Details

analyze2.5s (13.9%)

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 (48%)

Results

3.1s	16447×	body	128	invalid
2.1s	2193×	body	4096	valid
1.4s	1205×	body	8192	valid
971.0ms	1309×	body	2048	valid
465.0ms	2469×	body	128	valid
377.0ms	605×	body	1024	valid
143.0ms	304×	body	512	valid
60.0ms	171×	body	256	valid
38.0ms	47×	body	2048	invalid
34.0ms	51×	body	1024	invalid
18.0ms	41×	body	512	invalid
8.0ms	5×	body	8192	exit
7.0ms	8×	body	4096	invalid
6.0ms	19×	body	256	invalid

Compiler

Compiled 176 to 65 computations (63.1% saved)

simplify41.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

599×	`times-frac_binary64`
518×	`distribute-neg-frac_binary64`
416×	`fma-def_binary64`
304×	`associate-/l*_binary64`
217×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	78
1	64	74
2	296	74
3	3103	67
4	4218	67
5	5365	67

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

60.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	62.0b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 d d) (/.f64 c0 (.f64 (.f64 w h) (.f64 D D))) (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)))))
▶	61.0b	(.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

62.0b

(*.f64 (/.f64 c0 (*.f64 2 w)) (fma.f64 (*.f64 d d) (/.f64 c0 (*.f64 (*.f64 w h) (*.f64 D D))) (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)))))

▶

61.0b

(*.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 130 computations (59.5% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	11.2b	(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)))
✓	11.9b	(.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)))))
✓	17.4b	(/.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))))

series1.2s (6.4%)

Counts

4 → 276

Calls

4 calls:

540.0ms	(.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)))))
238.0ms	(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)))
216.0ms	(+.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))))
179.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))

rewrite141.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`add-cbrt-cube_binary64`
82×	`add-exp-log_binary64`
43×	`cbrt-unprod_binary64`
43×	`prod-exp_binary64`
17×	`cbrt-undiv_binary64`

Counts

4 → 124

Calls

4 calls:

47.0ms	(.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)))))
37.0ms	(+.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))))
25.0ms	(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)))
10.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))

simplify314.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

550×	`associate-/r*_binary64`
531×	`associate-/l*_binary64`
317×	`associate-*l/_binary64`
229×	`fma-def_binary64`
172×	`*-commutative_binary64`

Counts

400 → 312

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	537	24212
1	1649	21889
2	5007	21889

prune504.0ms (2.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	424	8	432
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	425	9	434

Error

29.1b

Counts

434 → 9

Alt Table

Status	Error	Program
	62.0b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 d d) (/.f64 c0 (.f64 (.f64 w h) (.f64 D D))) (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)))))
	61.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	46.6b	(.f64 1/2 (/.f64 (.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w))
	41.8b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 1/2 (/.f64 (.f64 (pow.f64 D 2) (.f64 w (.f64 h (pow.f64 M 2)))) (*.f64 (pow.f64 d 2) c0))))
	62.7b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (neg.f64 (.f64 M M)))))
	61.0b	(.f64 (.f64 (cbrt.f64 (/.f64 c0 (.f64 2 w))) (cbrt.f64 (/.f64 c0 (.f64 2 w)))) (.f64 (cbrt.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))))))
	61.0b	(/.f64 (.f64 c0 (+.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))))) (*.f64 2 w))
	59.6b	(log.f64 (pow.f64 (exp.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (/.f64 (/.f64 (.f64 (pow.f64 d 4) (.f64 c0 c0)) (.f64 (.f64 w h) (.f64 w h))) (pow.f64 D 4)) (.f64 M M))))) (/.f64 c0 (.f64 2 w))))
▶	35.1b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))

Compiler

Compiled 30455 to 7911 computations (74% saved)

localize9.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	9.4b	(*.f64 (pow.f64 M 2) h)
✓	14.1b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
✓	14.5b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))

series137.0ms (0.7%)

Counts

3 → 40

Calls

3 calls:

102.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
27.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
7.0ms	(*.f64 (pow.f64 M 2) h)

rewrite28.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`add-exp-log_binary64`
87×	`prod-exp_binary64`
42×	`pow-exp_binary64`
42×	`pow-to-exp_binary64`
39×	`div-exp_binary64`

Counts

3 → 133

Calls

3 calls:

7.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
6.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
4.0ms	(*.f64 (pow.f64 M 2) h)

simplify116.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

468×	`associate-*l/_binary64`
391×	`associate-/l/_binary64`
373×	`*-commutative_binary64`
370×	`associate-*r/_binary64`
310×	`fma-def_binary64`

Counts

173 → 160

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	164	3095
1	332	2730
2	1361	2677
3	4128	2571
4	4913	2571
5	5086	2571

prune319.0ms (1.7%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	143	17	160
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	146	23	169

Error

20.4b

Counts

169 → 23

Alt Table

Status	Error	Program
	49.4b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 (sqrt.f64 M) 2) (.f64 h M))) (pow.f64 d 2)))
	51.1b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	62.0b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 d d) (/.f64 c0 (.f64 (.f64 w h) (.f64 D D))) (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)))))
	33.7b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 (.f64 (cbrt.f64 M) (cbrt.f64 M)) 2) (*.f64 (pow.f64 (cbrt.f64 M) 2) h))) (pow.f64 d 2)))
	61.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	32.3b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) d) d))
	61.0b	(.f64 (.f64 (cbrt.f64 (/.f64 c0 (.f64 2 w))) (cbrt.f64 (/.f64 c0 (.f64 2 w)))) (.f64 (cbrt.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))))))
	56.3b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	61.0b	(/.f64 (.f64 c0 (+.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))))) (*.f64 2 w))
	58.9b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (*.f64 (log.f64 d) 2))))
	34.2b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	34.8b	(.f64 1/4 (.f64 (.f64 D D) (/.f64 (.f64 h (.f64 M M)) (.f64 d d))))
	59.6b	(log.f64 (pow.f64 (exp.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (/.f64 (/.f64 (.f64 (pow.f64 d 4) (.f64 c0 c0)) (.f64 (.f64 w h) (.f64 w h))) (pow.f64 D 4)) (.f64 M M))))) (/.f64 c0 (.f64 2 w))))
	31.8b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	54.3b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (log.f64 (.f64 (pow.f64 M 2) h))) (.f64 (log.f64 d) 2))))
▶	31.7b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (*.f64 M M)) d)))
	58.7b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	45.9b	(.f64 1/4 (/.f64 (.f64 (pow.f64 (sqrt.f64 D) 2) (.f64 (pow.f64 (sqrt.f64 D) 2) (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	33.2b	(.f64 1/4 (.f64 (/.f64 (pow.f64 D 2) (pow.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) 2)) (/.f64 (.f64 (pow.f64 M 2) h) (pow.f64 (cbrt.f64 d) 2))))
	35.1b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 (.f64 (cbrt.f64 (pow.f64 M 2)) (cbrt.f64 (pow.f64 M 2))) (*.f64 (cbrt.f64 (pow.f64 M 2)) h))) (pow.f64 d 2)))
	32.8b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	62.7b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (neg.f64 (.f64 M M)))))
	56.0b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))

Compiler

Compiled 4752 to 3021 computations (36.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.2b	(/.f64 (.f64 h (.f64 M M)) d)
✓	6.8b	(/.f64 (*.f64 D D) d)
✓	9.4b	(.f64 h (.f64 M M))
✓	11.9b	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))

series157.0ms (0.9%)

Counts

4 → 132

Calls

4 calls:

105.0ms	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))
31.0ms	(/.f64 (.f64 h (.f64 M M)) d)
13.0ms	(/.f64 (*.f64 D D) d)
8.0ms	(.f64 h (.f64 M M))

rewrite36.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-cbrt-cube_binary64`
77×	`add-exp-log_binary64`
32×	`cbrt-unprod_binary64`
32×	`prod-exp_binary64`
22×	`cbrt-undiv_binary64`

Counts

4 → 123

Calls

4 calls:

9.0ms	(.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (.f64 M M)) d))
8.0ms	(.f64 h (.f64 M M))
5.0ms	(/.f64 (.f64 h (.f64 M M)) d)
3.0ms	(/.f64 (*.f64 D D) d)

simplify152.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

637×	`associate-/r*_binary64`
534×	`associate-/r/_binary64`
461×	`*-commutative_binary64`
309×	`log-div_binary64`
218×	`log-prod_binary64`

Counts

255 → 160

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	170	4137
1	400	3453
2	1576	3453
3	4069	3451
4	4865	3451
5	5026	3451

prune296.0ms (1.6%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	146	14	160
Fresh	7	15	22
Picked	1	0	1
Done	0	0	0
Total	154	29	183

Error

18.3b

Counts

183 → 29

Alt Table

Status	Error	Program
	56.1b	(.f64 1/4 (.f64 (/.f64 (*.f64 D D) d) (/.f64 (exp.f64 (+.f64 (log.f64 h) (+.f64 (log.f64 M) (log.f64 M)))) d)))
	35.1b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 (.f64 (cbrt.f64 (pow.f64 M 2)) (cbrt.f64 (pow.f64 M 2))) (*.f64 (cbrt.f64 (pow.f64 M 2)) h))) (pow.f64 d 2)))
	46.9b	(.f64 1/4 (.f64 (.f64 (/.f64 D (sqrt.f64 d)) (sqrt.f64 (/.f64 (.f64 h (.f64 M M)) d))) (.f64 (/.f64 D (sqrt.f64 d)) (sqrt.f64 (/.f64 (.f64 h (.f64 M M)) d)))))
	32.8b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	53.3b	(.f64 1/4 (.f64 (exp.f64 (-.f64 (+.f64 (log.f64 D) (log.f64 D)) (log.f64 d))) (/.f64 (.f64 h (.f64 M M)) d)))
	49.4b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 (sqrt.f64 M) 2) (.f64 h M))) (pow.f64 d 2)))
	51.1b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	27.5b	(.f64 1/4 (.f64 (/.f64 D (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 (.f64 h (.f64 M M)) d))))
	62.0b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 d d) (/.f64 c0 (.f64 (.f64 w h) (.f64 D D))) (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)))))
	61.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	31.2b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (.f64 M M) (/.f64 h (.f64 (cbrt.f64 d) (cbrt.f64 d)))) (cbrt.f64 d))))
	54.3b	(.f64 1/4 (exp.f64 (+.f64 (-.f64 (+.f64 (log.f64 D) (log.f64 D)) (log.f64 d)) (-.f64 (log.f64 (.f64 h (*.f64 M M))) (log.f64 d)))))
	61.0b	(.f64 (.f64 (cbrt.f64 (/.f64 c0 (.f64 2 w))) (cbrt.f64 (/.f64 c0 (.f64 2 w)))) (.f64 (cbrt.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))))))
	56.3b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	28.8b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (*.f64 h M) M) d)))
	31.1b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 h (/.f64 d (.f64 M M)))))
	43.3b	(.f64 1/4 (.f64 (/.f64 D (sqrt.f64 d)) (.f64 (/.f64 D (sqrt.f64 d)) (/.f64 (.f64 h (*.f64 M M)) d))))
	61.0b	(/.f64 (.f64 c0 (+.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))))) (*.f64 2 w))
	59.6b	(log.f64 (pow.f64 (exp.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (/.f64 (/.f64 (.f64 (pow.f64 d 4) (.f64 c0 c0)) (.f64 (.f64 w h) (.f64 w h))) (pow.f64 D 4)) (.f64 M M))))) (/.f64 c0 (.f64 2 w))))
	31.8b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
▶	27.4b	(.f64 1/4 (.f64 (/.f64 D 1) (.f64 (/.f64 D d) (/.f64 (.f64 h (*.f64 M M)) d))))
	45.9b	(.f64 1/4 (/.f64 (.f64 (pow.f64 (sqrt.f64 D) 2) (.f64 (pow.f64 (sqrt.f64 D) 2) (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	32.0b	(.f64 1/4 (.f64 (.f64 (/.f64 (.f64 D D) d) (/.f64 h (.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 (.f64 M M) (cbrt.f64 d))))
	45.6b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (.f64 (sqrt.f64 h) M) (.f64 (sqrt.f64 h) M)) d)))
	62.7b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (neg.f64 (.f64 M M)))))
	34.2b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	31.9b	(.f64 1/4 (.f64 (.f64 h (/.f64 (.f64 D D) d)) (/.f64 (*.f64 M M) d)))
	56.0b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	30.7b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (.f64 (/.f64 h (.f64 (cbrt.f64 d) (cbrt.f64 d))) (/.f64 (.f64 M M) (cbrt.f64 d)))))

Compiler

Compiled 5277 to 1921 computations (63.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.0b	(.f64 (/.f64 D 1) (.f64 (/.f64 D d) (/.f64 (.f64 h (.f64 M M)) d)))
	5.2b	(/.f64 (.f64 h (.f64 M M)) d)
✓	7.6b	(.f64 (/.f64 D d) (/.f64 (.f64 h (*.f64 M M)) d))
	9.4b	(.f64 h (.f64 M M))

series209.0ms (1.1%)

Counts

2 → 96

Calls

2 calls:

105.0ms	(.f64 (/.f64 D d) (/.f64 (.f64 h (*.f64 M M)) d))
104.0ms	(.f64 (/.f64 D 1) (.f64 (/.f64 D d) (/.f64 (.f64 h (.f64 M M)) d)))

rewrite76.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

169×	`add-exp-log_binary64`
127×	`add-cbrt-cube_binary64`
83×	`prod-exp_binary64`
60×	`cbrt-unprod_binary64`
58×	`div-exp_binary64`

Counts

2 → 130

Calls

2 calls:

43.0ms	(.f64 (/.f64 D 1) (.f64 (/.f64 D d) (/.f64 (.f64 h (.f64 M M)) d)))
9.0ms	(.f64 (/.f64 D d) (/.f64 (.f64 h (*.f64 M M)) d))

simplify159.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

446×	`associate-/r/_binary64`
257×	`associate-r_binary64`
225×	`times-frac_binary64`
224×	`cube-prod_binary64`
224×	`log-prod_binary64`

Counts

226 → 185

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	208	5272
1	446	4231
2	1872	4231
3	3513	4219
4	4813	4219
5	4978	4219

prune442.0ms (2.4%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	234	8	242
Fresh	10	18	28
Picked	1	0	1
Done	0	0	0
Total	245	26	271

Error

17.1b

Counts

271 → 26

Alt Table

Status	Error	Program
	32.8b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	53.3b	(.f64 1/4 (.f64 (exp.f64 (-.f64 (+.f64 (log.f64 D) (log.f64 D)) (log.f64 d))) (/.f64 (.f64 h (.f64 M M)) d)))
	27.5b	(.f64 1/4 (.f64 (/.f64 D 1) (.f64 (/.f64 D d) (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 h (.f64 M M)) d)) (cbrt.f64 (/.f64 (.f64 h (.f64 M M)) d))) (cbrt.f64 (/.f64 (.f64 h (*.f64 M M)) d))))))
	49.4b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 (sqrt.f64 M) 2) (.f64 h M))) (pow.f64 d 2)))
	51.1b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) (pow.f64 d 2)))
	45.6b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (.f64 (sqrt.f64 h) M) (.f64 (sqrt.f64 h) M)) d)))
	39.1b	(.f64 1/4 (cbrt.f64 (.f64 (pow.f64 (/.f64 (.f64 D (.f64 D h)) (*.f64 d d)) 3) (pow.f64 M 6))))
	26.9b	(.f64 1/4 (.f64 (/.f64 D 1) (.f64 (.f64 (/.f64 D d) (.f64 h (.f64 M M))) (/.f64 1 d))))
	27.3b	(.f64 1/4 (.f64 (/.f64 D 1) (.f64 (.f64 h (/.f64 D d)) (/.f64 (*.f64 M M) d))))
	62.0b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (.f64 d d) (/.f64 c0 (.f64 (.f64 w h) (.f64 D D))) (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)))))
	61.0b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	54.3b	(.f64 1/4 (exp.f64 (+.f64 (-.f64 (+.f64 (log.f64 D) (log.f64 D)) (log.f64 d)) (-.f64 (log.f64 (.f64 h (*.f64 M M))) (log.f64 d)))))
	61.0b	(.f64 (.f64 (cbrt.f64 (/.f64 c0 (.f64 2 w))) (cbrt.f64 (/.f64 c0 (.f64 2 w)))) (.f64 (cbrt.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))))))
	56.3b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	28.8b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 (*.f64 h M) M) d)))
	31.1b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 h (/.f64 d (.f64 M M)))))
	34.0b	(.f64 1/4 (.f64 (/.f64 D 1) (exp.f64 (log.f64 (/.f64 (.f64 D (.f64 (.f64 M M) h)) (.f64 d d))))))
	27.4b	(.f64 1/4 (.f64 (/.f64 D 1) (.f64 (/.f64 D d) (/.f64 (.f64 h (pow.f64 M 2)) d))))
	61.0b	(/.f64 (.f64 c0 (+.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))))) (*.f64 2 w))
	56.1b	(.f64 1/4 (.f64 (/.f64 (*.f64 D D) d) (/.f64 (exp.f64 (+.f64 (log.f64 h) (+.f64 (log.f64 M) (log.f64 M)))) d)))
	62.7b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (neg.f64 (.f64 M M)))))
	26.1b	(.f64 1/4 (/.f64 (.f64 D (.f64 (/.f64 D d) (.f64 h (.f64 M M)))) (.f64 1 d)))
	59.6b	(log.f64 (pow.f64 (exp.f64 (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.f64 D D)) (sqrt.f64 (-.f64 (/.f64 (/.f64 (.f64 (pow.f64 d 4) (.f64 c0 c0)) (.f64 (.f64 w h) (.f64 w h))) (pow.f64 D 4)) (.f64 M M))))) (/.f64 c0 (.f64 2 w))))
	56.0b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	23.8b	(.f64 1/4 (.f64 (/.f64 D 1) (.f64 (/.f64 D d) (/.f64 (.f64 (*.f64 h M) M) d))))
	32.0b	(.f64 1/4 (.f64 (.f64 (/.f64 (.f64 D D) d) (/.f64 h (.f64 (cbrt.f64 d) (cbrt.f64 d)))) (/.f64 (.f64 M M) (cbrt.f64 d))))

Compiler

Compiled 6943 to 2483 computations (64.2% saved)

regimes1.9s (10.3%)

Accuracy

Total 8.6b remaining (32.9%)

Threshold costs 0b (0%)

Counts

119 → 3

Compiler

Compiled 38218 to 24766 computations (35.2% saved)

bsearch375.0ms (2%)

Steps

Iters	Range		Point
11	1.684059325329547e+163	8.873131855041093e+187	1.0261799473837364e+177
8	7.183844310945085e-151	1.0795960608393537e-147	1.0667044981912174e-147

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	78
1	52	78
2	51	78

end363.0ms (2%)

Compiler: Compiled 901 to 565 computations (37.3% saved)

Details

analyze2.5s (13.9%)

sample8.8s (48%)

simplify41.0ms (0.2%)

prune5.0ms (0%)

localize20.0ms (0.1%)

series1.2s (6.4%)

rewrite141.0ms (0.8%)

simplify314.0ms (1.7%)

prune504.0ms (2.8%)

localize9.0ms (0%)

series137.0ms (0.7%)

rewrite28.0ms (0.2%)

simplify116.0ms (0.6%)

prune319.0ms (1.7%)

localize10.0ms (0.1%)

series157.0ms (0.9%)

rewrite36.0ms (0.2%)

simplify152.0ms (0.8%)

prune296.0ms (1.6%)

localize12.0ms (0.1%)

series209.0ms (1.1%)

rewrite76.0ms (0.4%)

simplify159.0ms (0.9%)

prune442.0ms (2.4%)

regimes1.9s (10.3%)

bsearch375.0ms (2%)

simplify3.0ms (0%)

end363.0ms (2%)

Profiling