Details

analyze2.8s (25%)

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
4.3%	95.4%	0.3%	13
6.6%	93.1%	0.3%	14

Compiler

Compiled 25 to 19 computations (24% saved)

sample2.3s (20.7%)

Results

1.5s	8256×	body	128	valid
758.0ms	4455×	body	128	invalid

Compiler

Compiled 50 to 38 computations (24% saved)

preprocess43.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

668×	`times-frac_binary64`
300×	`associate-/l*_binary64`
278×	`*-commutative_binary64`
260×	`neg-sub0_binary64`
260×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	125	432
1	394	432
2	1216	432
3	3619	432
0	6	6
1	6	6

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort M D)

Compiler

Compiled 24 to 18 computations (25% saved)

simplify21.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

418×	`associate-/l*_binary64`
372×	`cancel-sign-sub-inv_binary64`
251×	`associate-/l/_binary64`
229×	`*-commutative_binary64`
227×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	27
1	42	27
2	115	27
3	846	27
4	3817	27

Stop Event

1×	node limit

Counts

1 → 2

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

13.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (/.f64 D (.f64 2 d))) 2) (/.f64 h l)))))

Compiler

Compiled 90 to 65 computations (27.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.9b	(.f64 M (/.f64 D (.f64 2 d)))
✓	3.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (/.f64 D (.f64 2 d))) 2) (/.f64 h l)))))
✓	5.4b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (/.f64 D (*.f64 2 d))) 2) (/.f64 h l))))
✓	8.1b	(.f64 (pow.f64 (.f64 M (/.f64 D (*.f64 2 d))) 2) (/.f64 h l))

series557.0ms (5%)

Counts

4 → 204

Calls

57 calls:

23.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (/.f64 D (.f64 2 d))) 2) (/.f64 h l)))))	w0	-inf
23.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (/.f64 D (.f64 2 d))) 2) (/.f64 h l)))))	w0	0
23.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (/.f64 D (.f64 2 d))) 2) (/.f64 h l)))))	w0	inf
17.0ms	(.f64 (pow.f64 (.f64 M (/.f64 D (*.f64 2 d))) 2) (/.f64 h l))	M	-inf
17.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (/.f64 D (.f64 2 d))) 2) (/.f64 h l)))))	l	0

rewrite39.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

188×	`add-sqr-sqrt_binary64`
179×	`log1p-expm1-u_binary64`
179×	`expm1-log1p-u_binary64`
177×	`add-cbrt-cube_binary64`
175×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	80
1	386	80

Stop Event

1×	node limit

Counts

4 → 92

simplify135.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

638×	`fma-def_binary64`
262×	`times-frac_binary64`
244×	`associate-/r*_binary64`
230×	`associate-r_binary64`
226×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	310	8076
1	1240	8010
2	4070	7948

Stop Event

1×	node limit

Counts

296 → 212

prune223.0ms (2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	201	11	212
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	201	12	213

Error

5.5b

Counts

213 → 12

Alt Table

Status	Error	Program
✓	13.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (/.f64 D (.f64 2 d))) 2) (/.f64 h l)))))
	15.8b	w0
	60.8b	(.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)))
	37.3b	(fma.f64 (/.f64 (.f64 D D) (/.f64 (.f64 d d) (/.f64 (.f64 (.f64 M M) w0) (/.f64 l h)))) -1/8 w0)
	58.2b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (.f64 -1/4 (/.f64 h l)) (*.f64 (/.f64 M d) (/.f64 M d))))))
	14.0b	(.f64 w0 (exp.f64 (.f64 1/2 (log1p.f64 (.f64 (pow.f64 (.f64 M (*.f64 D (/.f64 1/2 d))) 2) (neg.f64 (/.f64 h l)))))))
▶	12.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) h) l))))
	13.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (pow.f64 (.f64 M (*.f64 D (/.f64 1/2 d))) 2) (/.f64 l h)))))
	62.6b	(neg.f64 (fma.f64 D (.f64 (sqrt.f64 (.f64 (.f64 -1/4 (/.f64 h l)) (.f64 (/.f64 M d) (/.f64 M d)))) w0) (/.f64 (/.f64 (.f64 1/2 w0) D) (sqrt.f64 (.f64 (.f64 -1/4 (/.f64 h l)) (.f64 (/.f64 M d) (/.f64 M d)))))))
	57.7b	(.f64 D (.f64 (sqrt.f64 (.f64 (.f64 -1/4 (/.f64 h l)) (*.f64 (/.f64 M d) (/.f64 M d)))) w0))
	61.0b	(.f64 D (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 h (pow.f64 M 2)) (*.f64 (pow.f64 d 2) l))))) w0))
	62.0b	(-.f64 (.f64 (/.f64 1/8 (pow.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 h D) D) (.f64 l (.f64 d d))) -1/4)) 3)) (/.f64 w0 (pow.f64 M 3))) (fma.f64 M (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 h D) D) (.f64 l (.f64 d d))) -1/4)) w0) (.f64 1/2 (/.f64 w0 (.f64 M (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 h D) D) (.f64 l (*.f64 d d))) -1/4)))))))

Compiler

Compiled 8902 to 5487 computations (38.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.1b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) h) l))))
✓	4.2b	(/.f64 (.f64 (pow.f64 (.f64 M (*.f64 D (/.f64 1/2 d))) 2) h) l)
✓	5.2b	(.f64 (pow.f64 (.f64 M (*.f64 D (/.f64 1/2 d))) 2) h)
✓	5.4b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (.f64 M (*.f64 D (/.f64 1/2 d))) 2) h) l)))

series696.0ms (6.2%)

Counts

4 → 216

Calls

60 calls:

45.0ms	(.f64 (pow.f64 (.f64 M (*.f64 D (/.f64 1/2 d))) 2) h)	D	inf
24.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) h) l))))	w0	-inf
22.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) h) l))))	w0	inf
22.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) h) l))))	w0	0
19.0ms	(/.f64 (.f64 (pow.f64 (.f64 M (*.f64 D (/.f64 1/2 d))) 2) h) l)	D	-inf

rewrite45.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

194×	`add-sqr-sqrt_binary64`
185×	`log1p-expm1-u_binary64`
185×	`expm1-log1p-u_binary64`
183×	`add-cbrt-cube_binary64`
181×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	86
1	404	86

Stop Event

1×	node limit

Counts

4 → 95

simplify179.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

610×	`fma-def_binary64`
263×	`times-frac_binary64`
246×	`associate-/r*_binary64`
239×	`fma-neg_binary64`
229×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	309	8766
1	1241	8706
2	4051	8644

Stop Event

1×	node limit

Counts

311 → 216

prune238.0ms (2.1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	210	6	216
Fresh	5	5	10
Picked	0	1	1
Done	0	1	1
Total	215	13	228

Error

4.4b

Counts

228 → 13

Alt Table

Status	Error	Program
✓	13.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (/.f64 D (.f64 2 d))) 2) (/.f64 h l)))))
	15.8b	w0
	60.8b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (.f64 (/.f64 h (*.f64 d d)) (/.f64 M (/.f64 l M))) -1/4))))
	62.0b	(-.f64 (.f64 (/.f64 1/8 (pow.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 h D) D) (.f64 l (.f64 d d))) -1/4)) 3)) (/.f64 w0 (pow.f64 M 3))) (fma.f64 M (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 h D) D) (.f64 l (.f64 d d))) -1/4)) w0) (.f64 1/2 (/.f64 w0 (.f64 M (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 h D) D) (.f64 l (*.f64 d d))) -1/4)))))))
	61.9b	(.f64 w0 (neg.f64 (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 (pow.f64 d 2) l))))) M))) (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 l (pow.f64 d 2)))))) M))))
	35.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (.f64 (.f64 (.f64 M (/.f64 1/2 d)) D) (sqrt.f64 h)) 1) (/.f64 (.f64 (.f64 (.f64 M (/.f64 1/2 d)) D) (sqrt.f64 h)) l)))))
▶	13.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (pow.f64 (.f64 (.f64 M (/.f64 1/2 d)) D) 2) l) h))))
	58.2b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (.f64 -1/4 (/.f64 h l)) (*.f64 (/.f64 M d) (/.f64 M d))))))
	60.5b	(.f64 D (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h (*.f64 d d)) (/.f64 M (/.f64 l M))) -1/4)) w0))
✓	12.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) h) l))))
	62.6b	(neg.f64 (fma.f64 D (.f64 (sqrt.f64 (.f64 (.f64 -1/4 (/.f64 h l)) (.f64 (/.f64 M d) (/.f64 M d)))) w0) (/.f64 (/.f64 (.f64 1/2 w0) D) (sqrt.f64 (.f64 (.f64 -1/4 (/.f64 h l)) (.f64 (/.f64 M d) (/.f64 M d)))))))
	57.7b	(.f64 D (.f64 (sqrt.f64 (.f64 (.f64 -1/4 (/.f64 h l)) (*.f64 (/.f64 M d) (/.f64 M d)))) w0))
	24.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 1/4 (.f64 (/.f64 D (/.f64 (.f64 d d) D)) (.f64 M (.f64 M h)))) l))))

Compiler

Compiled 9247 to 5786 computations (37.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.9b	(.f64 (/.f64 (pow.f64 (.f64 (*.f64 M (/.f64 1/2 d)) D) 2) l) h)
✓	5.4b	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (pow.f64 (.f64 (*.f64 M (/.f64 1/2 d)) D) 2) l) h)))
✓	6.7b	(/.f64 (pow.f64 (.f64 (.f64 M (/.f64 1/2 d)) D) 2) l)
✓	7.2b	(.f64 (.f64 M (/.f64 1/2 d)) D)

series466.0ms (4.2%)

Counts

4 → 192

Calls

51 calls:

21.0ms	(sqrt.f64 (-.f64 1 (.f64 (/.f64 (pow.f64 (.f64 (*.f64 M (/.f64 1/2 d)) D) 2) l) h)))	h	-inf
21.0ms	(.f64 (/.f64 (pow.f64 (.f64 (*.f64 M (/.f64 1/2 d)) D) 2) l) h)	M	-inf
15.0ms	(.f64 (/.f64 (pow.f64 (.f64 (*.f64 M (/.f64 1/2 d)) D) 2) l) h)	l	0
14.0ms	(.f64 (/.f64 (pow.f64 (.f64 (*.f64 M (/.f64 1/2 d)) D) 2) l) h)	h	0
14.0ms	(.f64 (/.f64 (pow.f64 (.f64 (*.f64 M (/.f64 1/2 d)) D) 2) l) h)	h	inf

rewrite74.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

527×	`prod-diff_binary64`
176×	`add-sqr-sqrt_binary64`
169×	`log1p-expm1-u_binary64`
169×	`expm1-log1p-u_binary64`
167×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	69
1	368	69
2	4641	69

Stop Event

1×	node limit

Counts

4 → 104

simplify100.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

266×	`associate-/r/_binary64`
252×	`fma-def_binary64`
249×	`unswap-sqr_binary64`
203×	`distribute-neg-frac_binary64`
188×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	5700
1	711	5662
2	2366	5644

Stop Event

1×	node limit

Counts

296 → 169

prune205.0ms (1.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	164	5	169
Fresh	5	5	10
Picked	0	1	1
Done	1	1	2
Total	170	12	182

Error

3.9b

Counts

182 → 12

Alt Table

Status	Error	Program
▶	11.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 (.f64 (.f64 M 1/2) D) d) (.f64 (/.f64 (.f64 (.f64 M 1/2) D) d) (pow.f64 l -1))) h))))
	62.6b	(neg.f64 (fma.f64 D (.f64 (sqrt.f64 (.f64 (.f64 -1/4 (/.f64 h l)) (.f64 (/.f64 M d) (/.f64 M d)))) w0) (/.f64 (/.f64 (.f64 1/2 w0) D) (sqrt.f64 (.f64 (.f64 -1/4 (/.f64 h l)) (.f64 (/.f64 M d) (/.f64 M d)))))))
	57.7b	(.f64 D (.f64 (sqrt.f64 (.f64 (.f64 -1/4 (/.f64 h l)) (*.f64 (/.f64 M d) (/.f64 M d)))) w0))
	60.0b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (.f64 (/.f64 M (/.f64 l M)) (/.f64 (/.f64 h d) d)) -1/4))))
	62.0b	(-.f64 (.f64 (/.f64 1/8 (pow.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 h D) D) (.f64 l (.f64 d d))) -1/4)) 3)) (/.f64 w0 (pow.f64 M 3))) (fma.f64 M (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 h D) D) (.f64 l (.f64 d d))) -1/4)) w0) (.f64 1/2 (/.f64 w0 (.f64 M (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 h D) D) (.f64 l (*.f64 d d))) -1/4)))))))
	60.7b	(.f64 w0 (.f64 -1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 (pow.f64 d 2) l))))) M)))
	20.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (.f64 1/4 (*.f64 (/.f64 D d) (/.f64 D d))) (/.f64 M (/.f64 l M))) h))))
✓	13.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (pow.f64 (.f64 (.f64 M (/.f64 1/2 d)) D) 2) l) h))))
	15.8b	w0
	60.5b	(.f64 D (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h (*.f64 d d)) (/.f64 M (/.f64 l M))) -1/4)) w0))
✓	12.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) h) l))))
	58.7b	(.f64 w0 (.f64 M (neg.f64 (sqrt.f64 (.f64 (.f64 (*.f64 (/.f64 D d) (/.f64 D d)) (/.f64 h l)) -1/4)))))

Compiler

Compiled 6229 to 3975 computations (36.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.8b	(.f64 (/.f64 (.f64 (*.f64 M 1/2) D) d) (pow.f64 l -1))
✓	3.9b	(.f64 (.f64 (/.f64 (.f64 (.f64 M 1/2) D) d) (.f64 (/.f64 (.f64 (*.f64 M 1/2) D) d) (pow.f64 l -1))) h)
✓	4.8b	(/.f64 (.f64 (.f64 M 1/2) D) d)
✓	5.4b	(sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 (.f64 (.f64 M 1/2) D) d) (.f64 (/.f64 (.f64 (*.f64 M 1/2) D) d) (pow.f64 l -1))) h)))

series345.0ms (3.1%)

Counts

4 → 192

Calls

51 calls:

14.0ms	(.f64 (.f64 (/.f64 (.f64 (.f64 M 1/2) D) d) (.f64 (/.f64 (.f64 (*.f64 M 1/2) D) d) (pow.f64 l -1))) h)	l	0
14.0ms	(.f64 (.f64 (/.f64 (.f64 (.f64 M 1/2) D) d) (.f64 (/.f64 (.f64 (*.f64 M 1/2) D) d) (pow.f64 l -1))) h)	h	-inf
14.0ms	(.f64 (.f64 (/.f64 (.f64 (.f64 M 1/2) D) d) (.f64 (/.f64 (.f64 (*.f64 M 1/2) D) d) (pow.f64 l -1))) h)	h	inf
14.0ms	(.f64 (.f64 (/.f64 (.f64 (.f64 M 1/2) D) d) (.f64 (/.f64 (.f64 (*.f64 M 1/2) D) d) (pow.f64 l -1))) h)	l	-inf
14.0ms	(.f64 (.f64 (/.f64 (.f64 (.f64 M 1/2) D) d) (.f64 (/.f64 (.f64 (*.f64 M 1/2) D) d) (pow.f64 l -1))) h)	h	0

rewrite40.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

187×	`add-sqr-sqrt_binary64`
174×	`add-cbrt-cube_binary64`
174×	`log1p-expm1-u_binary64`
174×	`expm1-log1p-u_binary64`
172×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	93
1	382	66

Stop Event

1×	node limit

Counts

4 → 128

simplify91.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

265×	`associate-/r/_binary64`
254×	`fma-def_binary64`
245×	`unswap-sqr_binary64`
203×	`distribute-neg-frac_binary64`
188×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	5268
1	715	5230
2	2360	5212

Stop Event

1×	node limit

Counts

320 → 193

prune300.0ms (2.7%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	239	2	241
Fresh	1	8	9
Picked	0	1	1
Done	0	2	2
Total	240	13	253

Error

3.7b

Counts

253 → 13

Alt Table

Status	Error	Program
✓	13.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (/.f64 (pow.f64 (.f64 (.f64 M (/.f64 1/2 d)) D) 2) l) h))))
	11.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 M 1/2) (.f64 (/.f64 (.f64 M 1/2) (.f64 l (/.f64 d D))) h)) (/.f64 d D)))))
	12.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (.f64 M 1/2) (.f64 l (/.f64 d D))) h) (/.f64 (/.f64 d M) (*.f64 1/2 D))))))
	15.8b	w0
✓	11.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (/.f64 (.f64 (.f64 M 1/2) D) d) (.f64 (/.f64 (.f64 (.f64 M 1/2) D) d) (pow.f64 l -1))) h))))
	62.6b	(neg.f64 (fma.f64 D (.f64 (sqrt.f64 (.f64 (.f64 -1/4 (/.f64 h l)) (.f64 (/.f64 M d) (/.f64 M d)))) w0) (/.f64 (/.f64 (.f64 1/2 w0) D) (sqrt.f64 (.f64 (.f64 -1/4 (/.f64 h l)) (.f64 (/.f64 M d) (/.f64 M d)))))))
	57.7b	(.f64 D (.f64 (sqrt.f64 (.f64 (.f64 -1/4 (/.f64 h l)) (*.f64 (/.f64 M d) (/.f64 M d)))) w0))
	60.0b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (.f64 (/.f64 M (/.f64 l M)) (/.f64 (/.f64 h d) d)) -1/4))))
	62.0b	(-.f64 (.f64 (/.f64 1/8 (pow.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 h D) D) (.f64 l (.f64 d d))) -1/4)) 3)) (/.f64 w0 (pow.f64 M 3))) (fma.f64 M (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 h D) D) (.f64 l (.f64 d d))) -1/4)) w0) (.f64 1/2 (/.f64 w0 (.f64 M (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 h D) D) (.f64 l (*.f64 d d))) -1/4)))))))
	60.7b	(.f64 w0 (.f64 -1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 (pow.f64 d 2) l))))) M)))
	60.5b	(.f64 D (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h (*.f64 d d)) (/.f64 M (/.f64 l M))) -1/4)) w0))
✓	12.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) h) l))))
	58.7b	(.f64 w0 (.f64 M (neg.f64 (sqrt.f64 (.f64 (.f64 (*.f64 (/.f64 D d) (/.f64 D d)) (/.f64 h l)) -1/4)))))

Compiler

Compiled 8578 to 5277 computations (38.5% saved)

regimes1.8s (16.3%)

Accuracy

Total 4.7b remaining (58.9%)

Threshold costs 0b (0%)

Counts

91 → 4

Compiler

Compiled 39075 to 28103 computations (28.1% saved)

bsearch4.0ms (0%)

Algorithm

3×	left-value

Calls

3 calls:

0.0ms

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

0.0ms

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

0.0ms

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

Steps

Iters

Point

Range

#hash((type . real) (value . +inf))

∈ [

#hash((type . real) (value . +inf))

#hash((type . real) (value . NaN))

]

1.6820622892440524e+307

∈ [

1.6820622892440524e+307

#hash((type . real) (value . +inf))

]

#hash((type . real) (value . -inf))

∈ [

#hash((type . real) (value . -inf))

-7.66985279987438e+297

]

Compiler

Compiled 24 to 18 computations (25% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

38×	`*-commutative_binary64`
19×	`+-commutative_binary64`
19×	`sub-neg_binary64`
17×	`neg-sub0_binary64`
17×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	215
1	101	215
2	137	215
3	172	215
4	205	215
5	220	215
6	226	215
7	227	215

Stop Event

1×

saturated

end376.0ms (3.4%)

Stop Event

1×

fuel

Compiler

Compiled 977 to 605 computations (38.1% saved)

Details

analyze2.8s (25%)

sample2.3s (20.7%)

preprocess43.0ms (0.4%)

simplify21.0ms (0.2%)

prune6.0ms (0.1%)

localize12.0ms (0.1%)

series557.0ms (5%)

rewrite39.0ms (0.4%)

simplify135.0ms (1.2%)

prune223.0ms (2%)

localize13.0ms (0.1%)

series696.0ms (6.2%)

rewrite45.0ms (0.4%)

simplify179.0ms (1.6%)

prune238.0ms (2.1%)

localize13.0ms (0.1%)

series466.0ms (4.2%)

rewrite74.0ms (0.7%)

simplify100.0ms (0.9%)

prune205.0ms (1.8%)

localize14.0ms (0.1%)

series345.0ms (3.1%)

rewrite40.0ms (0.4%)

simplify91.0ms (0.8%)

prune300.0ms (2.7%)

regimes1.8s (16.3%)

bsearch4.0ms (0%)

simplify9.0ms (0.1%)

end376.0ms (3.4%)

Profiling