Details

analyze3.4s (22.6%)

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)

sample72.0ms (0.5%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
9.0ms	98×	body	128	nan
4.0ms	40×	body	128	invalid

Compiler

Compiled 55 to 43 computations (21.8% saved)

simplify28.0ms (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

11.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	11.8b	(.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)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
✓	2.8b	(/.f64 (.f64 M D) (.f64 2 d))
✓	4.5b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
✓	8.2b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series829.0ms (5.6%)

Counts

4 → 204

Calls

4 calls:

348.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
275.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
189.0ms	(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))

rewrite38.0ms (0.3%)

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:

11.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
6.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.0ms	(/.f64 (.f64 M D) (.f64 2 d))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

simplify171.0ms (1.1%)

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

prune533.0ms (3.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	300	14	314
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	301	14	315

Error

3.9b

Counts

315 → 14

Alt Table

Status	Error	Program
	10.8b	(.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))))))
	55.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (exp.f64 (+.f64 (.f64 (log.f64 (/.f64 (.f64 M D) (.f64 2 d))) 2) (-.f64 (log.f64 h) (log.f64 l)))))))
	61.8b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	11.8b	(.f64 (.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	11.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
	60.8b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	36.6b	(.f64 (sqrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (sqrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))))
	58.9b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	13.8b	w0
	61.8b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
▶	10.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) (/.f64 1 l)))))
	12.9b	(.f64 (.f64 (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))
	58.9b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	60.8b	(.f64 w0 (.f64 -1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 l (pow.f64 d 2)))))) M)))

Compiler

Compiled 12474 to 7545 computations (39.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	2.8b	(/.f64 (.f64 M D) (.f64 2 d))
✓	4.2b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)
✓	4.4b	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) (/.f64 1 l))
✓	4.5b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) (/.f64 1 l))))

series667.0ms (4.5%)

Counts

3 → 156

Calls

3 calls:

238.0ms

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

234.0ms

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

194.0ms

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

rewrite36.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

152×	`add-exp-log_binary64`
87×	`prod-exp_binary64`
36×	`div-exp_binary64`
25×	`pow-exp_binary64`
21×	`add-sqr-sqrt_binary64`

Counts

3 → 115

Calls

3 calls:

9.0ms

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

6.0ms

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

6.0ms

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

simplify197.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

575×	`fma-def_binary64`
322×	`unswap-sqr_binary64`
296×	`cancel-sign-sub-inv_binary64`
255×	`associate-l_binary64`
241×	`associate-r_binary64`

Counts

271 → 222

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	354	7915
1	795	7298
2	3026	7215
3	4877	7215
4	4990	7215

prune348.0ms (2.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	260	1	261
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	261	14	275

Error

3.9b

Counts

275 → 14

Alt Table

Status	Error	Program
	61.8b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	11.8b	(.f64 (.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	11.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
	60.8b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	36.6b	(.f64 (sqrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (sqrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))))
	58.9b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
▶	9.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))) 2) (.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 M D) (*.f64 2 d))) 2) h)) (/.f64 1 l)))))
	10.8b	(.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))))))
	58.9b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	13.8b	w0
	61.8b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
✓	10.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) (/.f64 1 l)))))
	12.9b	(.f64 (.f64 (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))
	60.8b	(.f64 w0 (.f64 -1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 l (pow.f64 d 2)))))) M)))

Compiler

Compiled 9478 to 6138 computations (35.2% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	2.8b	(/.f64 (.f64 M D) (.f64 2 d))
✓	4.4b	(.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))) 2) (.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) 2) h)) (/.f64 1 l))
✓	4.5b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))) 2) (.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) 2) h)) (/.f64 1 l))))
✓	17.4b	(cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))

series1.4s (9.1%)

Counts

3 → 144

Calls

3 calls:

778.0ms

(cbrt.f64 (/.f64 (*.f64 M D) (*.f64 2 d)))

359.0ms

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

218.0ms

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

rewrite53.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

252×	`add-exp-log_binary64`
196×	`prod-exp_binary64`
48×	`pow-exp_binary64`
34×	`div-exp_binary64`
32×	`pow-to-exp_binary64`

Counts

3 → 134

Calls

3 calls:

12.0ms

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

5.0ms

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

4.0ms

(cbrt.f64 (/.f64 (*.f64 M D) (*.f64 2 d)))

simplify231.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

607×	`fma-def_binary64`
342×	`unswap-sqr_binary64`
313×	`associate-l_binary64`
291×	`associate-r_binary64`
186×	`*-commutative_binary64`

Counts

278 → 223

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	416	10259
1	915	8507
2	3264	8037
3	4955	8037
4	5008	8037

prune721.0ms (4.9%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	421	1	422
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	422	14	436

Error

3.9b

Counts

436 → 14

Alt Table

Status	Error	Program
	61.8b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	11.8b	(.f64 (.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	11.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
	60.8b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
	60.8b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	36.6b	(.f64 (sqrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (sqrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))))
	58.9b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
✓	9.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) (cbrt.f64 (/.f64 (.f64 M D) (.f64 2 d)))) 2) (.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 M D) (*.f64 2 d))) 2) h)) (/.f64 1 l)))))
▶	10.8b	(.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))))))
	58.9b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	13.8b	w0
	61.8b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
✓	10.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) (/.f64 1 l)))))
	12.9b	(.f64 (.f64 (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))

Compiler

Compiled 21117 to 13447 computations (36.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.2b	(.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))))))
	2.8b	(/.f64 (.f64 M D) (.f64 2 d))
✓	4.5b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
✓	8.2b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))

series617.0ms (4.2%)

Counts

3 → 168

Calls

3 calls:

346.0ms

(*.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))))))

218.0ms

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

52.0ms

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

rewrite32.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-cbrt-cube_binary64`
46×	`add-exp-log_binary64`
25×	`add-sqr-sqrt_binary64`
19×	`associate-r_binary64`
19×	`cbrt-unprod_binary64`

Counts

3 → 97

Calls

3 calls:

9.0ms

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

7.0ms

(*.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))))))

5.0ms

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

simplify151.0ms (1%)

Algorithm

1×	egg-herbie

Rules

604×	`times-frac_binary64`
414×	`associate-/l*_binary64`
405×	`associate-/r*_binary64`
333×	`associate-*r/_binary64`
281×	`associate-*l/_binary64`

Counts

265 → 270

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	498	10374
1	1286	9786
2	4989	9786

prune408.0ms (2.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	347	1	348
Fresh	0	11	11
Picked	1	0	1
Done	1	1	2
Total	349	13	362

Error

3.7b

Counts

362 → 13

Alt Table

Status	Error	Program
	61.8b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	11.8b	(.f64 (.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	11.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 (*.f64 2 d) D)) 2) (/.f64 h l)))))
	60.8b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
	60.8b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	36.6b	(.f64 (sqrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (sqrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l)))))))
	10.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 (.f64 (.f64 M D) h) (.f64 (.f64 2 d) l))))))
	58.9b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	13.8b	w0
	61.8b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))
✓	10.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) (/.f64 1 l)))))
	12.9b	(.f64 (.f64 (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))
	58.9b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))

Compiler

Compiled 14518 to 7842 computations (46% saved)

regimes2.3s (15.8%)

Accuracy

Total 3.7b remaining (46%)

Threshold costs 0b (0%)

Counts

111 → 3

Compiler

Compiled 60432 to 44226 computations (26.8% saved)

bsearch5.0ms (0%)

Compiler: Compiled 19 to 14 computations (26.3% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

23×	`*-commutative_binary64`
13×	`+-commutative_binary64`
13×	`sub-neg_binary64`
12×	`neg-sub0_binary64`
12×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	111
1	64	111
2	91	111
3	118	111
4	135	111
5	144	111
6	148	111
7	149	111
8	147	111

end9.0ms (0.1%)

Compiler: Compiled 240 to 144 computations (40% saved)

sample2.6s (17.2%)

Algorithm

1×

intervals

Results

836.0ms	8000×	body	128	valid
319.0ms	3234×	body	128	nan
141.0ms	1382×	body	128	invalid

Compiler

Compiled 495 to 343 computations (30.7% saved)

Iter	Nodes	Cost
0	37	111
1	64	111
2	91	111
3	118	111
4	135	111
5	144	111
6	148	111
7	149	111
8	147	111

Iter	Nodes	Cost
0	37	111
1	64	111
2	91	111
3	118	111
4	135	111
5	144	111
6	148	111
7	149	111
8	147	111

Details

analyze3.4s (22.6%)

sample72.0ms (0.5%)

simplify28.0ms (0.2%)

prune2.0ms (0%)

localize13.0ms (0.1%)

series829.0ms (5.6%)

rewrite38.0ms (0.3%)

simplify171.0ms (1.1%)

prune533.0ms (3.6%)

localize15.0ms (0.1%)

series667.0ms (4.5%)

rewrite36.0ms (0.2%)

simplify197.0ms (1.3%)

prune348.0ms (2.3%)

localize19.0ms (0.1%)

series1.4s (9.1%)

rewrite53.0ms (0.4%)

simplify231.0ms (1.6%)

prune721.0ms (4.9%)

localize13.0ms (0.1%)

series617.0ms (4.2%)

rewrite32.0ms (0.2%)

simplify151.0ms (1%)

prune408.0ms (2.8%)

regimes2.3s (15.8%)

bsearch5.0ms (0%)

simplify6.0ms (0%)

end9.0ms (0.1%)

sample2.6s (17.2%)

Profiling

Iter	Nodes	Cost
0	37	111
1	64	111
2	91	111
3	118	111
4	135	111
5	144	111
6	148	111
7	149	111
8	147	111