Details

analyze3.4s (25.4%)

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

23.0ms	256×	body	128	valid
9.0ms	103×	body	128	nan
4.0ms	45×	body	128	invalid

Compiler

Compiled 55 to 43 computations (21.8% saved)

simplify34.0ms (0.3%)

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

12.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	12.6b	(.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
✓	2.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
✓	3.6b	(/.f64 (.f64 M D) (.f64 2 d))
✓	3.8b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
✓	11.8b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite30.0ms (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 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))
3.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

series893.0ms (6.8%)

Counts

4 → 204

Calls

4 calls:

334.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
321.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
167.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
71.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify189.0ms (1.4%)

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 → 593

Iterations

Useful iterations: 1 (0.0ms)

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

prune437.0ms (3.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	576	17	593
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	577	17	594

Error

4.2b

Counts

594 → 17

Alt Table

Status	Error	Program
	12.6b	(.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))))))
	14.3b	w0
	12.7b	(.f64 (.f64 w0 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	10.5b	(.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))))))
	38.1b	(.f64 (sqrt.f64 w0) (.f64 (sqrt.f64 w0) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))))
	61.6b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	28.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 M D) (.f64 2 d))) 2) (.f64 (/.f64 (.f64 D M) (*.f64 2 d)) (/.f64 h l))))))
	62.0b	(.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)))
▶	10.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) l))))
	22.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (*.f64 M M) h) l))))))
	11.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 1 (.f64 (cbrt.f64 l) (cbrt.f64 l)))) (/.f64 h (cbrt.f64 l))))))
	61.4b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	26.2b	(-.f64 w0 (.f64 1/8 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (.f64 (*.f64 M M) h) w0) l))))
	59.2b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	38.1b	(.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)))))))
	49.7b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (sqrt.f64 h) (sqrt.f64 l))) (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (sqrt.f64 h) (sqrt.f64 l)))))))
	59.3b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))

Compiler

Compiled 12676 to 7677 computations (39.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	3.6b	(/.f64 (.f64 M D) (.f64 2 d))
✓	3.8b	(sqrt.f64 (-.f64 1 (/.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)
✓	6.3b	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)

rewrite23.0ms (0.2%)

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

series738.0ms (5.6%)

Counts

3 → 156

Calls

3 calls:

368.0ms	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)
227.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)
142.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)))

simplify162.0ms (1.2%)

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 → 462

Iterations

Useful iterations: 2 (0.0ms)

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

prune405.0ms (3.1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	538	3	541
Fresh	4	12	16
Picked	0	1	1
Done	0	0	0
Total	542	16	558

Error

4.1b

Counts

558 → 16

Alt Table

Status	Error	Program
	12.6b	(.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))))))
	14.3b	w0
	12.7b	(.f64 (.f64 w0 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	10.5b	(.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))))))
	38.1b	(.f64 (sqrt.f64 w0) (.f64 (sqrt.f64 w0) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))))
	61.6b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	26.2b	(-.f64 w0 (.f64 1/8 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (.f64 (*.f64 M M) h) w0) l))))
	24.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 M M) (/.f64 l h)))))))
	59.2b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	62.0b	(.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)))
	38.1b	(.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)))))))
✓	10.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) l))))
	12.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) h) l))))
▶	8.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)) l))))
	61.4b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	59.3b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))

Compiler

Compiled 8359 to 5319 computations (36.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	3.6b	(/.f64 (.f64 M D) (.f64 2 d))
✓	3.8b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h)) l)))
✓	5.0b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)
✓	6.3b	(/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h)) l)

rewrite41.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

226×	`add-cbrt-cube_binary64`
226×	`add-exp-log_binary64`
108×	`cbrt-unprod_binary64`
108×	`prod-exp_binary64`
79×	`cbrt-undiv_binary64`

Counts

3 → 135

Calls

3 calls:

13.0ms

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

8.0ms

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

6.0ms

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

series622.0ms (4.7%)

Counts

3 → 156

Calls

3 calls:

322.0ms

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

197.0ms

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

102.0ms

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

simplify218.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

584×	`associate-/l*_binary64`
485×	`associate-l_binary64`
455×	`associate-/r*_binary64`
414×	`associate-*l/_binary64`
390×	`associate-*r/_binary64`

Counts

291 → 535

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	458	9762
1	1205	8761
2	4703	8697
3	4996	8697

prune448.0ms (3.4%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	691	2	693
Fresh	2	12	14
Picked	0	1	1
Done	0	1	1
Total	693	16	709

Error

4.1b

Counts

709 → 16

Alt Table

Status	Error	Program
	12.6b	(.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))))))
	14.3b	w0
	38.1b	(.f64 (sqrt.f64 w0) (.f64 (sqrt.f64 w0) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))))
	61.6b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	12.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) h) l))))
▶	7.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (.f64 h (/.f64 (.f64 D M) (*.f64 2 d))) l)))))
	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 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
	26.2b	(-.f64 w0 (.f64 1/8 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (.f64 (*.f64 M M) h) w0) l))))
	12.7b	(.f64 (.f64 w0 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	24.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 M M) (/.f64 l h)))))))
	59.2b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	38.1b	(.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)))))))
✓	10.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) l))))
✓	8.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)) l))))
	61.4b	(/.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 12451 to 6840 computations (45.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.6b	(/.f64 (.f64 D M) (.f64 2 d))
✓	3.8b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (.f64 h (/.f64 (.f64 D M) (.f64 2 d))) l))))
✓	5.0b	(.f64 h (/.f64 (.f64 D M) (*.f64 2 d)))
✓	7.8b	(/.f64 (.f64 h (/.f64 (.f64 D M) (*.f64 2 d))) l)

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-cbrt-cube_binary64`
59×	`add-exp-log_binary64`
22×	`cbrt-unprod_binary64`
22×	`prod-exp_binary64`
18×	`cbrt-undiv_binary64`

Counts

4 → 103

Calls

4 calls:

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

series553.0ms (4.2%)

Counts

4 → 192

Calls

4 calls:

236.0ms	(/.f64 (.f64 h (/.f64 (.f64 D M) (*.f64 2 d))) l)
143.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (.f64 h (/.f64 (.f64 D M) (.f64 2 d))) l))))
115.0ms	(.f64 h (/.f64 (.f64 D M) (*.f64 2 d)))
58.0ms	(/.f64 (.f64 D M) (.f64 2 d))

simplify214.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

461×	`times-frac_binary64`
397×	`fma-def_binary64`
360×	`associate-/l*_binary64`
287×	`associate-r_binary64`
272×	`associate-/r*_binary64`

Counts

295 → 489

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	355	7289
1	926	6662
2	4367	6642
3	4979	6642
4	4985	6642

prune352.0ms (2.7%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	489	0	489
Fresh	0	13	13
Picked	0	1	1
Done	0	2	2
Total	489	16	505

Error

4.1b

Counts

505 → 16

Alt Table

Status	Error	Program
	12.6b	(.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))))))
	14.3b	w0
	38.1b	(.f64 (sqrt.f64 w0) (.f64 (sqrt.f64 w0) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))))
	61.6b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	12.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) h) l))))
✓	7.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 D M) (.f64 2 d)) (/.f64 (.f64 h (/.f64 (.f64 D M) (*.f64 2 d))) l)))))
	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 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) h) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
	26.2b	(-.f64 w0 (.f64 1/8 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (.f64 (*.f64 M M) h) w0) l))))
	12.7b	(.f64 (.f64 w0 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))) (cbrt.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))))))
	24.4b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 M M) (/.f64 l h)))))))
	59.2b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	38.1b	(.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)))))))
✓	10.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) l))))
✓	8.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)) l))))
	61.4b	(/.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 8740 to 4927 computations (43.6% saved)

regimes2.3s (17.4%)

Accuracy

Total 3.4b remaining (39%)

Threshold costs 0b (0%)

Compiler

Compiled 62545 to 45519 computations (27.2% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64`
9×	`+-commutative_binary64`
9×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	36
1	30	36
2	41	36
3	57	36
4	74	36
5	84	36
6	89	36
7	90	36
8	89	36

end7.0ms (0.1%)

Remove: (sort M D)
Compiler: Compiled 90 to 60 computations (33.3% saved)

sample2.0s (15.4%)

Algorithm

1×

intervals

Results

769.0ms	8000×	body	128	valid
320.0ms	3137×	body	128	nan
122.0ms	1279×	body	128	invalid

Compiler

Compiled 524 to 371 computations (29.2% saved)

Details

analyze3.4s (25.4%)

sample72.0ms (0.5%)

simplify34.0ms (0.3%)

prune2.0ms (0%)

localize13.0ms (0.1%)

rewrite30.0ms (0.2%)

series893.0ms (6.8%)

simplify189.0ms (1.4%)

prune437.0ms (3.3%)

localize13.0ms (0.1%)

rewrite23.0ms (0.2%)

series738.0ms (5.6%)

simplify162.0ms (1.2%)

prune405.0ms (3.1%)

localize15.0ms (0.1%)

rewrite41.0ms (0.3%)

series622.0ms (4.7%)

simplify218.0ms (1.6%)

prune448.0ms (3.4%)

localize15.0ms (0.1%)

rewrite27.0ms (0.2%)

series553.0ms (4.2%)

simplify214.0ms (1.6%)

prune352.0ms (2.7%)

regimes2.3s (17.4%)

simplify8.0ms (0.1%)

end7.0ms (0.1%)

sample2.0s (15.4%)

Profiling