Details

analyze8.4s (29.7%)

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)

sample204.0ms (0.7%)

Algorithm

1×

intervals

Symmetry

(sort M D)

Results

50.0ms	256×	body	128	valid
17.0ms	97×	body	128	nan
5.0ms	26×	body	128	invalid

Compiler

Compiled 55 to 43 computations (21.8% saved)

simplify46.0ms (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

prune5.0ms (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

12.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	12.2b	(.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)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.7b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
✓	4.2b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
✓	4.7b	(/.f64 (.f64 M D) (.f64 2 d))
✓	8.5b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series1.5s (5.5%)

Counts

4 → 204

Calls

4 calls:

667.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
492.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
354.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
34.0ms	(/.f64 (.f64 M D) (.f64 2 d))

rewrite62.0ms (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:

18.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
11.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
8.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
7.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify373.0ms (1.3%)

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

prune950.0ms (3.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	303	11	314
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	304	11	315

Error

3.6b

Counts

315 → 11

Alt Table

Status	Error	Program
	9.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) l))))
	61.8b	(.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))
	61.7b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))
	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 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	11.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
	14.4b	w0
	38.2b	(.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)))))))
▶	9.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
	58.5b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	60.8b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)

Compiler

Compiled 12220 to 7359 computations (39.8% saved)

localize75.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.7b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
✓	4.2b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
	4.7b	(/.f64 (.f64 M D) (.f64 2 d))
✓	4.8b	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l))))

series3.5s (12.2%)

Counts

3 → 168

Calls

3 calls:

2.9s

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

335.0ms

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

192.0ms

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

rewrite49.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

166×	`add-exp-log_binary64`
84×	`prod-exp_binary64`
48×	`div-exp_binary64`
25×	`pow-exp_binary64`
23×	`add-sqr-sqrt_binary64`

Counts

3 → 117

Calls

3 calls:

14.0ms

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

8.0ms

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

6.0ms

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

simplify197.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

458×	`times-frac_binary64`
443×	`associate-l_binary64`
336×	`associate-/r*_binary64`
334×	`associate-/l*_binary64`
267×	`associate-*r/_binary64`

Counts

285 → 293

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	587	14132
1	1420	11518
2	4961	11518

prune419.0ms (1.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	331	1	332
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	332	11	343

Error

3.4b

Counts

343 → 11

Alt Table

Status	Error	Program
	61.7b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))
	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 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	11.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
	14.4b	w0
	38.2b	(.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)))))))
✓	9.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
	58.5b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
▶	7.7b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (*.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
	61.8b	(.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))
	60.8b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)

Compiler

Compiled 16016 to 8077 computations (49.6% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.4b	(.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))
✓	1.7b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (*.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
✓	4.2b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
✓	4.7b	(/.f64 (.f64 D M) (.f64 2 d))

series822.0ms (2.9%)

Counts

4 → 204

Calls

4 calls:

345.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (*.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
274.0ms	(.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))
187.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
16.0ms	(/.f64 (.f64 D M) (.f64 2 d))

rewrite566.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

2234×	`add-exp-log_binary64`
1550×	`add-cbrt-cube_binary64`
1283×	`cbrt-unprod_binary64`
1283×	`prod-exp_binary64`
698×	`cbrt-undiv_binary64`

Counts

4 → 646

Calls

4 calls:

45.0ms	(.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))
13.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))))
12.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (*.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
4.0ms	(/.f64 (.f64 D M) (.f64 2 d))

simplify913.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

727×	`times-frac_binary64`
517×	`*-commutative_binary64`
479×	`associate-l_binary64`
351×	`associate-+l+_binary64`
346×	`fma-def_binary64`

Counts

850 → 865

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	1350	38768
1	2889	36321
2	4490	36261
3	3961	30927
4	5013	30927

prune1.1s (3.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	899	1	900
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	899	12	911

Error

3.2b

Counts

911 → 12

Alt Table

Status	Error	Program
▶	9.7b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (.f64 (.f64 D M) (cbrt.f64 h)) (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (cbrt.f64 h)) (.f64 (.f64 (*.f64 2 d) (cbrt.f64 l)) (cbrt.f64 l))))))
✓	7.7b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (*.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
	61.7b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))
	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 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	11.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
	14.4b	w0
	38.2b	(.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)))))))
✓	9.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
	58.5b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	61.8b	(.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))
	60.8b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)

Compiler

Compiled 54197 to 19972 computations (63.1% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.3b	(.f64 (.f64 (.f64 (.f64 D M) (cbrt.f64 h)) (.f64 (/.f64 (.f64 D M) (*.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (cbrt.f64 h))
✓	4.2b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (.f64 (.f64 D M) (cbrt.f64 h)) (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (cbrt.f64 h)) (.f64 (.f64 (.f64 2 d) (cbrt.f64 l)) (cbrt.f64 l)))))
	4.7b	(/.f64 (.f64 D M) (.f64 2 d))
✓	5.9b	(/.f64 (.f64 (.f64 (.f64 (.f64 D M) (cbrt.f64 h)) (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (cbrt.f64 h)) (.f64 (.f64 (.f64 2 d) (cbrt.f64 l)) (cbrt.f64 l)))

series1.8s (6.3%)

Counts

3 → 168

Calls

3 calls:

1.2s

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

291.0ms

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

248.0ms

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

rewrite349.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

1492×	`add-exp-log_binary64`
980×	`cbrt-unprod_binary64`
980×	`prod-exp_binary64`
887×	`add-cbrt-cube_binary64`
335×	`cbrt-undiv_binary64`

Counts

3 → 413

Calls

3 calls:

33.0ms

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

24.0ms

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

11.0ms

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

simplify528.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

653×	`*-commutative_binary64`
503×	`associate-*r/_binary64`
407×	`associate-*l/_binary64`
208×	`sub-neg_binary64`
172×	`associate-/r*_binary64`

Counts

581 → 686

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	806	35041
1	2200	27726
2	5198	27726

prune1.1s (3.8%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	721	0	721
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	721	12	733

Error

3.2b

Counts

733 → 12

Alt Table

Status	Error	Program
✓	9.7b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (.f64 (.f64 D M) (cbrt.f64 h)) (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (cbrt.f64 h)) (.f64 (.f64 (*.f64 2 d) (cbrt.f64 l)) (cbrt.f64 l))))))
✓	7.7b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l))) (.f64 (/.f64 (.f64 D M) (*.f64 2 d)) (/.f64 (cbrt.f64 h) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
	61.7b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))
	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 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	11.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
	14.4b	w0
	38.2b	(.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)))))))
✓	9.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 (.f64 (cbrt.f64 h) (cbrt.f64 h)) (*.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 (cbrt.f64 h) (cbrt.f64 l))))))
	58.5b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	61.8b	(.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))
	60.8b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)

Compiler

Compiled 40099 to 17573 computations (56.2% saved)

regimes3.1s (10.9%)

Accuracy

Total 4.1b remaining (51.1%)

Threshold costs 0b (0%)

Counts

140 → 3

Compiler

Compiled 72063 to 49791 computations (30.9% saved)

bsearch8.0ms (0%)

Compiler: Compiled 24 to 18 computations (25% saved)

simplify14.0ms (0%)

Algorithm

1×	egg-herbie

Rules

40×	`*-commutative_binary64`
24×	`+-commutative_binary64`
24×	`sub-neg_binary64`
22×	`neg-sub0_binary64`
22×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	210
1	88	210
2	123	210
3	165	210
4	200	210
5	229	210
6	240	210
7	244	210
8	245	210
9	244	210

end10.0ms (0%)

Compiler: Compiled 423 to 231 computations (45.4% saved)

sample2.2s (7.9%)

Algorithm

1×

intervals

Results

791.0ms	8000×	body	128	valid
302.0ms	3201×	body	128	nan
130.0ms	1264×	body	128	invalid

Compiler

Compiled 523 to 337 computations (35.6% saved)

Iter	Nodes	Cost
0	54	210
1	88	210
2	123	210
3	165	210
4	200	210
5	229	210
6	240	210
7	244	210
8	245	210
9	244	210

Iter	Nodes	Cost
0	54	210
1	88	210
2	123	210
3	165	210
4	200	210
5	229	210
6	240	210
7	244	210
8	245	210
9	244	210

Details

analyze8.4s (29.7%)

sample204.0ms (0.7%)

simplify46.0ms (0.2%)

prune5.0ms (0%)

localize32.0ms (0.1%)

series1.5s (5.5%)

rewrite62.0ms (0.2%)

simplify373.0ms (1.3%)

prune950.0ms (3.3%)

localize75.0ms (0.3%)

series3.5s (12.2%)

rewrite49.0ms (0.2%)

simplify197.0ms (0.7%)

prune419.0ms (1.5%)

localize17.0ms (0.1%)

series822.0ms (2.9%)

rewrite566.0ms (2%)

simplify913.0ms (3.2%)

prune1.1s (3.9%)

localize24.0ms (0.1%)

series1.8s (6.3%)

rewrite349.0ms (1.2%)

simplify528.0ms (1.9%)

prune1.1s (3.8%)

regimes3.1s (10.9%)

bsearch8.0ms (0%)

simplify14.0ms (0%)

end10.0ms (0%)

sample2.2s (7.9%)

Profiling

Iter	Nodes	Cost
0	54	210
1	88	210
2	123	210
3	165	210
4	200	210
5	229	210
6	240	210
7	244	210
8	245	210
9	244	210