Details

analyze2.7s (14.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
5.1%	94.6%	0.3%	13
7%	92.7%	0.3%	14

Compiler

Compiled 25 to 19 computations (24% saved)

sample101.0ms (0.6%)

Algorithm

1×

intervals

Symmetry

(sort M D)

Results

25.0ms	256×	body	128	valid
7.0ms	83×	body	128	nan
3.0ms	39×	body	128	invalid

Compiler

Compiled 55 to 43 computations (21.8% saved)

simplify34.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

645×	`distribute-neg-frac_binary64`
581×	`distribute-rgt-neg-in_binary64`
418×	`associate-/l*_binary64`
372×	`cancel-sign-sub-inv_binary64`
263×	`associate-/l/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	27
1	42	27
2	111	27
3	723	27
4	2855	27
5	4994	27

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

13.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	13.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))

Compiler

Compiled 72 to 54 computations (25% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
✓	3.8b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
✓	5.4b	(/.f64 (.f64 M D) (.f64 2 d))
✓	9.3b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series771.0ms (4.3%)

Counts

4 → 204

Calls

4 calls:

337.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
240.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
177.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
16.0ms	(/.f64 (.f64 M D) (.f64 2 d))

rewrite32.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64`
38×	`add-sqr-sqrt_binary64`
27×	`prod-exp_binary64`
23×	`add-cbrt-cube_binary64`
19×	`associate-r_binary64`

Counts

4 → 124

Calls

4 calls:

8.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
6.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
3.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

simplify168.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

517×	`times-frac_binary64`
399×	`associate-l_binary64`
365×	`associate-/l*_binary64`
342×	`associate-/r*_binary64`
258×	`associate-*r/_binary64`

Counts

328 → 314

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	516	11209
1	1262	10441
2	4988	10441

prune420.0ms (2.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	301	13	314
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	302	13	315

Error

3.9b

Counts

315 → 13

Alt Table

Status	Error	Program
	10.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))))))
	58.7b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	13.4b	(.f64 w0 (.f64 (fabs.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l))))) (sqrt.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))))))
▶	10.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) l))))
	14.8b	(.f64 w0 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))) 3)))
	59.3b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	62.0b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	18.1b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)) 3)))) (sqrt.f64 (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)) (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) (.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))
	38.7b	(.f64 (.f64 (sqrt.f64 w0) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (.f64 (sqrt.f64 w0) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))))
	61.7b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	10.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l)))))
	61.9b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (.f64 M w0))
	13.8b	w0

Compiler

Compiled 12448 to 7517 computations (39.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.8b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)))
✓	4.7b	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)
✓	5.4b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)
	5.4b	(/.f64 (.f64 M D) (.f64 2 d))

series547.0ms (3%)

Counts

3 → 156

Calls

3 calls:

227.0ms	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)
175.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)))
144.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-exp-log_binary64`
22×	`prod-exp_binary64`
19×	`add-sqr-sqrt_binary64`
16×	`div-exp_binary64`
12×	`*-un-lft-identity_binary64`

Counts

3 → 84

Calls

3 calls:

7.0ms	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)
6.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)))
5.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)

simplify140.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

315×	`fma-def_binary64`
298×	`unswap-sqr_binary64`
288×	`distribute-neg-frac_binary64`
241×	`cancel-sign-sub-inv_binary64`
191×	`times-frac_binary64`

Counts

240 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	334	7367
1	764	6748
2	2985	6661
3	4995	6661

prune465.0ms (2.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	227	2	229
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	227	15	242

Error

3.9b

Counts

242 → 15

Alt Table

Status	Error	Program
	10.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))))))
	58.7b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	13.4b	(.f64 w0 (.f64 (fabs.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l))))) (sqrt.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))))))
✓	10.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) l))))
	34.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (sqrt.f64 h)) (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (sqrt.f64 h))) l))))
	59.3b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	14.8b	(.f64 w0 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))) 3)))
	62.0b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	18.1b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)) 3)))) (sqrt.f64 (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)) (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) (.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))
	38.7b	(.f64 (.f64 (sqrt.f64 w0) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (.f64 (sqrt.f64 w0) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))))
	61.7b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
▶	10.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l)))))
	61.9b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (.f64 M w0))
	13.8b	w0
	22.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 M 2) 2) (*.f64 (pow.f64 (/.f64 D d) 2) h)) l))))

Compiler

Compiled 8351 to 5307 computations (36.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.8b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
✓	4.8b	(.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
✓	4.8b	(.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
✓	5.4b	(/.f64 (.f64 D M) (.f64 2 d))

series1.6s (9.1%)

Counts

4 → 192

Calls

4 calls:

1.1s	(.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
329.0ms	(.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
182.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
17.0ms	(/.f64 (.f64 D M) (.f64 2 d))

rewrite51.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`add-exp-log_binary64`
121×	`prod-exp_binary64`
43×	`div-exp_binary64`
33×	`add-cbrt-cube_binary64`
30×	`pow-exp_binary64`

Counts

4 → 153

Calls

4 calls:

13.0ms	(.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
9.0ms	(.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
4.0ms	(/.f64 (.f64 D M) (.f64 2 d))

simplify207.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

484×	`associate-l_binary64`
404×	`associate-r_binary64`
338×	`times-frac_binary64`
312×	`fma-def_binary64`
274×	`associate-/l*_binary64`

Counts

345 → 282

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	437	10560
1	1067	9125
2	4583	9125
3	5027	9125

prune438.0ms (2.4%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	281	1	282
Fresh	2	11	13
Picked	0	1	1
Done	0	1	1
Total	283	14	297

Error

3.2b

Counts

297 → 14

Alt Table

Status	Error	Program
	18.1b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)) 3)))) (sqrt.f64 (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)) (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) (.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))
	59.5b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 M d) 2)) -1/4))))
▶	13.4b	(.f64 w0 (.f64 (fabs.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l))))) (sqrt.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))))))
✓	10.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) l))))
	34.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (sqrt.f64 h)) (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (sqrt.f64 h))) l))))
	59.3b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	14.8b	(.f64 w0 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))) 3)))
	58.7b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	38.7b	(.f64 (.f64 (sqrt.f64 w0) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (.f64 (sqrt.f64 w0) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))))
	61.7b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
✓	10.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l)))))
	61.9b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (.f64 M w0))
	13.8b	w0
	22.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 M 2) 2) (*.f64 (pow.f64 (/.f64 D d) 2) h)) l))))

Compiler

Compiled 11300 to 5979 computations (47.1% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.1b	(.f64 w0 (.f64 (fabs.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l))))) (sqrt.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))))))
	5.4b	(/.f64 (.f64 D M) (.f64 2 d))
✓	5.5b	(cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (*.f64 2 d)) 2) (/.f64 h l))))
✓	9.3b	(.f64 (pow.f64 (/.f64 (.f64 D M) (*.f64 2 d)) 2) (/.f64 h l))

series2.6s (14.1%)

Counts

3 → 192

Calls

3 calls:

2.1s

(*.f64 w0 (*.f64 (fabs.f64 (cbrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 D M) (*.f64 2 d)) 2) (/.f64 h l))))) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 D M) (*.f64 2 d)) 2) (/.f64 h l)))))))

259.0ms

(cbrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 D M) (*.f64 2 d)) 2) (/.f64 h l))))

237.0ms

(*.f64 (pow.f64 (/.f64 (*.f64 D M) (*.f64 2 d)) 2) (/.f64 h l))

rewrite43.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-exp-log_binary64`
30×	`add-sqr-sqrt_binary64`
25×	`prod-exp_binary64`
15×	`div-exp_binary64`
14×	`cbrt-div_binary64`

Counts

3 → 101

Calls

3 calls:

12.0ms

(*.f64 w0 (*.f64 (fabs.f64 (cbrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 D M) (*.f64 2 d)) 2) (/.f64 h l))))) (sqrt.f64 (cbrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 D M) (*.f64 2 d)) 2) (/.f64 h l)))))))

9.0ms

(*.f64 (pow.f64 (/.f64 (*.f64 D M) (*.f64 2 d)) 2) (/.f64 h l))

3.0ms

(cbrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 (*.f64 D M) (*.f64 2 d)) 2) (/.f64 h l))))

simplify376.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

425×	`*-commutative_binary64`
387×	`associate-*l/_binary64`
287×	`fma-def_binary64`
205×	`associate-r_binary64`
171×	`sub-neg_binary64`

Counts

293 → 301

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	929	23230
1	2702	22098
2	4995	22098
3	4954	22098

prune1.1s (6%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	548	0	548
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	548	14	562

Error

3.2b

Counts

562 → 14

Alt Table

Status	Error	Program
	18.1b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)) 3)))) (sqrt.f64 (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)) (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) (.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))
	59.5b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 M d) 2)) -1/4))))
✓	13.4b	(.f64 w0 (.f64 (fabs.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l))))) (sqrt.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))))))
✓	10.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) l))))
	34.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (sqrt.f64 h)) (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (sqrt.f64 h))) l))))
	59.3b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	14.8b	(.f64 w0 (cbrt.f64 (pow.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (/.f64 h l)))) 3)))
	58.7b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	38.7b	(.f64 (.f64 (sqrt.f64 w0) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (.f64 (sqrt.f64 w0) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))))
	61.7b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
✓	10.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l)))))
	61.9b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (.f64 M w0))
	13.8b	w0
	22.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 M 2) 2) (*.f64 (pow.f64 (/.f64 D d) 2) h)) l))))

Compiler

Compiled 43499 to 26220 computations (39.7% saved)

regimes3.8s (21.1%)

Accuracy

Total 4.7b remaining (51.9%)

Threshold costs 0b (0%)

Counts

154 → 3

Compiler

Compiled 84974 to 60433 computations (28.9% saved)

bsearch11.0ms (0.1%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

33×	`*-commutative_binary64`
21×	`+-commutative_binary64`
21×	`sub-neg_binary64`
20×	`neg-sub0_binary64`
20×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	143
1	75	143
2	106	143
3	150	143
4	183	143
5	203	143
6	211	143
7	212	143
8	211	143

end9.0ms (0.1%)

Compiler: Compiled 297 to 177 computations (40.4% saved)

sample2.4s (13.3%)

Algorithm

1×

intervals

Results

761.0ms	8000×	body	128	valid
312.0ms	3110×	body	128	nan
147.0ms	1312×	body	128	invalid

Compiler

Compiled 559 to 388 computations (30.6% saved)

Iter	Nodes	Cost
0	49	143
1	75	143
2	106	143
3	150	143
4	183	143
5	203	143
6	211	143
7	212	143
8	211	143

Iter	Nodes	Cost
0	49	143
1	75	143
2	106	143
3	150	143
4	183	143
5	203	143
6	211	143
7	212	143
8	211	143

Details

analyze2.7s (14.7%)

sample101.0ms (0.6%)

simplify34.0ms (0.2%)

prune2.0ms (0%)

localize21.0ms (0.1%)

series771.0ms (4.3%)

rewrite32.0ms (0.2%)

simplify168.0ms (0.9%)

prune420.0ms (2.3%)

localize12.0ms (0.1%)

series547.0ms (3%)

rewrite24.0ms (0.1%)

simplify140.0ms (0.8%)

prune465.0ms (2.6%)

localize18.0ms (0.1%)

series1.6s (9.1%)

rewrite51.0ms (0.3%)

simplify207.0ms (1.1%)

prune438.0ms (2.4%)

localize18.0ms (0.1%)

series2.6s (14.1%)

rewrite43.0ms (0.2%)

simplify376.0ms (2.1%)

prune1.1s (6%)

regimes3.8s (21.1%)

bsearch11.0ms (0.1%)

simplify8.0ms (0%)

end9.0ms (0.1%)

sample2.4s (13.3%)

Profiling

Iter	Nodes	Cost
0	49	143
1	75	143
2	106	143
3	150	143
4	183	143
5	203	143
6	211	143
7	212	143
8	211	143