Details

analyze3.2s (30%)

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)

sample67.0ms (0.6%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
8.0ms	90×	body	128	nan
5.0ms	52×	body	128	invalid

Compiler

Compiled 55 to 43 computations (21.8% saved)

simplify47.0ms (0.4%)

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

prune4.0ms (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

10.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	10.6b	(.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
✓	1.0b	(.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))))
✓	4.5b	(/.f64 (.f64 M D) (.f64 2 d))
✓	10.5b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite32.0ms (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:

9.0ms	(.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))))

series936.0ms (8.7%)

Counts

4 → 204

Calls

4 calls:

356.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
354.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
164.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
62.0ms	(/.f64 (.f64 M D) (.f64 2 d))

simplify192.0ms (1.8%)

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

prune420.0ms (3.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	581	12	593
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	582	12	594

Error

2.9b

Counts

594 → 12

Alt Table

Status	Error	Program
	10.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
	56.7b	(.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)))))))
	21.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (*.f64 M M) h) l))))))
▶	9.8b	(.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))))))
	25.2b	(-.f64 w0 (.f64 1/8 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (.f64 (*.f64 M M) h) w0) l))))
	60.6b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	10.6b	(.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))))))
	61.7b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	60.8b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))
	13.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 D M) (.f64 2 d)) 3)) 2) (/.f64 h l)))))
	12.3b	w0
	61.7b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))

Compiler

Compiled 12258 to 7395 computations (39.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.0b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))
	4.5b	(/.f64 (.f64 M D) (.f64 2 d))
	4.5b	(/.f64 (.f64 M D) (.f64 2 d))
✓	8.4b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-cbrt-cube_binary64`
43×	`add-exp-log_binary64`
18×	`cbrt-unprod_binary64`
18×	`prod-exp_binary64`
17×	`add-sqr-sqrt_binary64`

Counts

2 → 71

Calls

2 calls:

9.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
4.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))

series364.0ms (3.4%)

Counts

2 → 108

Calls

2 calls:

210.0ms	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) (/.f64 h l))
154.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (/.f64 h l)))))

simplify157.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

454×	`fma-def_binary64`
406×	`times-frac_binary64`
307×	`associate-r_binary64`
302×	`associate-l_binary64`
295×	`associate-/l*_binary64`

Counts

179 → 336

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	344	5832
1	913	5360
2	4389	5341
3	4976	5341

prune316.0ms (2.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	570	3	573
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	573	12	585

Error

2.4b

Counts

585 → 12

Alt Table

Status	Error	Program
	60.1b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 M (.f64 M h)) (.f64 l (*.f64 d d))) -1/4))))
▶	10.6b	(.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))))))
✓	9.8b	(.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))))))
	25.2b	(-.f64 w0 (.f64 1/8 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (.f64 (*.f64 M M) h) w0) l))))
	60.6b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	13.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 1/2 (/.f64 (.f64 D (.f64 M h)) (.f64 l d)))))))
	13.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 D M) (*.f64 2 d)) 3)) (/.f64 h l))))))
	21.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (*.f64 M M) h) l))))))
	61.7b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	60.8b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))
	12.3b	w0
	61.7b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))

Compiler

Compiled 9774 to 5296 computations (45.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	4.5b	(/.f64 (.f64 M D) (.f64 2 d))
	4.5b	(/.f64 (.f64 M D) (.f64 2 d))
	10.5b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
	10.5b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify30.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune452.0ms (4.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	1647	0	1647
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	1647	12	1659

Error

2.4b

Counts

1659 → 12

Alt Table

Status	Error	Program
	60.1b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 M (.f64 M h)) (.f64 l (*.f64 d d))) -1/4))))
✓	10.6b	(.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))))))
✓	9.8b	(.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))))))
	25.2b	(-.f64 w0 (.f64 1/8 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (.f64 (*.f64 M M) h) w0) l))))
	60.6b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	13.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 1/2 (/.f64 (.f64 D (.f64 M h)) (.f64 l d)))))))
	13.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 D M) (*.f64 2 d)) 3)) (/.f64 h l))))))
	21.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (*.f64 M M) h) l))))))
	61.7b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	60.8b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))
▶	12.3b	w0
	61.7b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))

Compiler

Compiled 12511 to 7366 computations (41.1% saved)

localize1.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune9.0ms (0.1%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	9	9
Picked	1	1
Done	2	2
Total	12	12

Error

2.4b

Counts

12 → 12

Alt Table

Status	Error	Program
	60.1b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 M (.f64 M h)) (.f64 l (*.f64 d d))) -1/4))))
✓	10.6b	(.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))))))
✓	9.8b	(.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))))))
	25.2b	(-.f64 w0 (.f64 1/8 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (.f64 (*.f64 M M) h) w0) l))))
	60.6b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 M)))
	13.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 1/2 (/.f64 (.f64 D (.f64 M h)) (.f64 l d)))))))
	13.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (cbrt.f64 (pow.f64 (/.f64 (.f64 D M) (*.f64 2 d)) 3)) (/.f64 h l))))))
	21.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 1/4 (.f64 (pow.f64 (/.f64 D d) 2) (/.f64 (.f64 (*.f64 M M) h) l))))))
	61.7b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	60.8b	(.f64 D (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4)) w0))
✓	12.3b	w0
	61.7b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) l) -1/4)) d))

Compiler

Compiled 314 to 221 computations (29.6% saved)

regimes1.9s (17.8%)

Accuracy

Total 3.5b remaining (44.3%)

Threshold costs 0b (0%)

Compiler

Compiled 44811 to 33074 computations (26.2% saved)

bsearch4.0ms (0%)

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

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

29×	`*-commutative_binary64`
17×	`+-commutative_binary64`
17×	`sub-neg_binary64`
16×	`neg-sub0_binary64`
16×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	137
1	73	137
2	102	137
3	135	137
4	162	137
5	175	137
6	179	137
7	178	137

end10.0ms (0.1%)

Compiler: Compiled 291 to 177 computations (39.2% saved)

sample2.5s (23.1%)

Algorithm

1×

intervals

Results

797.0ms	8000×	body	128	valid
334.0ms	3133×	body	128	nan
126.0ms	1315×	body	128	invalid

Compiler

Compiled 442 to 305 computations (31% saved)

Details

analyze3.2s (30%)

sample67.0ms (0.6%)

simplify47.0ms (0.4%)

prune4.0ms (0%)

localize13.0ms (0.1%)

rewrite32.0ms (0.3%)

series936.0ms (8.7%)

simplify192.0ms (1.8%)

prune420.0ms (3.9%)

localize13.0ms (0.1%)

rewrite19.0ms (0.2%)

series364.0ms (3.4%)

simplify157.0ms (1.5%)

prune316.0ms (2.9%)

localize15.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify30.0ms (0.3%)

prune452.0ms (4.2%)

localize1.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify10.0ms (0.1%)

prune9.0ms (0.1%)

regimes1.9s (17.8%)

bsearch4.0ms (0%)

simplify10.0ms (0.1%)

end10.0ms (0.1%)

sample2.5s (23.1%)

Profiling