Details

analyze2.9s (24.6%)

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)

sample2.5s (21.2%)

Symmetry

(sort M D)

Results

1.6s	8256×	body	128	valid
804.0ms	4551×	body	128	invalid

Compiler

Compiled 74 to 56 computations (24.3% saved)

simplify22.0ms (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

prune5.0ms (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

15.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	16.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (/.f64 D (.f64 2 d))) 2) (/.f64 h l)))))
▶	15.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))

Compiler

Compiled 138 to 101 computations (26.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
✓	4.2b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
✓	4.3b	(/.f64 (.f64 M D) (.f64 2 d))
✓	11.5b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series556.0ms (4.8%)

Counts

4 → 204

Calls

4 calls:

222.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
187.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
131.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
15.0ms	(/.f64 (.f64 M D) (.f64 2 d))

rewrite63.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

190×	`add-sqr-sqrt_binary64`
179×	`log1p-expm1-u_binary64`
179×	`expm1-log1p-u_binary64`
177×	`add-cbrt-cube_binary64`
176×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	80
1	386	80

Stop Event

1×	node limit

Counts

4 → 119

Calls

4 calls:

60.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
60.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
60.0ms	(/.f64 (.f64 M D) (.f64 2 d))
60.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

simplify133.0ms (1.1%)

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

323 → 239

prune287.0ms (2.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	225	14	239
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	226	15	241

Error

5.4b

Counts

241 → 15

Alt Table

Status	Error	Program
	60.9b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 D (/.f64 l D)) (.f64 M (*.f64 M h))) -1/4)) d))
✓	15.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
	46.3b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) (/.f64 h l)))) w0) 3))
	16.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (-.f64 (+.f64 1 (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) (/.f64 h l))) 1))))
	59.5b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 D (/.f64 l D)) (/.f64 h (*.f64 d d))) -1/4)) (neg.f64 M)))
	61.1b	(.f64 D (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 h (pow.f64 M 2)) (*.f64 (pow.f64 d 2) l))))) w0))
	59.1b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 D (/.f64 l D)) (/.f64 h (.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
	60.3b	(.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)))
	28.6b	(fma.f64 (.f64 -1/8 (.f64 (/.f64 D d) (/.f64 D d))) (/.f64 (.f64 M (.f64 M h)) (/.f64 l w0)) w0)
	38.2b	(-.f64 w0 (.f64 1/8 (/.f64 (.f64 (pow.f64 D 2) (.f64 w0 (.f64 (pow.f64 M 2) h))) (*.f64 l (pow.f64 d 2)))))
	15.5b	w0
	15.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (.f64 M (/.f64 1/2 d))) 2) (/.f64 h l)))))
▶	11.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) h))))))
	60.3b	(.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)))
	61.4b	(.f64 D (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (/.f64 (.f64 M M) (.f64 d d))) -1/4)) w0))

Compiler

Compiled 9621 to 5929 computations (38.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.2b	(sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (.f64 (pow.f64 (.f64 M (*.f64 D (/.f64 1/2 d))) 2) h)))))
✓	5.1b	(.f64 (pow.f64 (.f64 M (*.f64 D (/.f64 1/2 d))) 2) h)
✓	5.4b	(/.f64 l (.f64 (pow.f64 (.f64 M (*.f64 D (/.f64 1/2 d))) 2) h))
✓	6.7b	(.f64 M (.f64 D (/.f64 1/2 d)))

series493.0ms (4.2%)

Counts

4 → 192

Calls

4 calls:

247.0ms	(/.f64 l (.f64 (pow.f64 (.f64 M (*.f64 D (/.f64 1/2 d))) 2) h))
118.0ms	(.f64 (pow.f64 (.f64 M (*.f64 D (/.f64 1/2 d))) 2) h)
113.0ms	(sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (.f64 (pow.f64 (.f64 M (*.f64 D (/.f64 1/2 d))) 2) h)))))
15.0ms	(.f64 M (.f64 D (/.f64 1/2 d)))

rewrite43.0ms (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

Calls

4 calls:

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

simplify97.0ms (0.8%)

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

prune235.0ms (2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	164	3	167
Fresh	1	12	13
Picked	0	1	1
Done	1	0	1
Total	166	16	182

Error

4.2b

Counts

182 → 16

Alt Table

Status	Error	Program
	46.3b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) (/.f64 h l)))) w0) 3))
	59.5b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 D (/.f64 l D)) (/.f64 h (*.f64 d d))) -1/4)) (neg.f64 M)))
	36.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (.f64 (/.f64 (pow.f64 (cbrt.f64 l) 2) (.f64 (.f64 D (.f64 (/.f64 1/2 d) M)) (sqrt.f64 h))) (/.f64 (cbrt.f64 l) (.f64 (.f64 D (.f64 (/.f64 1/2 d) M)) (sqrt.f64 h))))))))
	60.3b	(.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)))
	61.1b	(.f64 D (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 h (pow.f64 M 2)) (*.f64 (pow.f64 d 2) l))))) w0))
	59.1b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 D (/.f64 l D)) (/.f64 h (.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
	60.3b	(.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)))
	28.6b	(fma.f64 (.f64 -1/8 (.f64 (/.f64 D d) (/.f64 D d))) (/.f64 (.f64 M (.f64 M h)) (/.f64 l w0)) w0)
	38.2b	(-.f64 w0 (.f64 1/8 (/.f64 (.f64 (pow.f64 D 2) (.f64 w0 (.f64 (pow.f64 M 2) h))) (*.f64 l (pow.f64 d 2)))))
	15.5b	w0
	15.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (.f64 M (/.f64 1/2 d))) 2) (/.f64 h l)))))
	60.9b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 D (/.f64 l D)) (.f64 M (*.f64 M h))) -1/4)) d))
	15.0b	(.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))
▶	10.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (.f64 (pow.f64 (.f64 1/2 (/.f64 (.f64 D M) d)) 2) h))))))
✓	11.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) h))))))
	61.4b	(.f64 D (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (/.f64 (.f64 M M) (.f64 d d))) -1/4)) w0))

Compiler

Compiled 6514 to 4285 computations (34.2% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.2b	(sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (.f64 (pow.f64 (.f64 1/2 (/.f64 (*.f64 D M) d)) 2) h)))))
✓	4.3b	(/.f64 (*.f64 D M) d)
✓	5.1b	(.f64 (pow.f64 (.f64 1/2 (/.f64 (*.f64 D M) d)) 2) h)
✓	5.4b	(/.f64 l (.f64 (pow.f64 (.f64 1/2 (/.f64 (*.f64 D M) d)) 2) h))

series487.0ms (4.2%)

Counts

4 → 156

Calls

4 calls:

233.0ms	(/.f64 l (.f64 (pow.f64 (.f64 1/2 (/.f64 (*.f64 D M) d)) 2) h))
124.0ms	(.f64 (pow.f64 (.f64 1/2 (/.f64 (*.f64 D M) d)) 2) h)
117.0ms	(sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (.f64 (pow.f64 (.f64 1/2 (/.f64 (*.f64 D M) d)) 2) h)))))
13.0ms	(/.f64 (*.f64 D M) d)

rewrite45.0ms (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-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	69
1	392	66

Stop Event

1×	node limit

Counts

4 → 121

Calls

4 calls:

42.0ms	(sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (.f64 (pow.f64 (.f64 1/2 (/.f64 (*.f64 D M) d)) 2) h)))))
42.0ms	(/.f64 (*.f64 D M) d)
42.0ms	(.f64 (pow.f64 (.f64 1/2 (/.f64 (*.f64 D M) d)) 2) h)
42.0ms	(/.f64 l (.f64 (pow.f64 (.f64 1/2 (/.f64 (*.f64 D M) d)) 2) h))

simplify82.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

315×	`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	186	5336
1	705	5302
2	2370	5284

Stop Event

1×	node limit

Counts

277 → 183

prune258.0ms (2.2%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	179	4	183
Fresh	1	13	14
Picked	0	1	1
Done	0	1	1
Total	180	19	199

Error

2.8b

Counts

199 → 19

Alt Table

Status	Error	Program
	59.1b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 D (/.f64 (.f64 (.f64 d d) l) (.f64 D h))) -1/4)) (neg.f64 M)))
	60.9b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 D (/.f64 l D)) (.f64 M (*.f64 M h))) -1/4)) d))
	62.0b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 -1/4 h) l) (*.f64 (/.f64 M d) (/.f64 M d)))) (neg.f64 D)))
▶	15.0b	(.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))
✓	10.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (.f64 (pow.f64 (.f64 1/2 (/.f64 (.f64 D M) d)) 2) h))))))
	59.0b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 -1/4 h) l) (*.f64 (/.f64 M d) (/.f64 M d))))))
	23.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (.f64 1/4 (.f64 (.f64 (.f64 (/.f64 M d) (/.f64 M d)) h) (.f64 D D))))))))
✓	11.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) h))))))
	46.3b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) (/.f64 h l)))) w0) 3))
	59.5b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 D (/.f64 l D)) (/.f64 h (*.f64 d d))) -1/4)) (neg.f64 M)))
	61.1b	(.f64 D (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 h (pow.f64 M 2)) (*.f64 (pow.f64 d 2) l))))) w0))
	59.1b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 D (/.f64 l D)) (/.f64 h (.f64 d d))) -1/4)) (neg.f64 (*.f64 M w0)))
	60.3b	(.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)))
	28.6b	(fma.f64 (.f64 -1/8 (.f64 (/.f64 D d) (/.f64 D d))) (/.f64 (.f64 M (.f64 M h)) (/.f64 l w0)) w0)
	38.2b	(-.f64 w0 (.f64 1/8 (/.f64 (.f64 (pow.f64 D 2) (.f64 w0 (.f64 (pow.f64 M 2) h))) (*.f64 l (pow.f64 d 2)))))
	15.5b	w0
	15.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (.f64 M (/.f64 1/2 d))) 2) (/.f64 h l)))))
	36.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (.f64 (/.f64 (pow.f64 (cbrt.f64 l) 2) (.f64 (.f64 D (.f64 (/.f64 1/2 d) M)) (sqrt.f64 h))) (/.f64 (cbrt.f64 l) (.f64 (.f64 D (.f64 (/.f64 1/2 d) M)) (sqrt.f64 h))))))))
	61.4b	(.f64 D (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (/.f64 (.f64 M M) (.f64 d d))) -1/4)) w0))

Compiler

Compiled 7108 to 4464 computations (37.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.9b	(.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))
✓	4.1b	(.f64 D (.f64 (/.f64 1/2 d) M))
✓	7.2b	(pow.f64 (-.f64 1 (/.f64 (pow.f64 (.f64 D (.f64 (/.f64 1/2 d) M)) 2) (/.f64 l h))) 1/4)
✓	11.2b	(/.f64 (pow.f64 (.f64 D (.f64 (/.f64 1/2 d) M)) 2) (/.f64 l h))

series604.0ms (5.2%)

Counts

4 → 216

Calls

4 calls:

223.0ms	(.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))
188.0ms	(/.f64 (pow.f64 (.f64 D (.f64 (/.f64 1/2 d) M)) 2) (/.f64 l h))
178.0ms	(pow.f64 (-.f64 1 (/.f64 (pow.f64 (.f64 D (.f64 (/.f64 1/2 d) M)) 2) (/.f64 l h))) 1/4)
15.0ms	(.f64 D (.f64 (/.f64 1/2 d) M))

rewrite39.0ms (0.3%)

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

Calls

4 calls:

37.0ms	(.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))
37.0ms	(.f64 D (.f64 (/.f64 1/2 d) M))
37.0ms	(pow.f64 (-.f64 1 (/.f64 (pow.f64 (.f64 D (.f64 (/.f64 1/2 d) M)) 2) (/.f64 l h))) 1/4)
37.0ms	(/.f64 (pow.f64 (.f64 D (.f64 (/.f64 1/2 d) M)) 2) (/.f64 l h))

simplify114.0ms (1%)

Algorithm

1×	egg-herbie

Rules

623×	`associate-/l*_binary64`
569×	`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	1983	10946

Stop Event

1×	node limit

Counts

299 → 225

prune326.0ms (2.8%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	220	5	225
Fresh	3	13	16
Picked	1	0	1
Done	1	1	2
Total	225	19	244

Error

2.6b

Counts

244 → 19

Alt Table

Status	Error	Program
	39.7b	(pow.f64 (sqrt.f64 (.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (.f64 1/2 (/.f64 M d))) 2) (/.f64 h l)))))) 2)
	15.5b	w0
	13.4b	(.f64 w0 (pow.f64 (pow.f64 (-.f64 1 (.f64 (/.f64 (.f64 D (.f64 1/2 (/.f64 M d))) 1) (/.f64 (.f64 D (.f64 1/2 (/.f64 M d))) (/.f64 l h)))) 1/4) 2))
	15.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 D (.f64 M (/.f64 1/2 d))) 2) (/.f64 h l)))))
	59.1b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 D (/.f64 (.f64 (.f64 d d) l) (.f64 D h))) -1/4)) (neg.f64 M)))
	60.9b	(.f64 w0 (/.f64 (sqrt.f64 (.f64 (.f64 (/.f64 D (/.f64 l D)) (.f64 M (*.f64 M h))) -1/4)) d))
✓	10.6b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (/.f64 l (.f64 (pow.f64 (.f64 1/2 (/.f64 (.f64 D M) d)) 2) h))))))
	59.0b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 -1/4 h) l) (*.f64 (/.f64 M d) (/.f64 M d))))))
	9.6b	(.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))
	46.3b	(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (.f64 M (.f64 D (/.f64 1/2 d))) 2) (/.f64 h l)))) w0) 3))
	59.5b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 D (/.f64 l D)) (/.f64 h (*.f64 d d))) -1/4)) (neg.f64 M)))
	61.1b	(.f64 D (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 h (pow.f64 M 2)) (*.f64 (pow.f64 d 2) l))))) w0))
	28.6b	(fma.f64 (.f64 -1/8 (.f64 (/.f64 D d) (/.f64 D d))) (/.f64 (.f64 M (.f64 M h)) (/.f64 l w0)) w0)
	38.2b	(-.f64 w0 (.f64 1/8 (/.f64 (.f64 (pow.f64 D 2) (.f64 w0 (.f64 (pow.f64 M 2) h))) (*.f64 l (pow.f64 d 2)))))
	62.0b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 -1/4 h) l) (*.f64 (/.f64 M d) (/.f64 M d)))) (neg.f64 D)))
	60.4b	(.f64 (sqrt.f64 (.f64 (/.f64 (.f64 D D) (/.f64 (.f64 d d) (/.f64 h l))) -1/4)) (neg.f64 (*.f64 M w0)))
	61.9b	(.f64 (/.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 D D) (*.f64 M M)) (/.f64 l h)) -1/4)) d) w0)
	36.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 1 (.f64 (/.f64 (pow.f64 (cbrt.f64 l) 2) (.f64 (.f64 D (.f64 (/.f64 1/2 d) M)) (sqrt.f64 h))) (/.f64 (cbrt.f64 l) (.f64 (.f64 D (.f64 (/.f64 1/2 d) M)) (sqrt.f64 h))))))))
	61.4b	(.f64 D (.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (/.f64 (.f64 M M) (.f64 d d))) -1/4)) w0))

Compiler

Compiled 12663 to 7847 computations (38% saved)

regimes1.9s (16.3%)

Accuracy

Total 6.3b remaining (63.1%)

Threshold costs 0b (0%)

Counts

100 → 3

Compiler

Compiled 42949 to 32545 computations (24.2% saved)

bsearch4.0ms (0%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

22×	`*-commutative_binary64`
7×	`+-commutative_binary64`
7×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	116
1	72	116
2	89	116
3	104	116
4	112	116
5	116	116
6	117	116

Stop Event

1×

saturated

end433.0ms (3.7%)

Compiler: Compiled 829 to 557 computations (32.8% saved)

Details

analyze2.9s (24.6%)

sample2.5s (21.2%)

simplify22.0ms (0.2%)

prune5.0ms (0%)

localize15.0ms (0.1%)

series556.0ms (4.8%)

rewrite63.0ms (0.5%)

simplify133.0ms (1.1%)

prune287.0ms (2.5%)

localize14.0ms (0.1%)

series493.0ms (4.2%)

rewrite43.0ms (0.4%)

simplify97.0ms (0.8%)

prune235.0ms (2%)

localize16.0ms (0.1%)

series487.0ms (4.2%)

rewrite45.0ms (0.4%)

simplify82.0ms (0.7%)

prune258.0ms (2.2%)

localize17.0ms (0.1%)

series604.0ms (5.2%)

rewrite39.0ms (0.3%)

simplify114.0ms (1%)

prune326.0ms (2.8%)

regimes1.9s (16.3%)

bsearch4.0ms (0%)

simplify5.0ms (0%)

end433.0ms (3.7%)

Profiling