Details

analyze5.2s (7.6%)

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
0%	99.7%	0.3%	13
0%	99.7%	0.3%	14

Compiler

Compiled 25 to 19 computations (24% saved)

sample5.3s (7.8%)

Symmetry

(sort M D)

Results

2.7s	8256×	body	128	valid
1.3s	698×	body	8192	exit
1.1s	3697×	body	128	invalid

Compiler

Compiled 49 to 37 computations (24.5% saved)

simplify90.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

656×	`cancel-sign-sub-inv_binary64`
490×	`associate-/l*_binary64`
389×	`*-commutative_binary64`
280×	`associate-/l/_binary64`
269×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	27
1	43	27
2	132	27
3	935	27
4	4204	27

prune8.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

13.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))

Compiler

Compiled 90 to 65 computations (27.8% saved)

localize55.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
✓	3.5b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
✓	4.6b	(/.f64 (.f64 M D) (.f64 2 d))
✓	11.6b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series2.3s (3.4%)

Counts

4 → 204

Calls

4 calls:

1.0s	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
675.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
530.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
41.0ms	(/.f64 (.f64 M D) (.f64 2 d))

rewrite108.0ms (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:

31.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
19.0ms	(.f64 w0 (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))
8.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

simplify15.3s (22.5%)

Algorithm

1×	egg-herbie

Rules

560×	`times-frac_binary64`
375×	`associate-/l*_binary64`
363×	`associate-/r*_binary64`
199×	`associate-*l/_binary64`
182×	`*-commutative_binary64`

Counts

328 → 315

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	523	11209
1	1849	10441

prune604.0ms (0.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	301	14	315
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	302	14	316

Error

4.1b

Counts

316 → 14

Alt Table

Status	Error	Program
▶	10.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l))))
	13.3b	(.f64 (.f64 w0 (sqrt.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))) (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (sqrt.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	12.0b	w0
	15.3b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 (pow.f64 1 3) (pow.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.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)))))))
	60.2b	(.f64 w0 (.f64 M (neg.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)))))
	10.0b	(.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)) 1)) (/.f64 (cbrt.f64 h) l)))))
	37.0b	(.f64 (sqrt.f64 w0) (.f64 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))) (sqrt.f64 w0)))
	61.3b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	60.0b	(.f64 D (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (*.f64 (/.f64 M d) (/.f64 M d))) -1/4)) w0))
	61.2b	(.f64 D (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 h (pow.f64 M 2)) (*.f64 (pow.f64 d 2) l))))) w0))
	61.0b	(.f64 -1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 (pow.f64 d 2) l))))) (.f64 w0 M)))
	61.6b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (.f64 M w0))
	60.6b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 D (/.f64 l D)) (.f64 (*.f64 M M) h)) -1/4)) d))
	60.0b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (.f64 (/.f64 h l) (*.f64 (/.f64 M d) (/.f64 M d))) -1/4))))

Compiler

Compiled 12510 to 7556 computations (39.6% saved)

localize23.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.5b	(sqrt.f64 (-.f64 1 (/.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l)))
✓	4.5b	(/.f64 M (/.f64 2 (/.f64 D d)))
✓	4.6b	(/.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l)
✓	5.0b	(*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2))

series1.1s (1.6%)

Counts

4 → 192

Calls

4 calls:

434.0ms	(/.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l)
309.0ms	(sqrt.f64 (-.f64 1 (/.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l)))
292.0ms	(*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2))
45.0ms	(/.f64 M (/.f64 2 (/.f64 D d)))

rewrite250.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

735×	`times-frac_binary64`
366×	`add-sqr-sqrt_binary64`
347×	`*-un-lft-identity_binary64`
344×	`add-cube-cbrt_binary64`
142×	`associate-r_binary64`

Counts

4 → 415

Calls

4 calls:

63.0ms	(*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2))
49.0ms	(/.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l)
16.0ms	(/.f64 M (/.f64 2 (/.f64 D d)))
11.0ms	(sqrt.f64 (-.f64 1 (/.f64 (*.f64 h (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2)) l)))

simplify6.6s (9.7%)

Algorithm

1×	egg-herbie

Rules

399×	`associate-/l/_binary64`
316×	`times-frac_binary64`
309×	`associate-/r/_binary64`
292×	`sqr-pow_binary64`
219×	`*-commutative_binary64`

Counts

607 → 815

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1034	15946
1	2891	15645

prune1.4s (2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	812	3	815
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	814	15	829

Error

3.6b

Counts

829 → 15

Alt Table

Status	Error	Program
	25.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (*.f64 D h) (pow.f64 (/.f64 M (/.f64 2 (/.f64 (sqrt.f64 D) d))) 2)) l))))
	37.0b	(.f64 (sqrt.f64 w0) (.f64 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))) (sqrt.f64 w0)))
	61.6b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (.f64 M w0))
▶	8.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (*.f64 h (/.f64 M (/.f64 2 (/.f64 D d)))) (/.f64 M (/.f64 2 (/.f64 D d)))) l))))
	12.0b	w0
	15.3b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 (pow.f64 1 3) (pow.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.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)))))))
	28.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h (.f64 (/.f64 M 2) (/.f64 D d))) (pow.f64 (sqrt.f64 (/.f64 M (/.f64 2 (/.f64 D d)))) 2)) l))))
	60.2b	(.f64 w0 (.f64 M (neg.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)))))
	10.0b	(.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)) 1)) (/.f64 (cbrt.f64 h) l)))))
	13.3b	(.f64 (.f64 w0 (sqrt.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))) (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (sqrt.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	61.3b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	60.0b	(.f64 D (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (*.f64 (/.f64 M d) (/.f64 M d))) -1/4)) w0))
	61.2b	(.f64 D (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 h (pow.f64 M 2)) (*.f64 (pow.f64 d 2) l))))) w0))
	61.0b	(.f64 -1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 (pow.f64 d 2) l))))) (.f64 w0 M)))
	60.6b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 D (/.f64 l D)) (.f64 (*.f64 M M) h)) -1/4)) d))

Compiler

Compiled 28007 to 16094 computations (42.5% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.5b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h (/.f64 M (/.f64 2 (/.f64 D d)))) (/.f64 M (/.f64 2 (/.f64 D d)))) l)))
	4.5b	(/.f64 M (/.f64 2 (/.f64 D d)))
✓	4.6b	(/.f64 (.f64 (.f64 h (/.f64 M (/.f64 2 (/.f64 D d)))) (/.f64 M (/.f64 2 (/.f64 D d)))) l)
✓	6.2b	(*.f64 h (/.f64 M (/.f64 2 (/.f64 D d))))

series475.0ms (0.7%)

Counts

3 → 156

Calls

3 calls:

240.0ms

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

199.0ms

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

35.0ms

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

rewrite119.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

339×	`times-frac_binary64`
175×	`add-sqr-sqrt_binary64`
160×	`*-un-lft-identity_binary64`
157×	`add-cube-cbrt_binary64`
149×	`add-cbrt-cube_binary64`

Counts

3 → 248

Calls

3 calls:

28.0ms

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

27.0ms

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

7.0ms

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

simplify7.9s (11.6%)

Algorithm

1×	egg-herbie

Rules

841×	`times-frac_binary64`
552×	`associate-/r/_binary64`
406×	`associate-/l/_binary64`
236×	`*-commutative_binary64`
183×	`associate-*r/_binary64`

Counts

404 → 475

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	752	11695
1	2507	10858

prune3.0s (4.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	1214	3	1217
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	1217	15	1232

Error

3.4b

Counts

1232 → 15

Alt Table

Status	Error	Program
	25.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (*.f64 D h) (pow.f64 (/.f64 M (/.f64 2 (/.f64 (sqrt.f64 D) d))) 2)) l))))
	37.0b	(.f64 (sqrt.f64 w0) (.f64 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))) (sqrt.f64 w0)))
	12.0b	w0
	15.3b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 (pow.f64 1 3) (pow.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.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)))))))
	18.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h M) M) (.f64 l (*.f64 (/.f64 2 (/.f64 D d)) (/.f64 2 (/.f64 D d))))))))
	60.2b	(.f64 w0 (.f64 M (neg.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)))))
	10.0b	(.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)) 1)) (/.f64 (cbrt.f64 h) l)))))
	13.3b	(.f64 (.f64 w0 (sqrt.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))) (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (sqrt.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	61.3b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	60.0b	(.f64 D (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (*.f64 (/.f64 M d) (/.f64 M d))) -1/4)) w0))
	61.2b	(.f64 D (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 h (pow.f64 M 2)) (*.f64 (pow.f64 d 2) l))))) w0))
	61.0b	(.f64 -1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 (pow.f64 d 2) l))))) (.f64 w0 M)))
	61.6b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (.f64 M w0))
▶	7.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (/.f64 M (/.f64 2 (/.f64 D d)))) (/.f64 l (/.f64 M (/.f64 2 (/.f64 D d))))))))
	10.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h M) (/.f64 M (/.f64 2 (/.f64 D d)))) (.f64 l (/.f64 2 (/.f64 D d)))))))

Compiler

Compiled 47512 to 24702 computations (48% saved)

localize23.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.5b	(sqrt.f64 (-.f64 1 (/.f64 (*.f64 h (/.f64 M (/.f64 2 (/.f64 D d)))) (/.f64 l (/.f64 M (/.f64 2 (/.f64 D d)))))))
	4.5b	(/.f64 M (/.f64 2 (/.f64 D d)))
✓	4.6b	(/.f64 l (/.f64 M (/.f64 2 (/.f64 D d))))
	6.2b	(*.f64 h (/.f64 M (/.f64 2 (/.f64 D d))))

series364.0ms (0.5%)

Counts

2 → 96

Calls

2 calls:

300.0ms	(sqrt.f64 (-.f64 1 (/.f64 (*.f64 h (/.f64 M (/.f64 2 (/.f64 D d)))) (/.f64 l (/.f64 M (/.f64 2 (/.f64 D d)))))))
63.0ms	(/.f64 l (/.f64 M (/.f64 2 (/.f64 D d))))

rewrite671.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

1731×	`times-frac_binary64`
745×	`add-sqr-sqrt_binary64`
744×	`*-un-lft-identity_binary64`
741×	`add-cube-cbrt_binary64`
137×	`associate-/r*_binary64`

Counts

2 → 592

Calls

2 calls:

350.0ms	(sqrt.f64 (-.f64 1 (/.f64 (*.f64 h (/.f64 M (/.f64 2 (/.f64 D d)))) (/.f64 l (/.f64 M (/.f64 2 (/.f64 D d)))))))
43.0ms	(/.f64 l (/.f64 M (/.f64 2 (/.f64 D d))))

simplify5.0s (7.3%)

Algorithm

1×	egg-herbie

Rules

392×	`associate-/l*_binary64`
208×	`times-frac_binary64`
204×	`associate-/r*_binary64`
177×	`associate-r_binary64`
149×	`associate-*r/_binary64`

Counts

688 → 1012

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1566	24653
1	2713	24488

prune5.7s (8.4%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	2052	2	2054
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	2052	17	2069

Error

2.7b

Counts

2069 → 17

Alt Table

Status	Error	Program
	60.8b	(.f64 w0 (.f64 M (neg.f64 (sqrt.f64 (.f64 (.f64 -1/4 (/.f64 (*.f64 D D) l)) (/.f64 (/.f64 h d) d))))))
	13.3b	(.f64 (.f64 w0 (sqrt.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))) (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (sqrt.f64 (cbrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	25.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (*.f64 D h) (pow.f64 (/.f64 M (/.f64 2 (/.f64 (sqrt.f64 D) d))) 2)) l))))
	37.0b	(.f64 (sqrt.f64 w0) (.f64 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))) (sqrt.f64 w0)))
	12.0b	w0
	15.3b	(/.f64 (.f64 w0 (sqrt.f64 (-.f64 (pow.f64 1 3) (pow.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.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)))))))
	18.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h M) M) (.f64 l (*.f64 (/.f64 2 (/.f64 D d)) (/.f64 2 (/.f64 D d))))))))
	60.2b	(.f64 w0 (.f64 M (neg.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)))))
	10.0b	(.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)) 1)) (/.f64 (cbrt.f64 h) l)))))
	60.2b	(.f64 w0 (.f64 D (sqrt.f64 (/.f64 (.f64 -1/4 h) (.f64 (/.f64 l M) (/.f64 (*.f64 d d) M))))))
	61.3b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	60.0b	(.f64 D (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (*.f64 (/.f64 M d) (/.f64 M d))) -1/4)) w0))
	61.2b	(.f64 D (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 h (pow.f64 M 2)) (*.f64 (pow.f64 d 2) l))))) w0))
	61.0b	(.f64 -1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 (pow.f64 d 2) l))))) (.f64 w0 M)))
	61.6b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (.f64 M w0))
✓	7.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 h (/.f64 M (/.f64 2 (/.f64 D d)))) (/.f64 l (/.f64 M (/.f64 2 (/.f64 D d))))))))
	10.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 h M) (/.f64 M (/.f64 2 (/.f64 D d)))) (.f64 l (/.f64 2 (/.f64 D d)))))))

Compiler

Compiled 82431 to 42082 computations (48.9% saved)

regimes6.0s (8.9%)

Accuracy

Total 6.0b remaining (66.9%)

Threshold costs 0b (0%)

Counts

170 → 1

Compiler

Compiled 75550 to 55273 computations (26.8% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	36
1	24	36
2	30	36
3	40	36
4	49	36
5	56	36
6	60	36
7	61	36

soundness5.0ms (0%)

Compiler: Compiled 220 to 164 computations (25.5% saved)

end458.0ms (0.7%)

Compiler: Compiled 637 to 439 computations (31.1% saved)

Details

analyze5.2s (7.6%)

sample5.3s (7.8%)

simplify90.0ms (0.1%)

prune8.0ms (0%)

localize55.0ms (0.1%)

series2.3s (3.4%)

rewrite108.0ms (0.2%)

simplify15.3s (22.5%)

prune604.0ms (0.9%)

localize23.0ms (0%)

series1.1s (1.6%)

rewrite250.0ms (0.4%)

simplify6.6s (9.7%)

prune1.4s (2%)

localize14.0ms (0%)

series475.0ms (0.7%)

rewrite119.0ms (0.2%)

simplify7.9s (11.6%)

prune3.0s (4.4%)

localize23.0ms (0%)

series364.0ms (0.5%)

rewrite671.0ms (1%)

simplify5.0s (7.3%)

prune5.7s (8.4%)

regimes6.0s (8.9%)

simplify4.0ms (0%)

soundness5.0ms (0%)

end458.0ms (0.7%)

Profiling