Details

analyze3.5s (20.2%)

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
0%	98.1%	1.9%	13
0%	98.1%	1.9%	14

Compiler

Compiled 59 to 22 computations (62.7% saved)

sample8.9s (51.6%)

Results

3.2s	16742×	body	128	invalid
2.0s	2181×	body	4096	valid
1.4s	1218×	body	8192	valid
1.0s	1300×	body	2048	valid
459.0ms	2465×	body	128	valid
390.0ms	626×	body	1024	valid
148.0ms	320×	body	512	valid
47.0ms	146×	body	256	valid
42.0ms	56×	body	2048	invalid
29.0ms	50×	body	1024	invalid
21.0ms	36×	body	512	invalid
13.0ms	14×	body	4096	invalid
7.0ms	22×	body	256	invalid
7.0ms	7×	body	8192	exit

Compiler

Compiled 176 to 65 computations (63.1% saved)

simplify31.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

599×	`times-frac_binary64`
416×	`fma-def_binary64`
302×	`associate-/l*_binary64`
217×	`fma-neg_binary64`
189×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	78
1	64	74
2	314	74
3	3572	67
4	4695	67

Stop Event

1×	node limit

Counts

1 → 2

prune7.0ms (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

58.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	62.3b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 d d) (/.f64 (/.f64 (/.f64 c0 (.f64 D D)) h) w) (sqrt.f64 (-.f64 (.f64 (/.f64 c0 (.f64 w h)) (.f64 (.f64 (/.f64 d D) (pow.f64 (/.f64 d D) 3)) (/.f64 c0 (.f64 w h)))) (.f64 M M)))))
▶	58.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))

Status

Error

Program

62.3b

(*.f64 (/.f64 c0 (*.f64 2 w)) (fma.f64 (*.f64 d d) (/.f64 (/.f64 (/.f64 c0 (*.f64 D D)) h) w) (sqrt.f64 (-.f64 (*.f64 (/.f64 c0 (*.f64 w h)) (*.f64 (*.f64 (/.f64 d D) (pow.f64 (/.f64 d D) 3)) (/.f64 c0 (*.f64 w h)))) (*.f64 M M)))))

▶

58.7b

(*.f64 (/.f64 c0 (*.f64 2 w)) (+.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (sqrt.f64 (-.f64 (*.f64 (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D))) (/.f64 (*.f64 c0 (*.f64 d d)) (*.f64 (*.f64 w h) (*.f64 D D)))) (*.f64 M M)))))

Compiler

Compiled 321 to 134 computations (58.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	14.2b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))
✓	14.4b	(sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M)))
✓	17.0b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	29.7b	(+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M))))

series882.0ms (5.1%)

Counts

4 → 276

Calls

4 calls:

336.0ms	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))
210.0ms	(+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M))))
190.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M)))
145.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))

rewrite48.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

251×	`add-sqr-sqrt_binary64`
240×	`log1p-expm1-u_binary64`
240×	`expm1-log1p-u_binary64`
239×	`add-cbrt-cube_binary64`
236×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	160
1	503	156

Stop Event

1×	node limit

Counts

4 → 82

Calls

4 calls:

46.0ms	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M)))))
46.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M)))
46.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
46.0ms	(+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (*.f64 M M))))

simplify176.0ms (1%)

Algorithm

1×	egg-herbie

Rules

477×	`associate-r_binary64`
441×	`times-frac_binary64`
330×	`associate-l_binary64`
298×	`associate-/r*_binary64`
266×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	307	15852
1	1180	15734

Stop Event

1×	node limit

Counts

358 → 208

prune285.0ms (1.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	237	11	248
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	239	11	250

Error

13.2b

Counts

250 → 11

Alt Table

Status	Error	Program
	58.8b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.f64 (.f64 c0 (.f64 d d)) (/.f64 1 (.f64 w (.f64 h (.f64 D D))))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M)))))
	48.3b	(.f64 1/2 (/.f64 (.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w))
▶	22.7b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (*.f64 M h))))
	34.3b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	57.4b	(fma.f64 (.f64 (/.f64 d D) (/.f64 d D)) (.f64 (/.f64 c0 h) (/.f64 c0 (.f64 w w))) (.f64 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (.f64 M h))) -1/4))
	59.4b	(.f64 (/.f64 (.f64 c0 c0) (.f64 D D)) (/.f64 (.f64 d d) (.f64 w (.f64 w h))))
	38.2b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (/.f64 (.f64 h (.f64 w (.f64 M M))) c0))))
	55.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (.f64 (.f64 (/.f64 d D) (/.f64 d D)) (/.f64 c0 (.f64 w h)))))
	59.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	47.0b	(log.f64 (pow.f64 (exp.f64 (/.f64 c0 (.f64 w 2))) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (*.f64 M M))))))
	60.1b	(/.f64 (.f64 c0 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (.f64 M M))))) (.f64 w 2))

Compiler

Compiled 14315 to 6003 computations (58.1% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 M (.f64 M h))
✓	0.2b	(*.f64 (/.f64 D d) (/.f64 D d))
✓	11.7b	(.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (.f64 M h)))

series151.0ms (0.9%)

Counts

3 → 96

Calls

3 calls:

109.0ms	(.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (.f64 M h)))
28.0ms	(*.f64 (/.f64 D d) (/.f64 D d))
13.0ms	(.f64 M (.f64 M h))

rewrite50.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

626×	`log-prod_binary64`
190×	`expm1-udef_binary64`
190×	`log1p-udef_binary64`
176×	`log-pow_binary64`
125×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	212	29
2	2920	29

Stop Event

1×	node limit

Counts

3 → 82

Calls

3 calls:

48.0ms	(.f64 M (.f64 M h))
48.0ms	(*.f64 (/.f64 D d) (/.f64 D d))
48.0ms	(.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (.f64 M h)))

simplify109.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

627×	`times-frac_binary64`
444×	`associate-/l*_binary64`
295×	`associate-l_binary64`
293×	`unswap-sqr_binary64`
236×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	1320
1	37	1320
2	105	1320
3	464	1320
4	3703	1320
5	4269	1320
6	4363	1320
7	4510	1320
8	4674	1320
9	4852	1320

Stop Event

1×	node limit

Counts

178 → 90

prune111.0ms (0.6%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	81	9	90
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	84	17	101

Error

9.3b

Counts

101 → 17

Alt Table

Status	Error	Program
	26.2b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 h (pow.f64 M 2))))
✓	22.7b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (*.f64 M h))))
	38.7b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (exp.f64 (log.f64 (.f64 h (*.f64 M M))))))
	28.7b	(.f64 1/4 (.f64 (.f64 D D) (.f64 (*.f64 (/.f64 M d) M) (/.f64 h d))))
	57.4b	(fma.f64 (.f64 (/.f64 d D) (/.f64 d D)) (.f64 (/.f64 c0 h) (/.f64 c0 (.f64 w w))) (.f64 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (.f64 M h))) -1/4))
	24.4b	(.f64 1/4 (.f64 (/.f64 D (.f64 (/.f64 d D) d)) (.f64 M (*.f64 M h))))
	58.8b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.f64 (.f64 c0 (.f64 d d)) (/.f64 1 (.f64 w (.f64 h (.f64 D D))))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M)))))
	26.1b	(.f64 1/4 (/.f64 (.f64 D (.f64 (/.f64 D d) (.f64 h (*.f64 M M)))) d))
	59.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
▶	24.4b	(.f64 1/4 (/.f64 (.f64 (/.f64 D d) (.f64 h (.f64 M M))) (/.f64 d D)))
	47.0b	(log.f64 (pow.f64 (exp.f64 (/.f64 c0 (.f64 w 2))) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (*.f64 M M))))))
	59.4b	(.f64 (/.f64 (.f64 c0 c0) (.f64 D D)) (/.f64 (.f64 d d) (.f64 w (.f64 w h))))
	41.1b	(.f64 1/4 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2))
	41.2b	(.f64 1/4 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2)) 3))
	45.7b	(.f64 1/4 (pow.f64 (pow.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2) 3) 1/3))
	55.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (.f64 (.f64 (/.f64 d D) (/.f64 d D)) (/.f64 c0 (.f64 w h)))))
	60.1b	(/.f64 (.f64 c0 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (.f64 M M))))) (.f64 w 2))

Compiler

Compiled 2488 to 1191 computations (52.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	3.0b	(/.f64 (.f64 (/.f64 D d) (.f64 h (*.f64 M M))) (/.f64 d D))
✓	6.5b	(.f64 h (.f64 M M))
✓	8.0b	(.f64 (/.f64 D d) (.f64 h (*.f64 M M)))

series154.0ms (0.9%)

Counts

3 → 120

Calls

3 calls:

100.0ms	(/.f64 (.f64 (/.f64 D d) (.f64 h (*.f64 M M))) (/.f64 d D))
47.0ms	(.f64 (/.f64 D d) (.f64 h (*.f64 M M)))
7.0ms	(.f64 h (.f64 M M))

rewrite57.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
212×	`log-div_binary64`
201×	`log-pow_binary64`
127×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	239	36
2	3607	36

Stop Event

1×	node limit

Counts

3 → 102

Calls

3 calls:

55.0ms	(/.f64 (.f64 (/.f64 D d) (.f64 h (*.f64 M M))) (/.f64 d D))
55.0ms	(.f64 h (.f64 M M))
55.0ms	(.f64 (/.f64 D d) (.f64 h (*.f64 M M)))

simplify79.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

693×	`times-frac_binary64`
490×	`associate-/l*_binary64`
354×	`associate-l_binary64`
350×	`unswap-sqr_binary64`
268×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	1704
1	48	1704
2	125	1704
3	528	1704
4	4164	1704
5	4827	1704
6	4926	1704

Stop Event

1×	node limit

Counts

222 → 111

prune184.0ms (1.1%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	102	9	111
Fresh	4	11	15
Picked	1	0	1
Done	0	1	1
Total	107	21	128

Error

7.3b

Counts

128 → 21

Alt Table

Status	Error	Program
	32.3b	(.f64 1/4 (/.f64 (pow.f64 (pow.f64 (.f64 h (.f64 (.f64 M M) (/.f64 D d))) 3) 1/3) (/.f64 d D)))
	24.7b	(.f64 1/4 (.f64 (/.f64 (.f64 (/.f64 D d) h) (pow.f64 (cbrt.f64 (/.f64 d D)) 2)) (/.f64 (.f64 M M) (cbrt.f64 (/.f64 d D)))))
	23.4b	(.f64 1/4 (/.f64 (pow.f64 (.f64 h (.f64 (.f64 M M) (/.f64 D d))) 1) (/.f64 d D)))
	31.6b	(.f64 1/4 (.f64 (/.f64 (.f64 (sqrt.f64 (.f64 (/.f64 D d) h)) M) (pow.f64 (cbrt.f64 (/.f64 d D)) 2)) (/.f64 (.f64 (sqrt.f64 (.f64 (/.f64 D d) h)) M) (cbrt.f64 (/.f64 d D)))))
✓	22.7b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (*.f64 M h))))
	38.7b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (exp.f64 (log.f64 (.f64 h (*.f64 M M))))))
	28.7b	(.f64 1/4 (.f64 (.f64 D D) (.f64 (*.f64 (/.f64 M d) M) (/.f64 h d))))
	57.4b	(fma.f64 (.f64 (/.f64 d D) (/.f64 d D)) (.f64 (/.f64 c0 h) (/.f64 c0 (.f64 w w))) (.f64 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (.f64 M h))) -1/4))
▶	17.8b	(.f64 1/4 (.f64 M (.f64 (/.f64 D d) (.f64 (/.f64 h (/.f64 d D)) M))))
	59.4b	(.f64 (/.f64 (.f64 c0 c0) (.f64 D D)) (/.f64 (.f64 d d) (.f64 w (.f64 w h))))
	24.4b	(.f64 1/4 (.f64 (/.f64 D (.f64 (/.f64 d D) d)) (.f64 M (*.f64 M h))))
	58.8b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.f64 (.f64 c0 (.f64 d d)) (/.f64 1 (.f64 w (.f64 h (.f64 D D))))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M)))))
	45.7b	(.f64 1/4 (pow.f64 (pow.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2) 3) 1/3))
	26.5b	(.f64 1/4 (.f64 D (/.f64 (/.f64 D d) (/.f64 d (.f64 h (.f64 M M))))))
	55.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (.f64 (.f64 (/.f64 d D) (/.f64 d D)) (/.f64 c0 (.f64 w h)))))
	30.8b	(.f64 1/4 (/.f64 (exp.f64 (log.f64 (.f64 h (.f64 (.f64 M M) (/.f64 D d))))) (/.f64 d D)))
	23.1b	(.f64 1/4 (/.f64 (/.f64 1 (/.f64 (/.f64 (/.f64 d D) (.f64 M M)) h)) (/.f64 d D)))
	18.6b	(.f64 1/4 (/.f64 (.f64 M (*.f64 (/.f64 h (/.f64 d D)) M)) (/.f64 d D)))
	41.1b	(.f64 1/4 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2))
	59.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	60.1b	(/.f64 (.f64 c0 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (.f64 M M))))) (.f64 w 2))

Compiler

Compiled 3197 to 1449 computations (54.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.7b	(.f64 (/.f64 D d) (.f64 (/.f64 h (/.f64 d D)) M))
✓	3.0b	(.f64 M (.f64 (/.f64 D d) (*.f64 (/.f64 h (/.f64 d D)) M)))
✓	3.9b	(/.f64 h (/.f64 d D))
✓	5.1b	(*.f64 (/.f64 h (/.f64 d D)) M)

series245.0ms (1.4%)

Counts

4 → 180

Calls

4 calls:

112.0ms	(.f64 M (.f64 (/.f64 D d) (*.f64 (/.f64 h (/.f64 d D)) M)))
100.0ms	(.f64 (/.f64 D d) (.f64 (/.f64 h (/.f64 d D)) M))
21.0ms	(*.f64 (/.f64 h (/.f64 d D)) M)
12.0ms	(/.f64 h (/.f64 d D))

rewrite63.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

223×	`expm1-udef_binary64`
223×	`log1p-udef_binary64`
206×	`log-div_binary64`
204×	`log-pow_binary64`
148×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	52
1	239	46
2	3529	46

Stop Event

1×	node limit

Counts

4 → 123

Calls

4 calls:

61.0ms	(.f64 (/.f64 D d) (.f64 (/.f64 h (/.f64 d D)) M))
61.0ms	(.f64 M (.f64 (/.f64 D d) (*.f64 (/.f64 h (/.f64 d D)) M)))
61.0ms	(/.f64 h (/.f64 d D))
61.0ms	(*.f64 (/.f64 h (/.f64 d D)) M)

simplify82.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

686×	`associate-/l*_binary64`
477×	`associate-l_binary64`
355×	`associate-/r*_binary64`
337×	`associate-r_binary64`
313×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	2412
1	66	2412
2	167	2412
3	662	2412
4	4320	2412
5	4889	2412

Stop Event

1×	node limit

Counts

303 → 133

prune243.0ms (1.4%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	124	9	133
Fresh	5	14	19
Picked	1	0	1
Done	1	0	1
Total	131	23	154

Error

6.5b

Counts

154 → 23

Alt Table

Status	Error	Program
	32.3b	(.f64 1/4 (/.f64 (pow.f64 (pow.f64 (.f64 h (.f64 (.f64 M M) (/.f64 D d))) 3) 1/3) (/.f64 d D)))
	24.7b	(.f64 1/4 (.f64 (/.f64 (.f64 (/.f64 D d) h) (pow.f64 (cbrt.f64 (/.f64 d D)) 2)) (/.f64 (.f64 M M) (cbrt.f64 (/.f64 d D)))))
	38.7b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (exp.f64 (log.f64 (.f64 h (*.f64 M M))))))
	28.7b	(.f64 1/4 (.f64 (.f64 D D) (.f64 (*.f64 (/.f64 M d) M) (/.f64 h d))))
	19.4b	(.f64 1/4 (.f64 M (/.f64 1 (/.f64 d (.f64 D (.f64 (*.f64 h (/.f64 D d)) M))))))
	57.4b	(fma.f64 (.f64 (/.f64 d D) (/.f64 d D)) (.f64 (/.f64 c0 h) (/.f64 c0 (.f64 w w))) (.f64 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 M (.f64 M h))) -1/4))
	18.0b	(.f64 1/4 (.f64 M (.f64 (/.f64 D d) (pow.f64 (cbrt.f64 (.f64 (*.f64 h (/.f64 D d)) M)) 3))))
	59.4b	(.f64 (/.f64 (.f64 c0 c0) (.f64 D D)) (/.f64 (.f64 d d) (.f64 w (.f64 w h))))
	24.4b	(.f64 1/4 (.f64 (/.f64 D (.f64 (/.f64 d D) d)) (.f64 M (*.f64 M h))))
	58.8b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (.f64 (.f64 c0 (.f64 d d)) (/.f64 1 (.f64 w (.f64 h (.f64 D D))))) (sqrt.f64 (-.f64 (.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D)))) (.f64 M M)))))
	45.7b	(.f64 1/4 (pow.f64 (pow.f64 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2) 3) 1/3))
	26.5b	(.f64 1/4 (.f64 D (/.f64 (/.f64 D d) (/.f64 d (.f64 h (.f64 M M))))))
	20.1b	(.f64 1/4 (.f64 M (.f64 (/.f64 D d) (.f64 (*.f64 (/.f64 1 d) (/.f64 h (/.f64 1 D))) M))))
	55.5b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (.f64 (.f64 (/.f64 d D) (/.f64 d D)) (/.f64 c0 (.f64 w h)))))
	32.4b	(.f64 1/4 (.f64 M (.f64 (/.f64 D d) (.f64 (exp.f64 (log.f64 (*.f64 h (/.f64 D d)))) M))))
	23.1b	(.f64 1/4 (/.f64 (/.f64 1 (/.f64 (/.f64 (/.f64 d D) (.f64 M M)) h)) (/.f64 d D)))
	18.4b	(.f64 1/4 (.f64 M (/.f64 (.f64 (/.f64 D d) (.f64 h M)) (/.f64 d D))))
	20.6b	(.f64 1/4 (/.f64 (.f64 (.f64 D (.f64 (*.f64 h (/.f64 D d)) M)) M) d))
	17.4b	(.f64 1/4 (/.f64 (.f64 (.f64 M (/.f64 D d)) (.f64 h M)) (/.f64 d D)))
	28.2b	(.f64 1/4 (.f64 M (.f64 (/.f64 D d) (-.f64 (exp.f64 (log1p.f64 (.f64 (*.f64 h (/.f64 D d)) M))) 1))))
	59.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	18.0b	(.f64 1/4 (.f64 M (.f64 (/.f64 D d) (.f64 (pow.f64 (cbrt.f64 (*.f64 h (/.f64 D d))) 3) M))))
	60.1b	(/.f64 (.f64 c0 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (pow.f64 (.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D))) 2) (.f64 M M))))) (.f64 w 2))

Compiler

Compiled 2964 to 1449 computations (51.1% saved)

regimes1.6s (9%)

Accuracy

Total 10.0b remaining (54.3%)

Threshold costs 0b (0%)

Counts

102 → 4

Compiler

Compiled 31312 to 19763 computations (36.9% saved)

bsearch5.0ms (0%)

Compiler: Compiled 58 to 21 computations (63.8% saved)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Rules

23×	`*-commutative_binary64`
5×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	405
1	88	405
2	95	405
3	99	405
4	101	405

Stop Event

1×

saturated

end310.0ms (1.8%)

Compiler: Compiled 1164 to 529 computations (54.6% saved)

Details

analyze3.5s (20.2%)

sample8.9s (51.6%)

simplify31.0ms (0.2%)

prune7.0ms (0%)

localize17.0ms (0.1%)

series882.0ms (5.1%)

rewrite48.0ms (0.3%)

simplify176.0ms (1%)

prune285.0ms (1.6%)

localize8.0ms (0%)

series151.0ms (0.9%)

rewrite50.0ms (0.3%)

simplify109.0ms (0.6%)

prune111.0ms (0.6%)

localize9.0ms (0.1%)

series154.0ms (0.9%)

rewrite57.0ms (0.3%)

simplify79.0ms (0.5%)

prune184.0ms (1.1%)

localize9.0ms (0.1%)

series245.0ms (1.4%)

rewrite63.0ms (0.4%)

simplify82.0ms (0.5%)

prune243.0ms (1.4%)

regimes1.6s (9%)

bsearch5.0ms (0%)

simplify9.0ms (0%)

end310.0ms (1.8%)

Profiling