))))
40.0ms	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
38.0ms	(exp.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))))
8.0ms	(/.f64 (+.f64 1 x) (+.f64 x -1))

Compiler

Compiled 3944 to 3004 computations (23.8% saved)

series77.0ms (2.4%)

Error

0.1b

Counts

4 → 40

Calls

4 calls:

17.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))))
15.0ms	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
14.0ms	(exp.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1))))
14.0ms	(/.f64 (+.f64 1 x) (+.f64 x -1))

Compiler

Compiled 973 to 822 computations (15.5% saved)

simplify184.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

403×	`times-frac_binary64`
380×	`exp-prod_binary64`
305×	`distribute-rgt-in_binary64`
257×	`distribute-lft-in_binary64`
192×	`log-pow_binary64`

Counts

245 → 176

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	267	5705
1	669	5431
2	1941	4597
3	4390	4597
4	4918	4597

prune73.0ms (2.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	176	5	181

Error

0.1b

Counts

181 → 5

Alt Table

Status	Error	Program
✓	28.9b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
✓	28.9b	(log.f64 (exp.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))))
	32.2b	(-.f64 (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 4))))
	31.6b	(+.f64 1 (*.f64 3 x))
▶	30.2b	(/.f64 (-.f64 (-.f64 (.f64 x x) x) (.f64 (+.f64 1 x) (+.f64 1 x))) (+.f64 (*.f64 x x) -1))

Compiler

Compiled 1611 to 1169 computations (27.4% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 (-.f64 (.f64 x x) x) (.f64 (+.f64 1 x) (+.f64 1 x))) (+.f64 (*.f64 x x) -1))
0.0b	(*.f64 (+.f64 1 x) (+.f64 1 x))
0.0b	(-.f64 (*.f64 x x) x)
18.5b	(-.f64 (-.f64 (.f64 x x) x) (.f64 (+.f64 1 x) (+.f64 1 x)))

rewrite271.0ms (8.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

35×	`*-un-lft-identity_binary64`
32×	`frac-sub_binary64`
31×	`flip3-+_binary64` `flip-+_binary64`
29×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64` `frac-times_binary64`

Counts

4 → 150

Calls

4 calls:

16.0ms	(/.f64 (-.f64 (-.f64 (.f64 x x) x) (.f64 (+.f64 1 x) (+.f64 1 x))) (+.f64 (*.f64 x x) -1))
11.0ms	(-.f64 (-.f64 (.f64 x x) x) (.f64 (+.f64 1 x) (+.f64 1 x)))
9.0ms	(*.f64 (+.f64 1 x) (+.f64 1 x))
4.0ms	(-.f64 (*.f64 x x) x)

Compiler

Compiled 5845 to 2860 computations (51.1% saved)

series60.0ms (1.8%)

Error

0.0b

Counts

4 → 31

Calls

4 calls:

15.0ms	(*.f64 (+.f64 1 x) (+.f64 1 x))
12.0ms	(/.f64 (-.f64 (-.f64 (.f64 x x) x) (.f64 (+.f64 1 x) (+.f64 1 x))) (+.f64 (*.f64 x x) -1))
11.0ms	(-.f64 (*.f64 x x) x)
9.0ms	(-.f64 (-.f64 (.f64 x x) x) (.f64 (+.f64 1 x) (+.f64 1 x)))

Compiler

Compiled 898 to 622 computations (30.7% saved)

simplify178.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

642×	`times-frac_binary64`
389×	`distribute-rgt-in_binary64`
367×	`distribute-lft-in_binary64`
276×	`div-sub_binary64`
229×	`associate-r_binary64`

Counts

181 → 159

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	284	5191
1	764	4850
2	3204	4761
3	4998	4761
4	4949	4761

prune106.0ms (3.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	158	1	159
Fresh	1	1	2
Picked	1	0	1
Done	2	0	2
Total	162	2	164

Error

0.0b

Counts

164 → 2

Alt Table

Status	Error	Program
	32.2b	(-.f64 (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 4))))
▶	15.9b	(/.f64 (-.f64 -1 (.f64 3 x)) (+.f64 (.f64 x x) -1))

Compiler

Compiled 4223 to 2208 computations (47.7% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (*.f64 x x) -1)
15.9b	(/.f64 (-.f64 -1 (.f64 3 x)) (+.f64 (.f64 x x) -1))

rewrite61.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

12×	`times-frac_binary64`
11×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
5×	`difference-of-sqr--1_binary64`
4×	`add-exp-log_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64` `associate-/r*_binary64`
3×	`associate-/l*_binary64`

Counts

2 → 48

Calls

2 calls:

8.0ms	(/.f64 (-.f64 -1 (.f64 3 x)) (+.f64 (.f64 x x) -1))
4.0ms	(+.f64 (*.f64 x x) -1)

Compiler

Compiled 1014 to 697 computations (31.3% saved)

series28.0ms (0.9%)

Error

0.0b

Counts

2 → 16

Calls

2 calls:

12.0ms	(/.f64 (-.f64 -1 (.f64 3 x)) (+.f64 (.f64 x x) -1))
10.0ms	(+.f64 (*.f64 x x) -1)

Compiler

Compiled 343 to 287 computations (16.3% saved)

simplify95.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

506×	`div-sub_binary64`
277×	`distribute-rgt-in_binary64`
271×	`associate-l_binary64`
231×	`distribute-lft-in_binary64`
225×	`associate-r_binary64`

Counts

64 → 33

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	113	1295
1	294	1190
2	888	1188
3	3450	1188
4	4997	1188
5	4944	1188

prune29.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	32	1	33
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	32	3	35

Error

Counts

35 → 3

Alt Table

Status	Error	Program
	0.3b	(/.f64 (/.f64 (-.f64 -1 (*.f64 3 x)) (+.f64 1 x)) (-.f64 x 1))
	32.2b	(-.f64 (-.f64 (/.f64 -3 x) (/.f64 1 (*.f64 x x))) (+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 4))))
	15.9b	(/.f64 (-.f64 -1 (.f64 3 x)) (+.f64 (.f64 x x) -1))

Compiler

Compiled 464 to 338 computations (27.2% saved)

regimes305.0ms (9.3%)

Accuracy

Total 0.1b remaining (96.6%)

Threshold costs 0.1b (96.6%)

Compiler

Compiled 6129 to 4083 computations (33.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-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`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	23	19
2	30	19
3	34	19
4	37	19
5	38	19
6	35	19

end1.0ms (0%)

Compiler: Compiled 14 to 11 computations (21.4% saved)

sample833.0ms (25.4%)

Algorithm

1×

intervals

Results

260.0ms	2035×	body	1024	valid
140.0ms	4257×	body	128	valid
98.0ms	1035×	body	512	valid
32.0ms	478×	body	256	valid
30.0ms	195×	body	2048	valid

Compiler

Compiled 78 to 60 computations (23.1% 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

analyze93.0ms (2.8%)

sample24.0ms (0.7%)

simplify78.0ms (2.4%)

prune6.0ms (0.2%)

localize6.0ms (0.2%)

rewrite202.0ms (6.2%)

series40.0ms (1.2%)

simplify120.0ms (3.7%)

prune63.0ms (1.9%)

localize9.0ms (0.3%)

rewrite310.0ms (9.5%)

series77.0ms (2.4%)

simplify184.0ms (5.6%)

prune73.0ms (2.2%)

localize9.0ms (0.3%)

rewrite271.0ms (8.3%)

series60.0ms (1.8%)

simplify178.0ms (5.4%)

prune106.0ms (3.3%)

localize8.0ms (0.3%)

rewrite61.0ms (1.9%)

series28.0ms (0.9%)

simplify95.0ms (2.9%)

prune29.0ms (0.9%)

regimes305.0ms (9.3%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample833.0ms (25.4%)

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