Details

analyze2.7s (24.7%)

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)

sample2.2s (20.4%)

Results

1.5s	8256×	body	128	valid
752.0ms	4574×	body	128	invalid

Compiler

Compiled 50 to 38 computations (24% saved)

preprocess42.0ms (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)

simplify20.0ms (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

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

14.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	15.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
▶	15.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (/.f64 D (.f64 2 d))) 2) (/.f64 h l)))))

Compiler

Compiled 138 to 101 computations (26.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.2b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (/.f64 D (.f64 2 d))) 2) (/.f64 h l)))))
✓	4.3b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (/.f64 D (*.f64 2 d))) 2) (/.f64 h l))))
✓	5.5b	(.f64 M (/.f64 D (.f64 2 d)))
✓	10.1b	(.f64 (pow.f64 (.f64 M (/.f64 D (*.f64 2 d))) 2) (/.f64 h l))

series529.0ms (4.8%)

Counts

4 → 204

Calls

57 calls:

25.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (/.f64 D (.f64 2 d))) 2) (/.f64 h l)))))	l	0
24.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (/.f64 D (.f64 2 d))) 2) (/.f64 h l)))))	w0	-inf
21.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (/.f64 D (.f64 2 d))) 2) (/.f64 h l)))))	w0	inf
20.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (/.f64 D (.f64 2 d))) 2) (/.f64 h l)))))	w0	0
17.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (/.f64 D (.f64 2 d))) 2) (/.f64 h l)))))	h	inf

rewrite54.0ms (0.5%)

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

simplify133.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

640×	`fma-def_binary64`
262×	`times-frac_binary64`
243×	`associate-/r*_binary64`
231×	`associate-r_binary64`
226×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	310	8076
1	1242	8010
2	4071	7948

Stop Event

1×	node limit

Counts

296 → 212

prune239.0ms (2.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	203	9	212
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	204	10	214

Error

5.4b

Counts

214 → 10

Alt Table

Status	Error	Program
	27.8b	(fma.f64 (.f64 -1/8 (.f64 (/.f64 D d) (/.f64 D d))) (/.f64 (.f64 M (.f64 M h)) (/.f64 l w0)) w0)
	48.0b	(sqrt.f64 (.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) (/.f64 h l))) (*.f64 w0 w0)))
	26.8b	(.f64 w0 (sqrt.f64 (fma.f64 (.f64 -1/4 (/.f64 D (/.f64 l D))) (/.f64 (.f64 M (.f64 M h)) (*.f64 d d)) 1)))
	15.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
	60.4b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 D (/.f64 l D)) (/.f64 h (.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
	60.7b	(.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)))
	14.1b	w0
	62.1b	(.f64 w0 (/.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) d))
▶	11.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) h))))))
	60.4b	(.f64 D (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (/.f64 (.f64 M M) (.f64 d d))) -1/4)) w0))

Compiler

Compiled 8710 to 5348 computations (38.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.3b	(sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (.f64 (pow.f64 (.f64 M (*.f64 D (/.f64 1/2 d))) 2) h)))))
✓	4.7b	(.f64 (pow.f64 (.f64 M (*.f64 D (/.f64 1/2 d))) 2) h)
✓	5.2b	(/.f64 l (.f64 (pow.f64 (.f64 M (*.f64 D (/.f64 1/2 d))) 2) h))
✓	5.5b	(.f64 M (.f64 D (/.f64 1/2 d)))

series1.1s (9.8%)

Counts

4 → 192

Calls

51 calls:

595.0ms	(/.f64 l (.f64 (pow.f64 (.f64 M (*.f64 D (/.f64 1/2 d))) 2) h))	h	0
27.0ms	(.f64 (pow.f64 (.f64 M (*.f64 D (/.f64 1/2 d))) 2) h)	D	-inf
22.0ms	(/.f64 l (.f64 (pow.f64 (.f64 M (*.f64 D (/.f64 1/2 d))) 2) h))	h	inf
19.0ms	(/.f64 l (.f64 (pow.f64 (.f64 M (*.f64 D (/.f64 1/2 d))) 2) h))	l	inf
18.0ms	(/.f64 l (.f64 (pow.f64 (.f64 M (*.f64 D (/.f64 1/2 d))) 2) h))	l	-inf

rewrite41.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

188×	`add-sqr-sqrt_binary64`
180×	`log1p-expm1-u_binary64`
180×	`expm1-log1p-u_binary64`
178×	`add-cbrt-cube_binary64`
175×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	72
1	393	69

Stop Event

1×	node limit

Counts

4 → 103

simplify96.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

322×	`associate-/r/_binary64`
262×	`fma-def_binary64`
232×	`unswap-sqr_binary64`
216×	`distribute-neg-frac_binary64`
188×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	5696
1	715	5662
2	2390	5644

Stop Event

1×	node limit

Counts

295 → 167

prune206.0ms (1.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	163	4	167
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	164	13	177

Error

4.5b

Counts

177 → 13

Alt Table

Status	Error	Program
	27.8b	(fma.f64 (.f64 -1/8 (.f64 (/.f64 D d) (/.f64 D d))) (/.f64 (.f64 M (.f64 M h)) (/.f64 l w0)) w0)
	48.0b	(sqrt.f64 (.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) (/.f64 h l))) (*.f64 w0 w0)))
	26.8b	(.f64 w0 (sqrt.f64 (fma.f64 (.f64 -1/4 (/.f64 D (/.f64 l D))) (/.f64 (.f64 M (.f64 M h)) (*.f64 d d)) 1)))
	15.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
▶	14.0b	(.f64 w0 (pow.f64 (pow.f64 (-.f64 1 (/.f64 (pow.f64 (.f64 D (*.f64 (/.f64 1/2 d) M)) 2) (/.f64 l h))) 1/4) 2))
✓	11.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) h))))))
	60.4b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 D (/.f64 l D)) (/.f64 h (.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
	60.7b	(.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)))
	14.1b	w0
	33.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (.f64 (/.f64 1 (.f64 (.f64 D (.f64 (/.f64 1/2 d) M)) (sqrt.f64 h))) (/.f64 l (.f64 (.f64 D (.f64 (/.f64 1/2 d) M)) (sqrt.f64 h))))))))
	61.8b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (/.f64 M (/.f64 l M)) h) (*.f64 D D)) -1/4)) d))
	60.1b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (/.f64 M (/.f64 l M)) h) (*.f64 d d)) -1/4))))
	60.4b	(.f64 D (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (/.f64 (.f64 M M) (.f64 d d))) -1/4)) w0))

Compiler

Compiled 6346 to 4151 computations (34.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.2b	(.f64 w0 (pow.f64 (pow.f64 (-.f64 1 (/.f64 (pow.f64 (.f64 D (*.f64 (/.f64 1/2 d) M)) 2) (/.f64 l h))) 1/4) 2))
✓	6.5b	(pow.f64 (-.f64 1 (/.f64 (pow.f64 (.f64 D (.f64 (/.f64 1/2 d) M)) 2) (/.f64 l h))) 1/4)
✓	6.5b	(.f64 D (.f64 (/.f64 1/2 d) M))
✓	9.9b	(/.f64 (pow.f64 (.f64 D (.f64 (/.f64 1/2 d) M)) 2) (/.f64 l h))

series631.0ms (5.7%)

Counts

4 → 216

Calls

57 calls:

49.0ms	(.f64 w0 (pow.f64 (pow.f64 (-.f64 1 (/.f64 (pow.f64 (.f64 D (*.f64 (/.f64 1/2 d) M)) 2) (/.f64 l h))) 1/4) 2))	h	inf
24.0ms	(.f64 w0 (pow.f64 (pow.f64 (-.f64 1 (/.f64 (pow.f64 (.f64 D (*.f64 (/.f64 1/2 d) M)) 2) (/.f64 l h))) 1/4) 2))	w0	-inf
24.0ms	(.f64 w0 (pow.f64 (pow.f64 (-.f64 1 (/.f64 (pow.f64 (.f64 D (*.f64 (/.f64 1/2 d) M)) 2) (/.f64 l h))) 1/4) 2))	w0	0
21.0ms	(.f64 w0 (pow.f64 (pow.f64 (-.f64 1 (/.f64 (pow.f64 (.f64 D (*.f64 (/.f64 1/2 d) M)) 2) (/.f64 l h))) 1/4) 2))	w0	inf
18.0ms	(pow.f64 (-.f64 1 (/.f64 (pow.f64 (.f64 D (.f64 (/.f64 1/2 d) M)) 2) (/.f64 l h))) 1/4)	M	inf

rewrite57.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

212×	`add-sqr-sqrt_binary64`
209×	`log1p-expm1-u_binary64`
209×	`expm1-log1p-u_binary64`
204×	`add-cbrt-cube_binary64`
202×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	82
1	457	81

Stop Event

1×	node limit

Counts

4 → 83

simplify133.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

623×	`associate-/l*_binary64`
570×	`associate-/r*_binary64`
193×	`*-commutative_binary64`
176×	`associate-*l/_binary64`
161×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	492	11058
1	1986	10946

Stop Event

1×	node limit

Counts

299 → 225

prune294.0ms (2.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	223	2	225
Fresh	2	9	11
Picked	0	1	1
Done	0	1	1
Total	225	13	238

Error

4.5b

Counts

238 → 13

Alt Table

Status	Error	Program
	27.8b	(fma.f64 (.f64 -1/8 (.f64 (/.f64 D d) (/.f64 D d))) (/.f64 (.f64 M (.f64 M h)) (/.f64 l w0)) w0)
	48.0b	(sqrt.f64 (.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) (/.f64 h l))) (*.f64 w0 w0)))
	26.8b	(.f64 w0 (sqrt.f64 (fma.f64 (.f64 -1/4 (/.f64 D (/.f64 l D))) (/.f64 (.f64 M (.f64 M h)) (*.f64 d d)) 1)))
	15.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
✓	14.0b	(.f64 w0 (pow.f64 (pow.f64 (-.f64 1 (/.f64 (pow.f64 (.f64 D (*.f64 (/.f64 1/2 d) M)) 2) (/.f64 l h))) 1/4) 2))
✓	11.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) h))))))
	60.4b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 D (/.f64 l D)) (/.f64 h (.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
	14.1b	w0
▶	9.2b	(.f64 w0 (pow.f64 (pow.f64 (-.f64 1 (.f64 (/.f64 (.f64 D (.f64 1/2 (/.f64 M d))) l) (/.f64 (.f64 D (.f64 1/2 (/.f64 M d))) (/.f64 1 h)))) 1/4) 2))
	61.8b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (/.f64 M (/.f64 l M)) h) (*.f64 D D)) -1/4)) d))
	60.1b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (/.f64 M (/.f64 l M)) h) (*.f64 d d)) -1/4))))
	60.5b	(.f64 (.f64 M w0) (neg.f64 (sqrt.f64 (.f64 (/.f64 (/.f64 (.f64 D D) (/.f64 l h)) (*.f64 d d)) -1/4))))
	60.4b	(.f64 D (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (/.f64 (.f64 M M) (.f64 d d))) -1/4)) w0))

Compiler

Compiled 12753 to 7894 computations (38.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.6b	(/.f64 (.f64 D (.f64 1/2 (/.f64 M d))) l)
✓	6.5b	(pow.f64 (-.f64 1 (.f64 (/.f64 (.f64 D (.f64 1/2 (/.f64 M d))) l) (/.f64 (.f64 D (*.f64 1/2 (/.f64 M d))) (/.f64 1 h)))) 1/4)
✓	6.5b	(/.f64 (.f64 D (.f64 1/2 (/.f64 M d))) (/.f64 1 h))
✓	6.5b	(.f64 D (.f64 1/2 (/.f64 M d)))

series264.0ms (2.4%)

Counts

4 → 192

Calls

48 calls:

19.0ms	(pow.f64 (-.f64 1 (.f64 (/.f64 (.f64 D (.f64 1/2 (/.f64 M d))) l) (/.f64 (.f64 D (*.f64 1/2 (/.f64 M d))) (/.f64 1 h)))) 1/4)	M	-inf
17.0ms	(pow.f64 (-.f64 1 (.f64 (/.f64 (.f64 D (.f64 1/2 (/.f64 M d))) l) (/.f64 (.f64 D (*.f64 1/2 (/.f64 M d))) (/.f64 1 h)))) 1/4)	D	inf
16.0ms	(pow.f64 (-.f64 1 (.f64 (/.f64 (.f64 D (.f64 1/2 (/.f64 M d))) l) (/.f64 (.f64 D (*.f64 1/2 (/.f64 M d))) (/.f64 1 h)))) 1/4)	d	0
16.0ms	(pow.f64 (-.f64 1 (.f64 (/.f64 (.f64 D (.f64 1/2 (/.f64 M d))) l) (/.f64 (.f64 D (*.f64 1/2 (/.f64 M d))) (/.f64 1 h)))) 1/4)	M	inf
16.0ms	(pow.f64 (-.f64 1 (.f64 (/.f64 (.f64 D (.f64 1/2 (/.f64 M d))) l) (/.f64 (.f64 D (*.f64 1/2 (/.f64 M d))) (/.f64 1 h)))) 1/4)	D	-inf

rewrite42.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

199×	`add-sqr-sqrt_binary64`
190×	`log1p-expm1-u_binary64`
190×	`expm1-log1p-u_binary64`
188×	`add-cbrt-cube_binary64`
186×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	76
1	407	61

Stop Event

1×	node limit

Counts

4 → 110

simplify91.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

837×	`times-frac_binary64`
439×	`associate-/r*_binary64`
439×	`associate-/l*_binary64`
164×	`associate-*r/_binary64`
131×	`associate-*l/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	329	7374
1	1323	7290

Stop Event

1×	node limit

Counts

302 → 194

prune343.0ms (3.1%)

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	210	4	214
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	210	17	227

Error

3.1b

Counts

227 → 17

Alt Table

Status	Error	Program
	27.8b	(fma.f64 (.f64 -1/8 (.f64 (/.f64 D d) (/.f64 D d))) (/.f64 (.f64 M (.f64 M h)) (/.f64 l w0)) w0)
	48.0b	(sqrt.f64 (.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) (/.f64 h l))) (*.f64 w0 w0)))
	19.4b	(.f64 w0 (pow.f64 (pow.f64 (-.f64 1 (.f64 (/.f64 (.f64 D (.f64 1/2 (/.f64 M d))) l) (pow.f64 (sqrt.f64 (.f64 (.f64 (*.f64 D 1/2) (/.f64 M d)) h)) 2))) 1/4) 2))
	26.8b	(.f64 w0 (sqrt.f64 (fma.f64 (.f64 -1/4 (/.f64 D (/.f64 l D))) (/.f64 (.f64 M (.f64 M h)) (*.f64 d d)) 1)))
	15.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
✓	9.2b	(.f64 w0 (pow.f64 (pow.f64 (-.f64 1 (.f64 (/.f64 (.f64 D (.f64 1/2 (/.f64 M d))) l) (/.f64 (.f64 D (.f64 1/2 (/.f64 M d))) (/.f64 1 h)))) 1/4) 2))
	60.0b	(.f64 w0 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (.f64 (.f64 (/.f64 h l) (.f64 (/.f64 D d) (/.f64 D d))) -1/4)) (*.f64 (log.f64 (/.f64 -1 M)) -2))) 2))
	61.8b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (.f64 (.f64 (/.f64 M (/.f64 l M)) h) (*.f64 D D)) -1/4)) d))
	58.5b	(.f64 w0 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (.f64 (.f64 (/.f64 h l) (.f64 (/.f64 M d) (/.f64 M d))) -1/4)) (*.f64 (log.f64 D) 2))) 2))
✓	14.0b	(.f64 w0 (pow.f64 (pow.f64 (-.f64 1 (/.f64 (pow.f64 (.f64 D (*.f64 (/.f64 1/2 d) M)) 2) (/.f64 l h))) 1/4) 2))
✓	11.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) h))))))
	60.4b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 D (/.f64 l D)) (/.f64 h (.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
	14.1b	w0
	61.4b	(.f64 w0 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 (.f64 1/4 (.f64 (.f64 (/.f64 M d) (/.f64 M d)) (/.f64 D (/.f64 l D))))) (log.f64 (/.f64 -1 h)))) 2))
	60.1b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (/.f64 M (/.f64 l M)) h) (*.f64 d d)) -1/4))))
	60.5b	(.f64 (.f64 M w0) (neg.f64 (sqrt.f64 (.f64 (/.f64 (/.f64 (.f64 D D) (/.f64 l h)) (*.f64 d d)) -1/4))))
	60.4b	(.f64 D (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (/.f64 (.f64 M M) (.f64 d d))) -1/4)) w0))

Compiler

Compiled 11648 to 7367 computations (36.8% saved)

regimes1.2s (11.3%)

Accuracy

Total 4.2b remaining (55.8%)

Threshold costs 0b (0%)

Counts

59 → 3

Compiler

Compiled 25364 to 18513 computations (27% saved)

bsearch6.0ms (0.1%)

Algorithm

2×	left-value

Calls

2 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)))))

Steps

Iters	Point		Range
6.874178835402741e+263	∈ [	6.874178835402741e+263	,	4.2479390320688884e+271	]
#hash((type . real) (value . -inf))	∈ [	#hash((type . real) (value . -inf))	,	-2.7026130358224874e+302	]

Compiler

Compiled 24 to 18 computations (25% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

29×	`*-commutative_binary64`
17×	`+-commutative_binary64`
16×	`sub-neg_binary64`
14×	`distribute-rgt-neg-in_binary64`
14×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	174
1	83	174
2	105	174
3	132	174
4	162	174
5	183	174
6	193	174
7	197	174
8	198	174

Stop Event

1×

saturated

end440.0ms (4%)

Stop Event

1×

fuel

Compiler

Compiled 940 to 638 computations (32.1% saved)

Iter	Nodes	Cost
0	55	174
1	83	174
2	105	174
3	132	174
4	162	174
5	183	174
6	193	174
7	197	174
8	198	174

Iter	Nodes	Cost
0	55	174
1	83	174
2	105	174
3	132	174
4	162	174
5	183	174
6	193	174
7	197	174
8	198	174

Details

analyze2.7s (24.7%)

sample2.2s (20.4%)

preprocess42.0ms (0.4%)

simplify20.0ms (0.2%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series529.0ms (4.8%)

rewrite54.0ms (0.5%)

simplify133.0ms (1.2%)

prune239.0ms (2.2%)

localize14.0ms (0.1%)

series1.1s (9.8%)

rewrite41.0ms (0.4%)

simplify96.0ms (0.9%)

prune206.0ms (1.9%)

localize15.0ms (0.1%)

series631.0ms (5.7%)

rewrite57.0ms (0.5%)

simplify133.0ms (1.2%)

prune294.0ms (2.7%)

localize15.0ms (0.1%)

series264.0ms (2.4%)

rewrite42.0ms (0.4%)

simplify91.0ms (0.8%)

prune343.0ms (3.1%)

regimes1.2s (11.3%)

bsearch6.0ms (0.1%)

simplify8.0ms (0.1%)

end440.0ms (4%)

Profiling

Iter	Nodes	Cost
0	55	174
1	83	174
2	105	174
3	132	174
4	162	174
5	183	174
6	193	174
7	197	174
8	198	174