Details

analyze33.0ms (1.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	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 13 to 11 computations (15.4% saved)

sample20.0ms (0.7%)

Algorithm

1×

intervals

Results

5.0ms	65×	body	512	valid
4.0ms	146×	body	128	valid
2.0ms	16×	body	1024	valid
2.0ms	29×	body	256	valid

Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify13.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

16×	`sub-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
10×	`distribute-rgt-in_binary64`
9×	`neg-mul-1_binary64`
8×	`associate--r+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	28	16
4	35	16
5	51	16
6	73	16
7	82	16
8	94	16
9	96	16
10	90	16
11	76	16

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

16.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	16.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 36 to 30 computations (16.7% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
3.9b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

rewrite246.0ms (8%)

Algorithm

1×	rewrite-expression-head

Error

14.7b

Rules

118×	`*-un-lft-identity_binary64`
95×	`add-sqr-sqrt_binary64`
90×	`times-frac_binary64`
43×	`add-cube-cbrt_binary64`
30×	`distribute-lft-out--_binary64`

Counts

3 → 151

Calls

3 calls:

37.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
6.0ms	(/.f64 1 (-.f64 x 1))
5.0ms	(/.f64 1 (+.f64 x 1))

Compiler

Compiled 2350 to 1966 computations (16.3% saved)

series61.0ms (2%)

Error

0.1b

Counts

3 → 32

Calls

3 calls:

13.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
13.0ms	(/.f64 1 (-.f64 x 1))
12.0ms	(/.f64 1 (+.f64 x 1))

Compiler

Compiled 848 to 697 computations (17.8% saved)

simplify162.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

807×	`div-sub_binary64`
278×	`sub-neg_binary64`
257×	`associate-l_binary64`
255×	`associate-r_binary64`
228×	`associate-*l/_binary64`

Counts

183 → 155

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	192	2885
1	495	2818
2	1352	2683
3	3737	2669
4	4364	2669
5	5493	2669

prune67.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	153	2	155
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	153	3	156

Error

0.1b

Counts

156 → 3

Alt Table

Status	Error	Program
	31.4b	(-.f64 (/.f64 -2 (*.f64 x x)) (/.f64 2 (pow.f64 x 4)))
✓	16.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
▶	0.1b	(/.f64 -2 (+.f64 (*.f64 x x) -1))

Compiler

Compiled 1327 to 1056 computations (20.4% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.1b	(/.f64 -2 (+.f64 (*.f64 x x) -1))

rewrite47.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

1 → 33

Calls

1 calls:

6.0ms

(/.f64 -2 (+.f64 (*.f64 x x) -1))

Compiler

Compiled 510 to 346 computations (32.2% saved)

series17.0ms (0.5%)

Error

0.1b

Counts

1 → 8

Calls

1 calls:

12.0ms

(/.f64 -2 (+.f64 (*.f64 x x) -1))

Compiler

Compiled 202 to 175 computations (13.4% saved)

simplify73.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

548×	`times-frac_binary64`
417×	`associate-/r*_binary64`
294×	`div-sub_binary64`
253×	`associate-/l/_binary64`
232×	`associate-/l*_binary64`

Counts

41 → 20

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	93	705
1	191	651
2	480	648
3	1466	645
4	4061	645
5	4978	645

prune19.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	18	2	20
Fresh	1	0	1
Picked	0	1	1
Done	1	0	1
Total	20	3	23

Error

0.0b

Counts

23 → 3

Alt Table

Status	Error	Program
	10.4b	(cbrt.f64 (/.f64 8 (pow.f64 (-.f64 1 (*.f64 x x)) 3)))
✓	0.1b	(/.f64 -2 (+.f64 (*.f64 x x) -1))
▶	0.2b	(*.f64 (/.f64 1 (+.f64 x 1)) (/.f64 -2 (+.f64 x -1)))

Compiler

Compiled 247 to 179 computations (27.5% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 -2 (+.f64 x -1))
0.2b	(*.f64 (/.f64 1 (+.f64 x 1)) (/.f64 -2 (+.f64 x -1)))

rewrite202.0ms (6.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

69×	`*-un-lft-identity_binary64`
63×	`add-sqr-sqrt_binary64`
61×	`times-frac_binary64`
39×	`add-cube-cbrt_binary64`
31×	`add-exp-log_binary64`

Counts

3 → 143

Calls

3 calls:

20.0ms	(*.f64 (/.f64 1 (+.f64 x 1)) (/.f64 -2 (+.f64 x -1)))
6.0ms	(/.f64 -2 (+.f64 x -1))
5.0ms	(/.f64 1 (+.f64 x 1))

Compiler

Compiled 2454 to 2061 computations (16% saved)

series58.0ms (1.9%)

Error

0.0b

Counts

3 → 32

Calls

3 calls:

15.0ms	(/.f64 -2 (+.f64 x -1))
12.0ms	(*.f64 (/.f64 1 (+.f64 x 1)) (/.f64 -2 (+.f64 x -1)))
12.0ms	(/.f64 1 (+.f64 x 1))

Compiler

Compiled 929 to 778 computations (16.3% saved)

simplify150.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

433×	`times-frac_binary64`
395×	`associate-/l*_binary64`
346×	`associate-*l/_binary64`
273×	`associate-*r/_binary64`
247×	`sub-neg_binary64`

Counts

175 → 130

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	2819
1	556	2456
2	1577	2444
3	4251	2444
4	4937	2444

prune108.0ms (3.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	127	3	130
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	127	6	133

Error

0.0b

Counts

133 → 6

Alt Table

Status	Error	Program
	10.4b	(cbrt.f64 (/.f64 8 (pow.f64 (-.f64 1 (*.f64 x x)) 3)))
▶	0.4b	(.f64 (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (.f64 (/.f64 -2 (+.f64 x -1)) (/.f64 (cbrt.f64 1) (cbrt.f64 (+.f64 x 1)))))
✓	0.1b	(/.f64 -2 (+.f64 (*.f64 x x) -1))
	20.4b	(.f64 (/.f64 1 (+.f64 (pow.f64 x 3) (pow.f64 1 3))) (.f64 (+.f64 (*.f64 x x) (-.f64 1 x)) (/.f64 -2 (+.f64 x -1))))
	17.9b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))) (/.f64 (/.f64 -2 (+.f64 x -1)) (sqrt.f64 (+.f64 x 1))))
✓	0.2b	(*.f64 (/.f64 1 (+.f64 x 1)) (/.f64 -2 (+.f64 x -1)))

Compiler

Compiled 1615 to 1269 computations (21.4% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))
0.3b	(cbrt.f64 (+.f64 x 1))
0.3b	(cbrt.f64 (+.f64 x 1))
0.3b	(cbrt.f64 (+.f64 x 1))

rewrite190.0ms (6.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

36×	`cbrt-prod_binary64`
35×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
18×	`cbrt-div_binary64`
15×	`add-cube-cbrt_binary64`

Counts

4 → 95

Calls

4 calls:

11.0ms	(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))
3.0ms	(cbrt.f64 (+.f64 x 1))
3.0ms	(cbrt.f64 (+.f64 x 1))
3.0ms	(cbrt.f64 (+.f64 x 1))

Compiler

Compiled 3058 to 2611 computations (14.6% saved)

series132.0ms (4.3%)

Error

0.0b

Counts

4 → 34

Calls

4 calls:

23.0ms	(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))
22.0ms	(cbrt.f64 (+.f64 x 1))
20.0ms	(cbrt.f64 (+.f64 x 1))
19.0ms	(cbrt.f64 (+.f64 x 1))

Compiler

Compiled 2702 to 2365 computations (12.5% saved)

simplify161.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

454×	`cancel-sign-sub-inv_binary64`
420×	`*-commutative_binary64`
259×	`associate-l_binary64`
222×	`distribute-rgt-neg-in_binary64`
216×	`sub-neg_binary64`

Counts

129 → 112

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	121	1802
1	256	1802
2	604	1705
3	1538	1673
4	3014	1465
5	4346	1465
6	4664	1465
7	4998	1465

prune133.0ms (4.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	112	6	118

Error

0.0b

Counts

118 → 6

Alt Table

Status	Error	Program
	10.4b	(cbrt.f64 (/.f64 8 (pow.f64 (-.f64 1 (*.f64 x x)) 3)))
	0.4b	(.f64 (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (.f64 (/.f64 -2 (+.f64 x -1)) (/.f64 (cbrt.f64 1) (cbrt.f64 (+.f64 x 1)))))
	0.1b	(/.f64 -2 (+.f64 (*.f64 x x) -1))
	20.4b	(.f64 (/.f64 1 (+.f64 (pow.f64 x 3) (pow.f64 1 3))) (.f64 (+.f64 (*.f64 x x) (-.f64 1 x)) (/.f64 -2 (+.f64 x -1))))
	17.9b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))) (/.f64 (/.f64 -2 (+.f64 x -1)) (sqrt.f64 (+.f64 x 1))))
	0.2b	(*.f64 (/.f64 1 (+.f64 x 1)) (/.f64 -2 (+.f64 x -1)))

Compiler

Compiled 2494 to 2097 computations (15.9% saved)

regimes390.0ms (12.8%)

Accuracy

Total 0.1b remaining (78.7%)

Threshold costs 0.1b (78.7%)

Compiler

Compiled 6232 to 5210 computations (16.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	13	13
2	12	13

end1.0ms (0%)

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

sample737.0ms (24.1%)

Algorithm

1×

intervals

Results

177.0ms	1966×	body	512	valid
145.0ms	4652×	body	128	valid
55.0ms	988×	body	256	valid
43.0ms	394×	body	1024	valid

Compiler

Compiled 127 to 105 computations (17.3% saved)

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	28	16
4	35	16
5	51	16
6	73	16
7	82	16
8	94	16
9	96	16
10	90	16
11	76	16

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	28	16
4	35	16
5	51	16
6	73	16
7	82	16
8	94	16
9	96	16
10	90	16
11	76	16

Details

analyze33.0ms (1.1%)

sample20.0ms (0.7%)

simplify13.0ms (0.4%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

rewrite246.0ms (8%)

series61.0ms (2%)

simplify162.0ms (5.3%)

prune67.0ms (2.2%)

localize4.0ms (0.1%)

rewrite47.0ms (1.5%)

series17.0ms (0.5%)

simplify73.0ms (2.4%)

prune19.0ms (0.6%)

localize7.0ms (0.2%)

rewrite202.0ms (6.6%)

series58.0ms (1.9%)

simplify150.0ms (4.9%)

prune108.0ms (3.5%)

localize15.0ms (0.5%)

rewrite190.0ms (6.2%)

series132.0ms (4.3%)

simplify161.0ms (5.3%)

prune133.0ms (4.3%)

regimes390.0ms (12.8%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample737.0ms (24.1%)

Profiling

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	28	16
4	35	16
5	51	16
6	73	16
7	82	16
8	94	16
9	96	16
10	90	16
11	76	16