Details

analyze2.5s (15.9%)

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)

sample8.8s (55.5%)

Results

3.0s	16357×	body	128	invalid
2.0s	2211×	body	4096	valid
1.4s	1204×	body	8192	valid
1.0s	1320×	body	2048	valid
447.0ms	666×	body	1024	valid
441.0ms	2396×	body	128	valid
141.0ms	308×	body	512	valid
64.0ms	151×	body	256	valid
42.0ms	59×	body	2048	invalid
37.0ms	65×	body	1024	invalid
20.0ms	45×	body	512	invalid
10.0ms	12×	body	4096	invalid
8.0ms	8×	body	8192	exit
6.0ms	19×	body	256	invalid

Compiler

Compiled 176 to 65 computations (63.1% saved)

simplify33.0ms (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

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

59.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	61.9b	(.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)))))
▶	59.5b	(.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

61.9b

(*.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)))))

▶

59.5b

(*.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)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	11.8b	(.f64 (.f64 w h) (*.f64 D D))
✓	12.2b	(.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)))))
✓	16.9b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	28.3b	(+.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))))

series701.0ms (4.4%)

Counts

4 → 240

Calls

4 calls:

331.0ms	(.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))))
143.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
17.0ms	(.f64 (.f64 w h) (*.f64 D D))

rewrite45.0ms (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	140
1	503	136

Stop Event

1×	node limit

Counts

4 → 76

Calls

4 calls:

42.0ms	(.f64 (.f64 w h) (*.f64 D D))
42.0ms	(.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)))))
42.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
42.0ms	(+.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))))

simplify159.0ms (1%)

Algorithm

1×	egg-herbie

Rules

728×	`fma-def_binary64`
396×	`associate-r_binary64`
372×	`times-frac_binary64`
272×	`associate-l_binary64`
255×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	256	11102
1	979	11002
2	4470	10930

Stop Event

1×	node limit

Counts

316 → 168

prune240.0ms (1.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	228	12	240
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	230	12	242

Error

16.8b

Counts

242 → 12

Alt Table

Status	Error	Program
	44.1b	(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))))))
	49.0b	(.f64 1/2 (/.f64 (.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w))
▶	26.3b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 (*.f64 M M) h)))
	58.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	60.2b	(.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)) (pow.f64 (cbrt.f64 (.f64 w (.f64 h (.f64 D D)))) 3))) (*.f64 M M)))))
	61.0b	(.f64 (/.f64 c0 (.f64 2 w)) (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)))))
	60.9b	(/.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))
	37.3b	(.f64 (/.f64 c0 (.f64 2 w)) (/.f64 1/2 (/.f64 (.f64 d (.f64 d c0)) (.f64 D (.f64 D (.f64 h (.f64 (*.f64 M M) w)))))))
	54.2b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (.f64 (.f64 (/.f64 d D) (/.f64 d D)) (/.f64 c0 (.f64 w h)))))
	32.9b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	60.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (expm1.f64 (log1p.f64 (.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)))))
	61.0b	(.f64 (/.f64 c0 (.f64 2 w)) (pow.f64 (cbrt.f64 (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))))) 3))

Compiler

Compiled 13374 to 4807 computations (64.1% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 D d) (/.f64 D d))
✓	5.9b	(.f64 (.f64 M M) h)
✓	11.2b	(.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 (.f64 M M) h))

series121.0ms (0.8%)

Counts

3 → 96

Calls

3 calls:

90.0ms	(.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 (.f64 M M) h))
23.0ms	(*.f64 (/.f64 D d) (/.f64 D d))
9.0ms	(.f64 (.f64 M M) h)

rewrite56.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

601×	`log-prod_binary64`
186×	`expm1-udef_binary64`
186×	`log1p-udef_binary64`
176×	`pow3_binary64`
175×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	212	27
2	2900	27

Stop Event

1×	node limit

Counts

3 → 85

Calls

3 calls:

54.0ms	(*.f64 (/.f64 D d) (/.f64 D d))
54.0ms	(.f64 (.f64 M M) h)
54.0ms	(.f64 (.f64 (/.f64 D d) (/.f64 D d)) (.f64 (.f64 M M) h))

simplify105.0ms (0.7%)

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

181 → 93

prune130.0ms (0.8%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	79	14	93
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	85	20	105

Error

8.7b

Counts

105 → 20

Alt Table

Status	Error	Program
	29.7b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (expm1.f64 (log1p.f64 (.f64 M (*.f64 M h))))))
	25.9b	(.f64 1/4 (/.f64 (.f64 (.f64 D (/.f64 D d)) (.f64 M (*.f64 M h))) d))
	60.9b	(/.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))
	38.3b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (log.f64 (pow.f64 (exp.f64 h) (.f64 M M)))))
	25.1b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (pow.f64 (cbrt.f64 (.f64 M (*.f64 M h))) 3)))
	24.5b	(.f64 1/4 (/.f64 (.f64 D (.f64 (.f64 (/.f64 D d) (*.f64 M M)) h)) d))
	35.9b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (pow.f64 (pow.f64 (.f64 M (*.f64 M h)) 3) 1/3)))
	24.0b	(.f64 1/4 (/.f64 (.f64 (.f64 (/.f64 D d) (.f64 M M)) h) (/.f64 d D)))
	26.4b	(.f64 1/4 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 D d)) 2) 3) (.f64 (.f64 M M) h)))
	54.2b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (.f64 (.f64 (/.f64 d D) (/.f64 d D)) (/.f64 c0 (.f64 w h)))))
	60.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (expm1.f64 (log1p.f64 (.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)))))
	43.8b	(.f64 1/4 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2))
	60.2b	(.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)) (pow.f64 (cbrt.f64 (.f64 w (.f64 h (.f64 D D)))) 3))) (*.f64 M M)))))
	61.0b	(.f64 (/.f64 c0 (.f64 2 w)) (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)))))
	19.0b	(.f64 1/4 (pow.f64 (cbrt.f64 (.f64 h (pow.f64 (*.f64 (/.f64 D d) M) 2))) 3))
▶	18.8b	(.f64 1/4 (+.f64 0 (.f64 h (pow.f64 (*.f64 (/.f64 D d) M) 2))))
	30.9b	(.f64 1/4 (.f64 (.f64 D (/.f64 D (.f64 d d))) (.f64 (.f64 M M) h)))
	28.2b	(.f64 1/4 (.f64 (.f64 D D) (.f64 (*.f64 (/.f64 M d) M) (/.f64 h d))))
	58.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	29.4b	(.f64 1/4 (pow.f64 (pow.f64 (.f64 h (pow.f64 (*.f64 (/.f64 D d) M) 2)) 3) 1/3))

Compiler

Compiled 2718 to 1354 computations (50.2% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (*.f64 (/.f64 D d) M) 2)
✓	2.5b	(*.f64 (/.f64 D d) M)
✓	2.7b	(.f64 h (pow.f64 (.f64 (/.f64 D d) M) 2))

series119.0ms (0.8%)

Counts

3 → 120

Calls

3 calls:

89.0ms	(.f64 h (pow.f64 (.f64 (/.f64 D d) M) 2))
18.0ms	(pow.f64 (*.f64 (/.f64 D d) M) 2)
12.0ms	(*.f64 (/.f64 D d) M)

rewrite44.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

526×	`log-prod_binary64`
263×	`pow2_binary64`
187×	`pow1/3_binary64`
182×	`expm1-udef_binary64`
182×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	210	30
2	2610	30

Stop Event

1×	node limit

Counts

3 → 83

Calls

3 calls:

42.0ms	(pow.f64 (*.f64 (/.f64 D d) M) 2)
42.0ms	(*.f64 (/.f64 D d) M)
42.0ms	(.f64 h (pow.f64 (.f64 (/.f64 D d) M) 2))

simplify46.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

877×	`times-frac_binary64`
600×	`associate-/l*_binary64`
393×	`associate-l_binary64`
331×	`associate-/r*_binary64`
292×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	1740
1	45	1740
2	124	1740
3	589	1740

Stop Event

1×	node limit

Counts

203 → 88

prune174.0ms (1.1%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	4	15	19
Picked	1	0	1
Done	0	0	0
Total	84	24	108

Error

8.2b

Counts

108 → 24

Alt Table

Status	Error	Program
	29.7b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (expm1.f64 (log1p.f64 (.f64 M (*.f64 M h))))))
	25.9b	(.f64 1/4 (/.f64 (.f64 (.f64 D (/.f64 D d)) (.f64 M (*.f64 M h))) d))
	20.8b	(.f64 1/4 (+.f64 0 (.f64 h (.f64 M (.f64 (/.f64 D d) (*.f64 (/.f64 D d) M))))))
	60.9b	(/.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))
	31.0b	(.f64 1/4 (+.f64 0 (log.f64 (pow.f64 (exp.f64 h) (pow.f64 (.f64 (/.f64 D d) M) 2)))))
	30.8b	(.f64 1/4 (+.f64 0 (.f64 h (+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (/.f64 D d) M) 2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (/.f64 D d) M) 2))))))))
	35.9b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (pow.f64 (pow.f64 (.f64 M (*.f64 M h)) 3) 1/3)))
	24.0b	(.f64 1/4 (/.f64 (.f64 (.f64 (/.f64 D d) (.f64 M M)) h) (/.f64 d D)))
	27.7b	(.f64 1/4 (+.f64 0 (.f64 h (pow.f64 (pow.f64 (pow.f64 (*.f64 (/.f64 D d) M) 3) 1/3) 2))))
	49.5b	(.f64 1/4 (+.f64 0 (exp.f64 (fma.f64 2 (log.f64 (.f64 (/.f64 D d) M)) (log.f64 h)))))
	26.4b	(.f64 1/4 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 D d)) 2) 3) (.f64 (.f64 M M) h)))
	54.2b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (.f64 (.f64 (/.f64 d D) (/.f64 d D)) (/.f64 c0 (.f64 w h)))))
	60.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (expm1.f64 (log1p.f64 (.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)))))
	19.3b	(.f64 1/4 (+.f64 0 (.f64 h (pow.f64 (/.f64 (*.f64 D M) d) 2))))
	43.8b	(.f64 1/4 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2))
	60.2b	(.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)) (pow.f64 (cbrt.f64 (.f64 w (.f64 h (.f64 D D)))) 3))) (*.f64 M M)))))
	61.0b	(.f64 (/.f64 c0 (.f64 2 w)) (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)))))
	19.0b	(.f64 1/4 (pow.f64 (cbrt.f64 (.f64 h (pow.f64 (*.f64 (/.f64 D d) M) 2))) 3))
	26.6b	(.f64 1/4 (+.f64 0 (.f64 h (/.f64 (pow.f64 (.f64 D M) 2) (.f64 d d)))))
	24.5b	(.f64 1/4 (/.f64 (.f64 D (.f64 (.f64 (/.f64 D d) (*.f64 M M)) h)) d))
	19.1b	(.f64 1/4 (+.f64 0 (.f64 h (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 D d) M)) 3) 2))))
	58.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
▶	18.8b	(.f64 1/4 (+.f64 0 (.f64 h (pow.f64 (/.f64 M (/.f64 d D)) 2))))
	29.4b	(.f64 1/4 (pow.f64 (pow.f64 (.f64 h (pow.f64 (*.f64 (/.f64 D d) M) 2)) 3) 1/3))

Compiler

Compiled 2863 to 1751 computations (38.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (/.f64 M (/.f64 d D)) 2)
✓	2.5b	(/.f64 M (/.f64 d D))
✓	2.7b	(*.f64 h (pow.f64 (/.f64 M (/.f64 d D)) 2))

series125.0ms (0.8%)

Counts

3 → 120

Calls

3 calls:

94.0ms	(*.f64 h (pow.f64 (/.f64 M (/.f64 d D)) 2))
20.0ms	(pow.f64 (/.f64 M (/.f64 d D)) 2)
11.0ms	(/.f64 M (/.f64 d D))

rewrite48.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

563×	`log-prod_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`
176×	`pow3_binary64`
171×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	213	30
2	2819	30

Stop Event

1×	node limit

Counts

3 → 111

Calls

3 calls:

46.0ms	(pow.f64 (/.f64 M (/.f64 d D)) 2)
46.0ms	(/.f64 M (/.f64 d D))
46.0ms	(*.f64 h (pow.f64 (/.f64 M (/.f64 d D)) 2))

simplify38.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

877×	`times-frac_binary64`
600×	`associate-/l*_binary64`
393×	`associate-l_binary64`
331×	`associate-/r*_binary64`
292×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	1740
1	45	1740
2	124	1740
3	589	1740

Stop Event

1×	node limit

Counts

231 → 118

prune227.0ms (1.4%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	112	6	118
Fresh	6	17	23
Picked	1	0	1
Done	0	0	0
Total	119	23	142

Error

8.2b

Counts

142 → 23

Alt Table

Status	Error	Program
	60.9b	(/.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))
	31.0b	(.f64 1/4 (+.f64 0 (log.f64 (pow.f64 (exp.f64 h) (pow.f64 (.f64 (/.f64 D d) M) 2)))))
	30.8b	(.f64 1/4 (+.f64 0 (.f64 h (+.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (/.f64 D d) M) 2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (.f64 (/.f64 D d) M) 2))))))))
	35.9b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (pow.f64 (pow.f64 (.f64 M (*.f64 M h)) 3) 1/3)))
	27.7b	(.f64 1/4 (+.f64 0 (.f64 h (pow.f64 (pow.f64 (pow.f64 (*.f64 (/.f64 D d) M) 3) 1/3) 2))))
	49.5b	(.f64 1/4 (+.f64 0 (exp.f64 (fma.f64 2 (log.f64 (.f64 (/.f64 D d) M)) (log.f64 h)))))
	19.1b	(.f64 1/4 (+.f64 0 (.f64 h (pow.f64 (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 d D)) 2)) (/.f64 M (cbrt.f64 (/.f64 d D)))) 2))))
	54.2b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (.f64 (.f64 (/.f64 d D) (/.f64 d D)) (/.f64 c0 (.f64 w h)))))
	18.8b	(.f64 1/4 (+.f64 0 (.f64 h (pow.f64 (*.f64 (/.f64 (pow.f64 (cbrt.f64 M) 2) d) (/.f64 (cbrt.f64 M) (/.f64 1 D))) 2))))
	58.9b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	60.7b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (expm1.f64 (log1p.f64 (.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)))))
	43.8b	(.f64 1/4 (pow.f64 (.f64 (/.f64 D d) (*.f64 M (sqrt.f64 h))) 2))
	19.6b	(.f64 1/4 (+.f64 0 (.f64 h (/.f64 1 (.f64 (/.f64 d (.f64 M D)) (/.f64 d (*.f64 M D)))))))
	60.2b	(.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)) (pow.f64 (cbrt.f64 (.f64 w (.f64 h (.f64 D D)))) 3))) (*.f64 M M)))))
	61.0b	(.f64 (/.f64 c0 (.f64 2 w)) (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)))))
	19.0b	(.f64 1/4 (pow.f64 (cbrt.f64 (.f64 h (pow.f64 (*.f64 (/.f64 D d) M) 2))) 3))
	20.4b	(.f64 1/4 (+.f64 0 (.f64 h (.f64 (.f64 (*.f64 M (/.f64 D d)) (/.f64 M d)) D))))
	29.4b	(.f64 1/4 (pow.f64 (pow.f64 (.f64 h (pow.f64 (*.f64 (/.f64 D d) M) 2)) 3) 1/3))
	29.7b	(.f64 1/4 (.f64 (.f64 (/.f64 D d) (/.f64 D d)) (expm1.f64 (log1p.f64 (.f64 M (*.f64 M h))))))
	24.5b	(.f64 1/4 (/.f64 (.f64 D (.f64 (.f64 (/.f64 D d) (*.f64 M M)) h)) d))
	19.7b	(.f64 1/4 (+.f64 0 (.f64 h (/.f64 (.f64 M (.f64 M (/.f64 D d))) (/.f64 d D)))))
	19.1b	(.f64 1/4 (+.f64 0 (.f64 h (pow.f64 (pow.f64 (cbrt.f64 (*.f64 (/.f64 D d) M)) 3) 2))))
	18.5b	(.f64 1/4 (+.f64 0 (.f64 h (pow.f64 (*.f64 D (/.f64 M d)) 2))))

Compiler

Compiled 2808 to 1600 computations (43% saved)

regimes1.2s (7.4%)

Accuracy

Total 10.4b remaining (53.9%)

Threshold costs 0b (0%)

Counts

92 → 3

Compiler

Compiled 28093 to 17949 computations (36.1% saved)

bsearch560.0ms (3.5%)

Steps

Iters	Range		Point
9	3.9938080895749266e-178	2.8303059796465744e-173	4.188188085536091e-178
8	1.2209577386375042e-266	2.416441570490535e-262	2.380894459195274e-262

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`+-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	88
1	59	88

Stop Event

1×

saturated

end328.0ms (2.1%)

Compiler: Compiled 791 to 515 computations (34.9% saved)

Details

analyze2.5s (15.9%)

sample8.8s (55.5%)

simplify33.0ms (0.2%)

prune4.0ms (0%)

localize18.0ms (0.1%)

series701.0ms (4.4%)

rewrite45.0ms (0.3%)

simplify159.0ms (1%)

prune240.0ms (1.5%)

localize8.0ms (0%)

series121.0ms (0.8%)

rewrite56.0ms (0.4%)

simplify105.0ms (0.7%)

prune130.0ms (0.8%)

localize10.0ms (0.1%)

series119.0ms (0.8%)

rewrite44.0ms (0.3%)

simplify46.0ms (0.3%)

prune174.0ms (1.1%)

localize8.0ms (0.1%)

series125.0ms (0.8%)

rewrite48.0ms (0.3%)

simplify38.0ms (0.2%)

prune227.0ms (1.4%)

regimes1.2s (7.4%)

bsearch560.0ms (3.5%)

simplify3.0ms (0%)

end328.0ms (2.1%)

Profiling