Details

analyze2.5s (14.8%)

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)

sample284.0ms (1.7%)

Algorithm

1×

intervals

Results

46.0ms	355×	body	128	nan
41.0ms	71×	body	4096	valid
27.0ms	38×	body	8192	valid
18.0ms	39×	body	2048	valid
14.0ms	130×	body	128	invalid
8.0ms	21×	body	1024	valid
7.0ms	71×	body	128	valid
4.0ms	13×	body	512	valid
1.0ms	3×	body	1024	invalid
1.0ms	2×	body	2048	invalid
1.0ms	3×	body	256	valid
0.0ms	1×	body	512	invalid

Compiler

Compiled 123 to 49 computations (60.2% saved)

simplify44.0ms (0.3%)

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

60.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	62.6b	(.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)))))
▶	60.5b	(.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

62.6b

(*.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)))))

▶

60.5b

(*.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 130 computations (59.5% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	12.3b	(.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)))))
✓	13.9b	(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)))
✓	19.4b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	28.5b	(+.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))))

series1.4s (8.4%)

Counts

4 → 276

Calls

4 calls:

595.0ms	(.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)))))
324.0ms	(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)))
302.0ms	(+.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))))
205.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))

rewrite156.0ms (0.9%)

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:

45.0ms	(.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)))))
44.0ms	(+.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))))
30.0ms	(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)))
13.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))

simplify374.0ms (2.2%)

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

prune672.0ms (4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	420	12	432
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	422	12	434

Error

27.9b

Counts

434 → 12

Alt Table

Status	Error	Program
	61.5b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)) (sqrt.f64 (-.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)))))
▶	34.9b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	60.4b	(.f64 c0 (.f64 (/.f64 1 (.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))))))
	60.5b	(.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 1 (/.f64 (.f64 (.f64 w h) (.f64 D D)) (.f64 c0 (.f64 d d))))) (*.f64 M M)))))
	62.1b	(.f64 (/.f64 c0 (.f64 2 w)) (fma.f64 (/.f64 c0 (.f64 w h)) (/.f64 (.f64 d d) (.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)))))
	62.2b	(/.f64 (.f64 c0 (+.f64 (pow.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) 3) (pow.f64 (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))) 3))) (.f64 (.f64 2 w) (+.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 (.f64 (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))) (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 (/.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))))))))
	61.5b	(exp.f64 (log.f64 (.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)))))))
	60.7b	(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))))
	62.4b	(fma.f64 (/.f64 (.f64 d d) (.f64 D D)) (/.f64 (.f64 c0 c0) (.f64 h (.f64 w w))) (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (*.f64 d d)) -1/4))
	61.7b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	49.5b	(.f64 1/2 (/.f64 (.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w))
	41.2b	(.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))))

Compiler

Compiled 31097 to 8041 computations (74.1% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	7.5b	(*.f64 (pow.f64 M 2) h)
✓	14.1b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
✓	16.1b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))

series177.0ms (1%)

Counts

3 → 40

Calls

3 calls:

135.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
34.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
9.0ms	(*.f64 (pow.f64 M 2) h)

rewrite32.0ms (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:

8.0ms	(*.f64 (pow.f64 M 2) h)
7.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
5.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))

simplify123.0ms (0.7%)

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

prune340.0ms (2%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	145	15	160
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	150	22	172

Error

20.7b

Counts

172 → 22

Alt Table

Status	Error	Program
	51.8b	(.f64 1/4 (/.f64 (exp.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h)))) (pow.f64 d 2)))
	58.6b	(.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))))
	42.0b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (log.f64 (exp.f64 (*.f64 (pow.f64 M 2) h)))) (pow.f64 d 2)))
	62.2b	(/.f64 (.f64 c0 (+.f64 (pow.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) 3) (pow.f64 (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))) 3))) (.f64 (.f64 2 w) (+.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 (.f64 (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))) (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 (/.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))))))))
	32.7b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	33.7b	(.f64 1/4 (/.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 D) (cbrt.f64 D)) 2) (.f64 (pow.f64 (cbrt.f64 D) 2) (*.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	51.6b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	31.3b	(.f64 1/4 (/.f64 (pow.f64 D 2) (/.f64 d (/.f64 (.f64 h (*.f64 M M)) d))))
	57.3b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (*.f64 (log.f64 d) 2))))
	62.4b	(fma.f64 (/.f64 (.f64 d d) (.f64 D D)) (/.f64 (.f64 c0 c0) (.f64 h (.f64 w w))) (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (*.f64 d d)) -1/4))
	57.3b	(.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)))))
	61.7b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	60.4b	(.f64 c0 (.f64 (/.f64 1 (.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))))))
	60.5b	(.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 1 (/.f64 (.f64 (.f64 w h) (.f64 D D)) (.f64 c0 (.f64 d d))))) (*.f64 M M)))))
	32.5b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	60.7b	(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))))
	61.5b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)) (sqrt.f64 (-.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)))))
	33.0b	(.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))))
	56.6b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	34.4b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
▶	30.6b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) d) d))
	30.9b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (*.f64 M M)) d)))

Compiler

Compiled 5050 to 2977 computations (41% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.2b	(/.f64 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) d) d)
✓	4.8b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) d)
	7.5b	(*.f64 (pow.f64 M 2) h)
	14.1b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))

series198.0ms (1.2%)

Counts

2 → 72

Calls

2 calls:

131.0ms	(/.f64 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) d) d)
66.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) d)

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`add-exp-log_binary64`
42×	`prod-exp_binary64`
40×	`div-exp_binary64`
36×	`times-frac_binary64`
25×	`add-cbrt-cube_binary64`

Counts

2 → 97

Calls

2 calls:

8.0ms	(/.f64 (/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) d) d)
7.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) d)

simplify133.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

675×	`associate-*l/_binary64`
526×	`associate-*r/_binary64`
515×	`associate-/r/_binary64`
350×	`*-commutative_binary64`
221×	`fma-def_binary64`

Counts

169 → 139

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	3824
1	350	3490
2	1347	3478
3	3955	3379
4	4854	3379
5	4971	3379

prune544.0ms (3.2%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	215	14	229
Fresh	6	15	21
Picked	1	0	1
Done	0	0	0
Total	222	29	251

Error

19.2b

Counts

251 → 29

Alt Table

Status	Error	Program
	60.5b	(.f64 1/4 (/.f64 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h))) (log.f64 d))) d))
	58.6b	(.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))))
	42.0b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (log.f64 (exp.f64 (*.f64 (pow.f64 M 2) h)))) (pow.f64 d 2)))
	62.2b	(/.f64 (.f64 c0 (+.f64 (pow.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) 3) (pow.f64 (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))) 3))) (.f64 (.f64 2 w) (+.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 (.f64 (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))) (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 (/.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))))))))
	49.4b	(.f64 1/4 (/.f64 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) d) d))
	60.7b	(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))))
	47.3b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) (sqrt.f64 d)) (.f64 (/.f64 h (pow.f64 d 3/2)) (*.f64 M M))))
	51.0b	(.f64 1/4 (/.f64 (/.f64 (exp.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h)))) d) d))
	51.6b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	44.4b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 D 2) (exp.f64 (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h)))) d) d))
	57.3b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (*.f64 (log.f64 d) 2))))
	62.4b	(fma.f64 (/.f64 (.f64 d d) (.f64 D D)) (/.f64 (.f64 c0 c0) (.f64 h (.f64 w w))) (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (*.f64 d d)) -1/4))
	30.4b	(.f64 1/4 (.f64 (.f64 (/.f64 D (.f64 d (cbrt.f64 d))) D) (/.f64 (.f64 h (.f64 M M)) (*.f64 (cbrt.f64 d) (cbrt.f64 d)))))
	57.3b	(.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)))))
	61.7b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	30.7b	(.f64 1/4 (/.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 D D) (.f64 h (.f64 M M)))) (cbrt.f64 (.f64 (.f64 D D) (.f64 h (.f64 M M))))) (cbrt.f64 (.f64 (.f64 D D) (.f64 h (*.f64 M M))))) d) d))
	33.0b	(.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))))
	29.4b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 D) (cbrt.f64 D)) 2) (.f64 (.f64 h (.f64 M M)) (pow.f64 (cbrt.f64 D) 2))) d) d))
	31.2b	(.f64 1/4 (.f64 (/.f64 (/.f64 (pow.f64 D 2) (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (cbrt.f64 d) (cbrt.f64 d))) (/.f64 (/.f64 (*.f64 (pow.f64 M 2) h) (cbrt.f64 d)) (cbrt.f64 d))))
	56.6b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	28.0b	(.f64 1/4 (/.f64 (/.f64 (.f64 D (.f64 D (.f64 h (*.f64 M M)))) d) d))
	60.4b	(.f64 c0 (.f64 (/.f64 1 (.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))))))
▶	27.8b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 h M))) d) d))
	34.4b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	32.5b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	56.6b	(.f64 1/4 (exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h)))))
	61.5b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)) (sqrt.f64 (-.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)))))
	31.3b	(.f64 1/4 (/.f64 (/.f64 (pow.f64 D 2) 1) (.f64 d (/.f64 d (.f64 h (.f64 M M))))))
	50.5b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (/.f64 h d)))) d))

Compiler

Compiled 7179 to 3870 computations (46.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 M (.f64 h M))
✓	3.2b	(/.f64 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (*.f64 h M))) d) d)
✓	4.8b	(/.f64 (.f64 (pow.f64 D 2) (.f64 M (*.f64 h M))) d)
✓	14.1b	(.f64 (pow.f64 D 2) (.f64 M (*.f64 h M)))

series240.0ms (1.4%)

Counts

4 → 156

Calls

4 calls:

131.0ms	(/.f64 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (*.f64 h M))) d) d)
69.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 M (*.f64 h M))) d)
31.0ms	(.f64 (pow.f64 D 2) (.f64 M (*.f64 h M)))
9.0ms	(.f64 M (.f64 h M))

rewrite40.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

115×	`add-exp-log_binary64`
57×	`prod-exp_binary64`
52×	`add-cbrt-cube_binary64`
36×	`times-frac_binary64`
31×	`div-exp_binary64`

Counts

4 → 144

Calls

4 calls:

9.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 M (*.f64 h M))) d)
8.0ms	(/.f64 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (*.f64 h M))) d) d)
6.0ms	(.f64 (pow.f64 D 2) (.f64 M (*.f64 h M)))
4.0ms	(.f64 M (.f64 h M))

simplify176.0ms (1%)

Algorithm

1×	egg-herbie

Rules

648×	`associate-*l/_binary64`
547×	`associate-*r/_binary64`
520×	`associate-/r/_binary64`
430×	`*-commutative_binary64`
245×	`fma-def_binary64`

Counts

300 → 219

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	199	5602
1	456	5047
2	1521	5035
3	4422	5023
4	4975	5023
5	5019	5023

prune438.0ms (2.6%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	212	7	219
Fresh	9	19	28
Picked	1	0	1
Done	0	0	0
Total	222	26	248

Error

17.7b

Counts

248 → 26

Alt Table

Status	Error	Program
	62.2b	(/.f64 (.f64 c0 (+.f64 (pow.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) 3) (pow.f64 (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))) 3))) (.f64 (.f64 2 w) (+.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 (.f64 (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))) (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 (/.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))))))))
	27.6b	(.f64 1/4 (/.f64 (.f64 (/.f64 (pow.f64 D 2) 1) (/.f64 (.f64 M (.f64 h M)) d)) d))
	42.0b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (log.f64 (exp.f64 (*.f64 (pow.f64 M 2) h)))) (pow.f64 d 2)))
	49.4b	(.f64 1/4 (/.f64 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h))) d) d))
	47.3b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) (sqrt.f64 d)) (.f64 (/.f64 h (pow.f64 d 3/2)) (*.f64 M M))))
	51.0b	(.f64 1/4 (/.f64 (/.f64 (exp.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h)))) d) d))
	51.6b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (log.f64 (pow.f64 d 2)))))
	44.4b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 D 2) (exp.f64 (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h)))) d) d))
	57.3b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (*.f64 (log.f64 d) 2))))
	62.4b	(fma.f64 (/.f64 (.f64 d d) (.f64 D D)) (/.f64 (.f64 c0 c0) (.f64 h (.f64 w w))) (.f64 (/.f64 (.f64 (.f64 D D) (.f64 (.f64 M M) h)) (*.f64 d d)) -1/4))
	30.4b	(.f64 1/4 (.f64 (.f64 (/.f64 D (.f64 d (cbrt.f64 d))) D) (/.f64 (.f64 h (.f64 M M)) (*.f64 (cbrt.f64 d) (cbrt.f64 d)))))
	57.3b	(.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)))))
	61.7b	(/.f64 (.f64 (pow.f64 d 2) (pow.f64 c0 2)) (.f64 (pow.f64 D 2) (*.f64 (pow.f64 w 2) h)))
	56.6b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	24.5b	(.f64 1/4 (/.f64 (/.f64 (.f64 D (.f64 D (.f64 M (*.f64 h M)))) d) d))
	60.4b	(.f64 c0 (.f64 (/.f64 1 (.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))))))
	28.1b	(.f64 1/4 (.f64 (/.f64 (/.f64 (pow.f64 D 2) (.f64 (cbrt.f64 d) (cbrt.f64 d))) (.f64 (cbrt.f64 d) (cbrt.f64 d))) (/.f64 (/.f64 (.f64 M (.f64 h M)) (cbrt.f64 d)) (cbrt.f64 d))))
	41.9b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 (sqrt.f64 D) 2) (.f64 (pow.f64 (sqrt.f64 D) 2) (.f64 M (*.f64 h M)))) d) d))
	26.4b	(.f64 1/4 (/.f64 (/.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 D) (cbrt.f64 D)) 2) (.f64 (pow.f64 (cbrt.f64 D) 2) (.f64 M (.f64 h M)))) d) d))
	34.4b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	31.3b	(.f64 1/4 (/.f64 (/.f64 (pow.f64 D 2) 1) (.f64 d (/.f64 d (.f64 h (.f64 M M))))))
	27.9b	(.f64 1/4 (/.f64 (/.f64 (.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 h M)))) (cbrt.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 h M))))) (cbrt.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 h M))))) d) d))
	56.6b	(.f64 1/4 (exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 h)))))
	61.5b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (.f64 (sqrt.f64 (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)) (sqrt.f64 (-.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) M)))))
	26.9b	(.f64 1/4 (/.f64 (/.f64 (.f64 (.f64 (pow.f64 D 2) M) (.f64 h M)) d) d))
	50.5b	(.f64 1/4 (/.f64 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (/.f64 h d)))) d))

Compiler

Compiled 5898 to 2497 computations (57.7% saved)

regimes1.7s (10.3%)

Accuracy

Total 9.7b remaining (34.9%)

Threshold costs 0b (0%)

Counts

138 → 1

Compiler

Compiled 57993 to 30325 computations (47.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	18	22
2	18	22

end1.0ms (0%)

Compiler: Compiled 21 to 14 computations (33.3% saved)

sample7.2s (42.6%)

Algorithm

1×

intervals

Results

1.4s	2156×	body	4096	valid
1.2s	11889×	body	128	nan
921.0ms	1169×	body	8192	valid
694.0ms	1225×	body	2048	valid
511.0ms	3946×	body	128	invalid
272.0ms	668×	body	1024	valid
237.0ms	2387×	body	128	valid
72.0ms	259×	body	512	valid
27.0ms	48×	body	2048	invalid
25.0ms	136×	body	256	valid
22.0ms	60×	body	1024	invalid
9.0ms	32×	body	512	invalid
7.0ms	12×	body	4096	invalid
6.0ms	8×	body	8192	exit
4.0ms	23×	body	256	invalid

Compiler

Compiled 1000 to 543 computations (45.7% saved)

Details

analyze2.5s (14.8%)

sample284.0ms (1.7%)

simplify44.0ms (0.3%)

prune5.0ms (0%)

localize20.0ms (0.1%)

series1.4s (8.4%)

rewrite156.0ms (0.9%)

simplify374.0ms (2.2%)

prune672.0ms (4%)

localize10.0ms (0.1%)

series177.0ms (1%)

rewrite32.0ms (0.2%)

simplify123.0ms (0.7%)

prune340.0ms (2%)

localize11.0ms (0.1%)

series198.0ms (1.2%)

rewrite27.0ms (0.2%)

simplify133.0ms (0.8%)

prune544.0ms (3.2%)

localize10.0ms (0.1%)

series240.0ms (1.4%)

rewrite40.0ms (0.2%)

simplify176.0ms (1%)

prune438.0ms (2.6%)

regimes1.7s (10.3%)

simplify2.0ms (0%)

end1.0ms (0%)

sample7.2s (42.6%)

Profiling