Details

analyze25.0ms (1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
100%	0%	0%	2

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample12.0ms (0.5%)

Algorithm

1×

intervals

Results

5.0ms

256×

body

128

valid

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	9	10
2	8	10

prune2.0ms (0.1%)

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

11.8b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	11.8b	(/.f64 x (+.f64 (*.f64 x x) 1))

Compiler

Compiled 16 to 10 computations (37.5% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (*.f64 x x) 1)
11.8b	(/.f64 x (+.f64 (*.f64 x x) 1))

rewrite58.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

11.7b

Rules

10×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
9×	`times-frac_binary64`
4×	`add-exp-log_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`associate-/l_binary64` `associate-/r_binary64`
2×	`pow1_binary64` `flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64`

Counts

2 → 40

Calls

2 calls:

6.0ms	(/.f64 x (+.f64 (*.f64 x x) 1))
4.0ms	(+.f64 (*.f64 x x) 1)

Compiler

Compiled 619 to 318 computations (48.6% saved)

series36.0ms (1.4%)

Error

0.0b

Counts

2 → 17

Calls

2 calls:

17.0ms	(/.f64 x (+.f64 (*.f64 x x) 1))
9.0ms	(+.f64 (*.f64 x x) 1)

Compiler

Compiled 279 to 211 computations (24.4% saved)

simplify95.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

601×	`div-sub_binary64`
430×	`associate-/r*_binary64`
327×	`associate-/l/_binary64`
308×	`associate-*l/_binary64`
221×	`distribute-rgt-in_binary64`

Counts

57 → 45

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	87	876
1	200	802
2	467	802
3	1400	802
4	3900	802
5	4744	802
6	5661	802

prune35.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	42	3	45
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	42	4	46

Error

Counts

46 → 4

Alt Table

Status	Error	Program
▶	11.8b	(/.f64 1 (/.f64 (+.f64 1 (*.f64 x x)) x))
	38.0b	(.f64 (sqrt.f64 (/.f64 x (+.f64 1 (.f64 x x)))) (sqrt.f64 (/.f64 x (+.f64 1 (*.f64 x x)))))
	34.4b	(+.f64 (-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 5)))
✓	11.8b	(/.f64 x (+.f64 (*.f64 x x) 1))

Compiler

Compiled 624 to 353 computations (43.4% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1 (*.f64 x x))
0.1b	(/.f64 1 (/.f64 (+.f64 1 (*.f64 x x)) x))
11.7b	(/.f64 (+.f64 1 (*.f64 x x)) x)

rewrite114.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

84×	`times-frac_binary64`
53×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
16×	`add-exp-log_binary64` `associate-/r*_binary64`
10×	`add-cbrt-cube_binary64`
8×	`div-exp_binary64`

Counts

3 → 116

Calls

3 calls:

7.0ms	(/.f64 1 (/.f64 (+.f64 1 (*.f64 x x)) x))
5.0ms	(/.f64 (+.f64 1 (*.f64 x x)) x)
3.0ms	(+.f64 1 (*.f64 x x))

Compiler

Compiled 2257 to 1355 computations (40% saved)

series45.0ms (1.8%)

Error

Counts

3 → 23

Calls

3 calls:

15.0ms	(/.f64 1 (/.f64 (+.f64 1 (*.f64 x x)) x))
12.0ms	(/.f64 (+.f64 1 (*.f64 x x)) x)
10.0ms	(+.f64 1 (*.f64 x x))

Compiler

Compiled 372 to 287 computations (22.8% saved)

simplify154.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

353×	`div-sub_binary64`
334×	`times-frac_binary64`
328×	`cancel-sign-sub-inv_binary64`
312×	`distribute-rgt-in_binary64`
279×	`*-commutative_binary64`

Counts

139 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	2611
1	282	2344
2	729	2317
3	1995	2317
4	3403	2317
5	4516	2317
6	4917	2317

prune36.0ms (1.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	91	4	95

Error

Counts

95 → 4

Alt Table

Status	Error	Program
✓	11.8b	(/.f64 1 (/.f64 (+.f64 1 (*.f64 x x)) x))
	38.0b	(.f64 (sqrt.f64 (/.f64 x (+.f64 1 (.f64 x x)))) (sqrt.f64 (/.f64 x (+.f64 1 (*.f64 x x)))))
▶	34.4b	(+.f64 (-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 5)))
✓	11.8b	(/.f64 x (+.f64 (*.f64 x x) 1))

Compiler

Compiled 835 to 483 computations (42.2% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))
0.3b	(/.f64 1 (pow.f64 x 3))
0.4b	(/.f64 1 (pow.f64 x 5))
21.1b	(+.f64 (-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 5)))

rewrite384.0ms (15.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

194×	`times-frac_binary64`
165×	`add-sqr-sqrt_binary64`
157×	`*-un-lft-identity_binary64`
96×	`add-cube-cbrt_binary64`
80×	`cancel-sign-sub-inv_binary64`

Counts

4 → 287

Calls

4 calls:

84.0ms	(+.f64 (-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 5)))
33.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))
5.0ms	(/.f64 1 (pow.f64 x 3))
4.0ms	(/.f64 1 (pow.f64 x 5))

Compiler

Compiled 5603 to 4501 computations (19.7% saved)

series54.0ms (2.1%)

Error

Counts

4 → 19

Calls

4 calls:

15.0ms	(+.f64 (-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 5)))
12.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))
11.0ms	(/.f64 1 (pow.f64 x 3))
10.0ms	(/.f64 1 (pow.f64 x 5))

Compiler

Compiled 498 to 403 computations (19.1% saved)

simplify218.0ms (8.7%)

Algorithm

1×	egg-herbie

Rules

475×	`associate-/r*_binary64`
449×	`associate-/l*_binary64`
232×	`distribute-rgt-in_binary64`
216×	`distribute-lft-in_binary64`
211×	`log-div_binary64` `associate-/l/_binary64`

Counts

306 → 255

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	4897
1	449	4520
2	1299	4385
3	4501	4385
4	4971	4385
5	4969	4385

prune65.0ms (2.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	255	0	255
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	255	4	259

Error

Counts

259 → 4

Alt Table

Status	Error	Program
✓	11.8b	(/.f64 1 (/.f64 (+.f64 1 (*.f64 x x)) x))
▶	38.0b	(.f64 (sqrt.f64 (/.f64 x (+.f64 1 (.f64 x x)))) (sqrt.f64 (/.f64 x (+.f64 1 (*.f64 x x)))))
✓	34.4b	(+.f64 (-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 5)))
✓	11.8b	(/.f64 x (+.f64 (*.f64 x x) 1))

Compiler

Compiled 1517 to 1183 computations (22% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (/.f64 x (+.f64 1 (*.f64 x x))))
0.2b	(.f64 (sqrt.f64 (/.f64 x (+.f64 1 (.f64 x x)))) (sqrt.f64 (/.f64 x (+.f64 1 (*.f64 x x)))))
11.8b	(/.f64 x (+.f64 1 (*.f64 x x)))
11.8b	(/.f64 x (+.f64 1 (*.f64 x x)))

rewrite184.0ms (7.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

108×	`add-sqr-sqrt_binary64`
89×	`sqrt-prod_binary64`
76×	`times-frac_binary64`
59×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
20×	`pow1_binary64` `swap-sqr_binary64`

Counts

4 → 184

Calls

4 calls:

20.0ms	(.f64 (sqrt.f64 (/.f64 x (+.f64 1 (.f64 x x)))) (sqrt.f64 (/.f64 x (+.f64 1 (*.f64 x x)))))
6.0ms	(/.f64 x (+.f64 1 (*.f64 x x)))
5.0ms	(/.f64 x (+.f64 1 (*.f64 x x)))
4.0ms	(sqrt.f64 (/.f64 x (+.f64 1 (*.f64 x x))))

Compiler

Compiled 4614 to 2543 computations (44.9% saved)

series77.0ms (3%)

Error

Counts

4 → 33

Calls

4 calls:

19.0ms	(/.f64 x (+.f64 1 (*.f64 x x)))
18.0ms	(/.f64 x (+.f64 1 (*.f64 x x)))
14.0ms	(.f64 (sqrt.f64 (/.f64 x (+.f64 1 (.f64 x x)))) (sqrt.f64 (/.f64 x (+.f64 1 (*.f64 x x)))))
8.0ms	(sqrt.f64 (/.f64 x (+.f64 1 (*.f64 x x))))

Compiler

Compiled 1056 to 766 computations (27.5% saved)

simplify185.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

810×	`times-frac_binary64`
684×	`unswap-sqr_binary64`
394×	`associate-/l*_binary64`
224×	`associate-/r_binary64` `-commutative_binary64`
200×	`log-prod_binary64`

Counts

217 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	195	4129
1	353	3789
2	1176	3715
3	3697	3630
4	4815	3630
5	4898	3630

prune72.0ms (2.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	142	4	146

Error

Counts

146 → 4

Alt Table

Status	Error	Program
	11.8b	(/.f64 1 (/.f64 (+.f64 1 (*.f64 x x)) x))
	38.0b	(.f64 (sqrt.f64 (/.f64 x (+.f64 1 (.f64 x x)))) (sqrt.f64 (/.f64 x (+.f64 1 (*.f64 x x)))))
	34.4b	(+.f64 (-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 5)))
	11.8b	(/.f64 x (+.f64 (*.f64 x x) 1))

Compiler

Compiled 2129 to 1226 computations (42.4% saved)

regimes200.0ms (8%)

Accuracy

Total 0.1b remaining (93.5%)

Threshold costs 0.1b (93.5%)

Compiler

Compiled 2152 to 1453 computations (32.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	9	10
2	8	10

end1.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

sample426.0ms (16.9%)

Algorithm

1×

intervals

Results

176.0ms

8000×

body

128

valid

Compiler

Compiled 70 to 49 computations (30% saved)

Details

analyze25.0ms (1%)

sample12.0ms (0.5%)

simplify8.0ms (0.3%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

rewrite58.0ms (2.3%)

series36.0ms (1.4%)

simplify95.0ms (3.8%)

prune35.0ms (1.4%)

localize5.0ms (0.2%)

rewrite114.0ms (4.5%)

series45.0ms (1.8%)

simplify154.0ms (6.1%)

prune36.0ms (1.4%)

localize12.0ms (0.5%)

rewrite384.0ms (15.3%)

series54.0ms (2.1%)

simplify218.0ms (8.7%)

prune65.0ms (2.6%)

localize7.0ms (0.3%)

rewrite184.0ms (7.3%)

series77.0ms (3%)

simplify185.0ms (7.3%)

prune72.0ms (2.9%)

regimes200.0ms (8%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample426.0ms (16.9%)

Profiling