Details

analyze2.7s (20.1%)

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)

sample65.0ms (0.5%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
9.0ms	120×	body	128	nan
2.0ms	30×	body	128	invalid

Compiler

Compiled 55 to 43 computations (21.8% saved)

simplify48.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

893×	`div-sub_binary64`
645×	`distribute-neg-frac_binary64`
581×	`distribute-rgt-neg-in_binary64`
569×	`distribute-lft-neg-in_binary64`
418×	`associate-/l*_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	27
1	42	27
2	111	27
3	718	27
4	2816	27
5	4688	27
6	6103	27

prune3.0ms (0%)

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

11.6b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	11.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))

Compiler

Compiled 48 to 36 computations (25% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
5.8b	(/.f64 (.f64 M D) (.f64 2 d))
10.2b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite275.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

6.5b

Rules

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

Counts

4 → 116

Calls

4 calls:

11.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
8.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
6.0ms	(/.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))))

Compiler

Compiled 3232 to 1835 computations (43.2% saved)

series510.0ms (3.9%)

Error

6.2b

Counts

4 → 75

Calls

4 calls:

211.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
133.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
108.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
35.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 4527 to 3438 computations (24.1% saved)

simplify133.0ms (1%)

Algorithm

1×	egg-herbie

Rules

331×	`times-frac_binary64`
326×	`associate-l_binary64`
309×	`associate-r_binary64`
266×	`associate-/l*_binary64`
214×	`distribute-neg-frac_binary64`

Counts

191 → 147

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	300	4632
1	785	4334
2	3465	4321
3	4984	4321

prune158.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	135	12	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	136	12	148

Error

4.4b

Counts

148 → 12

Alt Table

Status	Error	Program
	9.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 1 l)))))
▶	9.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l)))))
	21.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M 2) 2) (*.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2))))))
	11.6b	(.f64 (.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	61.0b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 (*.f64 d d) l)) -1/4))))
	35.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (sqrt.f64 h)) (/.f64 (sqrt.f64 h) l)))))
	10.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 2 2)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))))))
	61.8b	(.f64 M (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) w0))
	58.9b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	15.8b	(.f64 w0 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) 3))) (sqrt.f64 (+.f64 1 (.f64 (/.f64 h l) (+.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 4))))))))
	11.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))))
	61.8b	(.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))

Compiler

Compiled 2754 to 1632 computations (40.7% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.0b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
4.3b	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
5.3b	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
5.8b	(/.f64 (.f64 M D) (.f64 2 d))

rewrite355.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

4.2b

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 → 145

Calls

4 calls:

18.0ms	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
11.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
6.0ms	(/.f64 (.f64 M D) (.f64 2 d))
5.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))

Compiler

Compiled 4891 to 2231 computations (54.4% saved)

series476.0ms (3.6%)

Error

4.4b

Counts

4 → 58

Calls

4 calls:

158.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (cbrt.f64 h) (cbrt.f64 h)))
140.0ms	(.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))
118.0ms	(sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (*.f64 (cbrt.f64 h) (cbrt.f64 h))) (/.f64 (cbrt.f64 h) l))))
38.0ms	(/.f64 (.f64 M D) (.f64 2 d))

Compiler

Compiled 3714 to 2844 computations (23.4% saved)

simplify174.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

429×	`associate-l_binary64`
322×	`associate-r_binary64`
281×	`times-frac_binary64`
255×	`log-prod_binary64`
241×	`associate-/l*_binary64`

Counts

203 → 174

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	306	5595
1	766	4514
2	3414	4412
3	4832	4382
4	5113	4382

prune192.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	172	2	174
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	174	12	186

Error

4.2b

Counts

186 → 12

Alt Table

Status	Error	Program
	9.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 1 l)))))
▶	7.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (*.f64 d 2)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l)))))
	11.6b	(.f64 (.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	61.0b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 (*.f64 d d) l)) -1/4))))
	35.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (sqrt.f64 h)) (/.f64 (sqrt.f64 h) l)))))
	10.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 2 2)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))))))
	16.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))))
	61.8b	(.f64 M (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) w0))
	58.9b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	15.8b	(.f64 w0 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) 3))) (sqrt.f64 (+.f64 1 (.f64 (/.f64 h l) (+.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 4))))))))
	11.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) (/.f64 h l)))))
	61.8b	(.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))

Compiler

Compiled 2895 to 1579 computations (45.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.5b	(.f64 (/.f64 (.f64 M D) (*.f64 d 2)) (cbrt.f64 h))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 d 2)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))))
5.3b	(.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 d 2)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))
5.8b	(/.f64 (.f64 M D) (.f64 d 2))

rewrite361.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

3.5b

Rules

98×	`add-exp-log_binary64`
47×	`prod-exp_binary64`
45×	`add-sqr-sqrt_binary64`
33×	`add-cbrt-cube_binary64`
28×	`associate-r_binary64`

Counts

4 → 133

Calls

4 calls:

15.0ms	(.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 d 2)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))
10.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 d 2)) (cbrt.f64 h))
6.0ms	(/.f64 (.f64 M D) (.f64 d 2))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 d 2)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))))

Compiler

Compiled 4200 to 2097 computations (50.1% saved)

series415.0ms (3.1%)

Error

4.2b

Counts

4 → 58

Calls

4 calls:

141.0ms	(.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 d 2)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))
115.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 (.f64 M D) (.f64 d 2)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))))
106.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 d 2)) (cbrt.f64 h))
37.0ms	(/.f64 (.f64 M D) (.f64 d 2))

Compiler

Compiled 3501 to 2667 computations (23.8% saved)

simplify170.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

423×	`associate-l_binary64`
392×	`log-prod_binary64`
349×	`associate-r_binary64`
308×	`times-frac_binary64`
242×	`associate-/l*_binary64`

Counts

191 → 160

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	289	4720
1	721	4381
2	3591	4365
3	4738	4365
4	5148	4365

prune206.0ms (1.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	156	4	160
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	159	13	172

Error

3.9b

Counts

172 → 13

Alt Table

Status	Error	Program
	9.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 1 l)))))
	61.3b	(.f64 w0 (neg.f64 (.f64 M (sqrt.f64 (.f64 -1/4 (/.f64 (.f64 (.f64 D D) h) (.f64 (*.f64 d d) l)))))))
	11.6b	(.f64 (.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	61.0b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 (*.f64 d d) l)) -1/4))))
	10.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 2 2)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))))))
	16.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))))
	61.8b	(.f64 M (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) w0))
	58.9b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	15.8b	(.f64 w0 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) 3))) (sqrt.f64 (+.f64 1 (.f64 (/.f64 h l) (+.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 4))))))))
	61.8b	(.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))
▶	7.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (.f64 1/2 (/.f64 (*.f64 M D) d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l)))))
	9.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 M d) (.f64 (cbrt.f64 h) (/.f64 D 2))) 2) (/.f64 (cbrt.f64 h) l)))))
	7.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (.f64 1/2 (.f64 (/.f64 (.f64 M D) d) (cbrt.f64 h))) 2) (*.f64 (cbrt.f64 (/.f64 (cbrt.f64 h) l)) (cbrt.f64 (/.f64 (cbrt.f64 h) l)))) (cbrt.f64 (/.f64 (cbrt.f64 h) l))))))

Compiler

Compiled 3186 to 1623 computations (49.1% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.5b	(.f64 (.f64 1/2 (/.f64 (*.f64 M D) d)) (cbrt.f64 h))
4.0b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (.f64 1/2 (/.f64 (.f64 M D) d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))))
5.3b	(.f64 (pow.f64 (.f64 (.f64 1/2 (/.f64 (.f64 M D) d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))
5.8b	(/.f64 (*.f64 M D) d)

rewrite350.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

3.5b

Rules

76×	`add-exp-log_binary64`
42×	`add-sqr-sqrt_binary64`
39×	`prod-exp_binary64`
28×	`associate-r_binary64`
27×	`times-frac_binary64`

Counts

4 → 124

Calls

4 calls:

17.0ms	(.f64 (pow.f64 (.f64 (.f64 1/2 (/.f64 (.f64 M D) d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))
10.0ms	(.f64 (.f64 1/2 (/.f64 (*.f64 M D) d)) (cbrt.f64 h))
5.0ms	(/.f64 (*.f64 M D) d)
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (.f64 1/2 (/.f64 (.f64 M D) d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))))

Compiler

Compiled 3872 to 1773 computations (54.2% saved)

series409.0ms (3.1%)

Error

3.9b

Counts

4 → 58

Calls

4 calls:

142.0ms	(.f64 (pow.f64 (.f64 (.f64 1/2 (/.f64 (.f64 M D) d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))
115.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (.f64 1/2 (/.f64 (.f64 M D) d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l))))
106.0ms	(.f64 (.f64 1/2 (/.f64 (*.f64 M D) d)) (cbrt.f64 h))
32.0ms	(/.f64 (*.f64 M D) d)

Compiler

Compiled 3501 to 2667 computations (23.8% saved)

simplify166.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

433×	`associate-l_binary64`
355×	`associate-r_binary64`
341×	`log-prod_binary64`
292×	`distribute-rgt-neg-in_binary64`
189×	`associate-/l*_binary64`

Counts

182 → 143

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	286	4359
1	699	4109
2	3214	4094
3	4890	4094
4	5161	4094

prune151.0ms (1.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	143	13	156

Error

3.9b

Counts

156 → 13

Alt Table

Status	Error	Program
	9.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 h (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2)) (/.f64 1 l)))))
	61.3b	(.f64 w0 (neg.f64 (.f64 M (sqrt.f64 (.f64 -1/4 (/.f64 (.f64 (.f64 D D) h) (.f64 (*.f64 d d) l)))))))
	11.6b	(.f64 (.f64 w0 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)))))) (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	61.0b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 (*.f64 d d) l)) -1/4))))
	10.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 2 2)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))))))
	16.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (log.f64 (pow.f64 (exp.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 d 2)) 2)) (/.f64 h l))))))
	61.8b	(.f64 M (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) w0))
	58.9b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	15.8b	(.f64 w0 (/.f64 (sqrt.f64 (-.f64 1 (pow.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2)) 3))) (sqrt.f64 (+.f64 1 (.f64 (/.f64 h l) (+.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (.f64 (/.f64 h l) (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 4))))))))
	61.8b	(.f64 w0 (.f64 M (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4))))
	7.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (.f64 1/2 (/.f64 (*.f64 M D) d)) (cbrt.f64 h)) 2) (/.f64 (cbrt.f64 h) l)))))
	9.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 (/.f64 M d) (.f64 (cbrt.f64 h) (/.f64 D 2))) 2) (/.f64 (cbrt.f64 h) l)))))
	7.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (.f64 1/2 (.f64 (/.f64 (.f64 M D) d) (cbrt.f64 h))) 2) (*.f64 (cbrt.f64 (/.f64 (cbrt.f64 h) l)) (cbrt.f64 (/.f64 (cbrt.f64 h) l)))) (cbrt.f64 (/.f64 (cbrt.f64 h) l))))))

Compiler

Compiled 2506 to 1162 computations (53.6% saved)

regimes3.7s (27.7%)

Accuracy

Total 3.9b remaining (42.4%)

Threshold costs 0b (0%)

Compiler

Compiled 78111 to 54641 computations (30% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

15×	`*-commutative_binary64`
10×	`sub-neg_binary64` `+-commutative_binary64`
9×	`neg-mul-1_binary64` `neg-sub0_binary64`
8×	`distribute-rgt-neg-in_binary64`
7×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	48
1	33	48
2	48	48
3	65	48
4	84	48
5	95	48
6	101	48
7	103	48
8	102	48

end11.0ms (0.1%)

Remove: (sort M D)
Compiler: Compiled 111 to 69 computations (37.8% saved)

sample2.2s (16.7%)

Algorithm

1×

intervals

Results

651.0ms	8000×	body	128	valid
242.0ms	3081×	body	128	nan
120.0ms	1372×	body	128	invalid

Compiler

Compiled 467 to 324 computations (30.6% saved)

Details

analyze2.7s (20.1%)

sample65.0ms (0.5%)

simplify48.0ms (0.4%)

prune3.0ms (0%)

localize15.0ms (0.1%)

rewrite275.0ms (2.1%)

series510.0ms (3.9%)

simplify133.0ms (1%)

prune158.0ms (1.2%)

localize22.0ms (0.2%)

rewrite355.0ms (2.7%)

series476.0ms (3.6%)

simplify174.0ms (1.3%)

prune192.0ms (1.4%)

localize18.0ms (0.1%)

rewrite361.0ms (2.7%)

series415.0ms (3.1%)

simplify170.0ms (1.3%)

prune206.0ms (1.6%)

localize18.0ms (0.1%)

rewrite350.0ms (2.6%)

series409.0ms (3.1%)

simplify166.0ms (1.3%)

prune151.0ms (1.1%)

regimes3.7s (27.7%)

simplify6.0ms (0%)

end11.0ms (0.1%)

sample2.2s (16.7%)

Profiling