Details

analyze2.7s (9.7%)

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)

sample9.0s (32.5%)

Results

3.2s	16173×	body	128	invalid
2.1s	2219×	body	4096	valid
1.3s	1155×	body	8192	valid
1.1s	1291×	body	2048	valid
490.0ms	2511×	body	128	valid
374.0ms	617×	body	1024	valid
150.0ms	322×	body	512	valid
51.0ms	141×	body	256	valid
40.0ms	27×	body	256	invalid
38.0ms	49×	body	2048	invalid
32.0ms	54×	body	1024	invalid
14.0ms	31×	body	512	invalid
11.0ms	9×	body	8192	exit
10.0ms	12×	body	4096	invalid

Compiler

Compiled 176 to 65 computations (63.1% saved)

simplify45.0ms (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

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

57.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	60.3b	(.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)))))
▶	57.9b	(.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)))))

Status

Error

Program

60.3b

(*.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)))))

▶

57.9b

(*.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)))))

Compiler

Compiled 321 to 130 computations (59.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	11.9b	(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)))
✓	12.9b	(.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)))))
✓	17.9b	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))
✓	28.1b	(+.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))))

series1.3s (4.8%)

Counts

4 → 276

Calls

4 calls:

485.0ms	(.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)))))
359.0ms	(+.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))))
304.0ms	(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)))
185.0ms	(/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (*.f64 D D)))

rewrite164.0ms (0.6%)

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:

62.0ms	(.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)))))
41.0ms	(+.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))))
26.0ms	(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)))

simplify308.0ms (1.1%)

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

prune488.0ms (1.8%)

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

28.2b

Counts

434 → 9

Alt Table

Status	Error	Program
	60.1b	(.f64 (/.f64 c0 (.f64 2 w)) (+.f64 (/.f64 (.f64 c0 (.f64 d d)) (.f64 (.f64 w h) (.f64 D D))) (neg.f64 (/.f64 (.f64 (.f64 d d) c0) (.f64 (.f64 D D) (.f64 w h))))))
	60.3b	(.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)))))
	49.6b	(.f64 1/2 (/.f64 (.f64 (sqrt.f64 (neg.f64 (pow.f64 M 2))) c0) w))
▶	35.7b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
	41.5b	(.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))))
	59.3b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	63.2b	(/.f64 (.f64 c0 (+.f64 (.f64 (.f64 c0 (.f64 d d)) (sqrt.f64 (+.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 (/.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 (.f64 M M) (.f64 M M)) (.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 w h) (.f64 D D)) (sqrt.f64 (-.f64 (pow.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)))) 3) (pow.f64 (.f64 M M) 3)))))) (.f64 (.f64 2 w) (.f64 (.f64 (.f64 w h) (.f64 D D)) (sqrt.f64 (+.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 (/.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 (.f64 M M) (.f64 M M)) (.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))))))))
	60.0b	(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))))
	60.1b	(.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)))))

Compiler

Compiled 30855 to 7925 computations (74.3% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
✓	8.6b	(*.f64 (pow.f64 M 2) h)
✓	13.9b	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
✓	15.0b	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))

series327.0ms (1.2%)

Counts

4 → 72

Calls

4 calls:

144.0ms	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
120.0ms	(/.f64 (.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h)) (pow.f64 d 2))
54.0ms	(.f64 (pow.f64 D 2) (.f64 (pow.f64 M 2) h))
9.0ms	(*.f64 (pow.f64 M 2) h)

rewrite50.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

290×	`add-exp-log_binary64`
190×	`prod-exp_binary64`
78×	`div-exp_binary64`
76×	`pow-exp_binary64`
76×	`pow-to-exp_binary64`

Counts

4 → 205

Calls

4 calls:

11.0ms	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))
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))
4.0ms	(*.f64 (pow.f64 M 2) h)

simplify139.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

506×	`*-commutative_binary64`
444×	`associate-/l/_binary64`
380×	`fma-def_binary64`
373×	`associate-/r/_binary64`
294×	`log-prod_binary64`

Counts

277 → 231

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	217	5669
1	422	5071
2	1672	5018
3	3936	4789
4	5006	4789

prune401.0ms (1.4%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	213	18	231
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	218	22	240

Error

20.5b

Counts

240 → 22

Alt Table

Status	Error	Program
	55.6b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (.f64 (log.f64 d) 2))))
	60.3b	(.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)))))
▶	32.3b	(.f64 1/4 (/.f64 (pow.f64 D 2) (/.f64 d (/.f64 (.f64 h (*.f64 M M)) d))))
	59.0b	(.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))))
	33.2b	(.f64 1/4 (/.f64 (.f64 D (.f64 D (.f64 (pow.f64 M 2) h))) (pow.f64 d 2)))
	53.7b	(.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)))))
	55.6b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (*.f64 (log.f64 d) 2))))
	36.5b	(.f64 1/4 (log1p.f64 (expm1.f64 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))))
	50.0b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (log.f64 (.f64 (pow.f64 M 2) h))) (log.f64 (pow.f64 d 2)))))
	32.4b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) d) (/.f64 (.f64 h (*.f64 M M)) d)))
	56.0b	(exp.f64 (fma.f64 (log.f64 d) -2 (fma.f64 2 (log.f64 (.f64 D M)) (log.f64 (.f64 h 1/4)))))
	32.7b	(.f64 1/4 (.f64 (/.f64 (.f64 D D) (.f64 d (cbrt.f64 d))) (/.f64 (.f64 h (.f64 M M)) (pow.f64 (cbrt.f64 d) 2))))
	60.1b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (*.f64 (log.f64 d) 2))))
	57.9b	(.f64 1/4 (/.f64 (exp.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h)))) (pow.f64 d 2)))
	60.0b	(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))))
	33.0b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	55.6b	(.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)))))
	35.3b	(.f64 1/4 (/.f64 (.f64 (*.f64 (pow.f64 D 2) (pow.f64 M 2)) h) (pow.f64 d 2)))
	55.9b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	60.1b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (.f64 (log.f64 d) 2))))
	59.3b	(.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 (.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)))))

Compiler

Compiled 6252 to 3990 computations (36.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.8b	(/.f64 d (/.f64 (.f64 h (.f64 M M)) d))
✓	5.7b	(/.f64 (.f64 h (.f64 M M)) d)
✓	8.6b	(.f64 h (.f64 M M))
✓	12.1b	(/.f64 (pow.f64 D 2) (/.f64 d (/.f64 (.f64 h (.f64 M M)) d)))

series355.0ms (1.3%)

Counts

4 → 144

Calls

4 calls:

230.0ms	(/.f64 (pow.f64 D 2) (/.f64 d (/.f64 (.f64 h (.f64 M M)) d)))
89.0ms	(/.f64 d (/.f64 (.f64 h (.f64 M M)) d))
26.0ms	(/.f64 (.f64 h (.f64 M M)) d)
9.0ms	(.f64 h (.f64 M M))

rewrite81.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

514×	`times-frac_binary64`
204×	`add-sqr-sqrt_binary64`
203×	`*-un-lft-identity_binary64`
203×	`add-cube-cbrt_binary64`
87×	`add-exp-log_binary64`

Counts

4 → 373

Calls

4 calls:

14.0ms	(/.f64 (pow.f64 D 2) (/.f64 d (/.f64 (.f64 h (.f64 M M)) d)))
6.0ms	(/.f64 d (/.f64 (.f64 h (.f64 M M)) d))
6.0ms	(.f64 h (.f64 M M))
5.0ms	(/.f64 (.f64 h (.f64 M M)) d)

simplify438.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

637×	`associate-/r/_binary64`
408×	`associate-*r/_binary64`
391×	`associate-/l/_binary64`
347×	`associate-/l*_binary64`
331×	`associate-*l/_binary64`

Counts

517 → 580

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	564	13914
1	1104	12140
2	4274	11899
3	4312	11823
4	4973	11823
5	5051	11823

prune1.1s (3.8%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	568	12	580
Fresh	7	14	21
Picked	1	0	1
Done	0	0	0
Total	576	26	602

Error

17.8b

Counts

602 → 26

Alt Table

Status	Error	Program
	55.6b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (.f64 (log.f64 d) 2))))
	60.3b	(.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)))))
	55.6b	(.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)))))
	47.5b	(.f64 1/4 (.f64 (/.f64 (pow.f64 (sqrt.f64 D) 2) (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (sqrt.f64 (/.f64 (.f64 h (.f64 M M)) d)))) (/.f64 (pow.f64 (sqrt.f64 D) 2) (/.f64 (cbrt.f64 d) (sqrt.f64 (/.f64 (.f64 h (*.f64 M M)) d))))))
	32.1b	(.f64 1/4 (.f64 (pow.f64 D 2) (/.f64 h (.f64 d (/.f64 d (.f64 M M))))))
	29.4b	(.f64 1/4 (.f64 (.f64 D h) (/.f64 D (.f64 d (/.f64 d (*.f64 M M))))))
	27.2b	(.f64 1/4 (.f64 (/.f64 D (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (/.f64 h (.f64 (cbrt.f64 d) (cbrt.f64 d))))) (/.f64 D (/.f64 (cbrt.f64 d) (/.f64 (*.f64 M M) (cbrt.f64 d))))))
	26.9b	(.f64 1/4 (.f64 (/.f64 D (/.f64 d h)) (/.f64 D (/.f64 d (*.f64 M M)))))
	27.2b	(.f64 1/4 (.f64 h (.f64 (/.f64 D (/.f64 d (.f64 M M))) (/.f64 D d))))
	53.7b	(.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)))))
	36.5b	(.f64 1/4 (log1p.f64 (expm1.f64 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))))
	28.7b	(.f64 1/4 (/.f64 (pow.f64 D 2) (/.f64 d (/.f64 (.f64 (*.f64 h M) M) d))))
	32.4b	(.f64 1/4 (.f64 (.f64 D (.f64 (.f64 M M) h)) (/.f64 D (.f64 d d))))
	45.4b	(.f64 1/4 (/.f64 (pow.f64 D 2) (/.f64 d (/.f64 (.f64 (.f64 (sqrt.f64 h) M) (.f64 (sqrt.f64 h) M)) d))))
	59.3b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	38.9b	(.f64 1/4 (/.f64 (pow.f64 D 2) (/.f64 d (/.f64 (exp.f64 (log.f64 (.f64 (*.f64 M M) h))) d))))
	60.1b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (*.f64 (log.f64 d) 2))))
	57.9b	(.f64 1/4 (/.f64 (exp.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h)))) (pow.f64 d 2)))
	60.0b	(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))))
	33.0b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	29.1b	(.f64 1/4 (.f64 (.f64 (.f64 M M) h) (*.f64 (/.f64 D d) (/.f64 D d))))
	59.0b	(.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))))
▶	26.9b	(.f64 1/4 (.f64 (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h d)) (/.f64 D (/.f64 (cbrt.f64 d) (/.f64 (.f64 M M) (cbrt.f64 d))))))
	55.9b	(.f64 1/4 (exp.f64 (fma.f64 2 (log.f64 (.f64 D M)) (fma.f64 (log.f64 d) -2 (log.f64 h)))))
	60.1b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (.f64 (log.f64 d) 2))))
	60.1b	(.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)))))

Compiler

Compiled 16812 to 6069 computations (63.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.9b	(/.f64 (cbrt.f64 d) (/.f64 (*.f64 M M) (cbrt.f64 d)))
✓	3.4b	(*.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h d))
✓	6.2b	(/.f64 D (/.f64 (cbrt.f64 d) (/.f64 (*.f64 M M) (cbrt.f64 d))))
✓	7.6b	(.f64 (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h d)) (/.f64 D (/.f64 (cbrt.f64 d) (/.f64 (*.f64 M M) (cbrt.f64 d)))))

series2.3s (8.3%)

Counts

4 → 144

Calls

4 calls:

931.0ms	(*.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h d))
859.0ms	(/.f64 D (/.f64 (cbrt.f64 d) (/.f64 (*.f64 M M) (cbrt.f64 d))))
358.0ms	(/.f64 (cbrt.f64 d) (/.f64 (*.f64 M M) (cbrt.f64 d)))
158.0ms	(.f64 (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h d)) (/.f64 D (/.f64 (cbrt.f64 d) (/.f64 (*.f64 M M) (cbrt.f64 d)))))

rewrite204.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

1198×	`times-frac_binary64`
491×	`add-sqr-sqrt_binary64`
472×	`*-un-lft-identity_binary64`
472×	`add-cube-cbrt_binary64`
401×	`cbrt-prod_binary64`

Counts

4 → 712

Calls

4 calls:

40.0ms	(.f64 (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h d)) (/.f64 D (/.f64 (cbrt.f64 d) (/.f64 (*.f64 M M) (cbrt.f64 d)))))
15.0ms	(/.f64 D (/.f64 (cbrt.f64 d) (/.f64 (*.f64 M M) (cbrt.f64 d))))
10.0ms	(*.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h d))
8.0ms	(/.f64 (cbrt.f64 d) (/.f64 (*.f64 M M) (cbrt.f64 d)))

simplify439.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

861×	`associate-/r/_binary64`
780×	`associate-/l*_binary64`
634×	`associate-/l/_binary64`
461×	`times-frac_binary64`
238×	`*-commutative_binary64`

Counts

856 → 1069

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	806	25604
1	2270	24068
2	5505	24068

prune2.4s (8.7%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	1058	11	1069
Fresh	8	17	25
Picked	1	0	1
Done	0	0	0
Total	1067	28	1095

Error

15.0b

Counts

1095 → 28

Alt Table

Status	Error	Program
	43.3b	(.f64 1/4 (.f64 (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h d)) (/.f64 (/.f64 D (/.f64 (cbrt.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d))) (/.f64 M (cbrt.f64 (sqrt.f64 d))))) (/.f64 (cbrt.f64 (cbrt.f64 d)) (/.f64 M (cbrt.f64 (sqrt.f64 d)))))))
	55.6b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (log.f64 (pow.f64 D 2)) (+.f64 (log.f64 (pow.f64 M 2)) (log.f64 h))) (.f64 (log.f64 d) 2))))
	60.3b	(.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)))))
	47.5b	(.f64 1/4 (.f64 (/.f64 (pow.f64 (sqrt.f64 D) 2) (/.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d)) (sqrt.f64 (/.f64 (.f64 h (.f64 M M)) d)))) (/.f64 (pow.f64 (sqrt.f64 D) 2) (/.f64 (cbrt.f64 d) (sqrt.f64 (/.f64 (.f64 h (*.f64 M M)) d))))))
	21.9b	(.f64 1/4 (.f64 (.f64 (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h d)) (/.f64 (.f64 (cbrt.f64 D) (cbrt.f64 D)) (/.f64 (.f64 (cbrt.f64 (cbrt.f64 d)) (cbrt.f64 (cbrt.f64 d))) M))) (/.f64 (cbrt.f64 D) (/.f64 (cbrt.f64 (cbrt.f64 d)) (/.f64 M (cbrt.f64 d))))))
	24.7b	(.f64 1/4 (.f64 (*.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h d)) (/.f64 D (/.f64 (/.f64 (cbrt.f64 d) M) (/.f64 M (cbrt.f64 d))))))
	21.6b	(.f64 1/4 (.f64 (.f64 (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h d)) (/.f64 1 (/.f64 1 (/.f64 M 1)))) (/.f64 D (/.f64 (cbrt.f64 d) (/.f64 M (cbrt.f64 d))))))
	21.7b	(.f64 1/4 (.f64 (/.f64 (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h d)) (/.f64 (.f64 (cbrt.f64 (cbrt.f64 d)) (cbrt.f64 (cbrt.f64 d))) (/.f64 M (*.f64 (cbrt.f64 (cbrt.f64 d)) (cbrt.f64 (cbrt.f64 d)))))) (/.f64 D (/.f64 (cbrt.f64 (cbrt.f64 d)) (/.f64 M (cbrt.f64 (cbrt.f64 d)))))))
	26.9b	(.f64 1/4 (.f64 (/.f64 D (/.f64 d h)) (/.f64 D (/.f64 d (*.f64 M M)))))
	27.2b	(.f64 1/4 (.f64 h (.f64 (/.f64 D (/.f64 d (.f64 M M))) (/.f64 D d))))
	60.1b	(.f64 1/4 (exp.f64 (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (.f64 (log.f64 d) 2))))
	21.8b	(.f64 1/4 (.f64 (.f64 (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h d)) (.f64 (.f64 (cbrt.f64 D) (cbrt.f64 D)) (/.f64 M (cbrt.f64 (*.f64 (cbrt.f64 d) (cbrt.f64 d)))))) (/.f64 (cbrt.f64 D) (/.f64 (cbrt.f64 d) (/.f64 M (cbrt.f64 (cbrt.f64 d)))))))
	36.5b	(.f64 1/4 (log1p.f64 (expm1.f64 (/.f64 (.f64 (pow.f64 D 2) (*.f64 (pow.f64 M 2) h)) (pow.f64 d 2)))))
	28.7b	(.f64 1/4 (/.f64 (pow.f64 D 2) (/.f64 d (/.f64 (.f64 (*.f64 h M) M) d))))
	32.4b	(.f64 1/4 (.f64 (.f64 D (.f64 (.f64 M M) h)) (/.f64 D (.f64 d d))))
	45.4b	(.f64 1/4 (/.f64 (pow.f64 D 2) (/.f64 d (/.f64 (.f64 (.f64 (sqrt.f64 h) M) (.f64 (sqrt.f64 h) M)) d))))
	59.3b	(.f64 (/.f64 c0 (.f64 2 w)) (.f64 2 (/.f64 (.f64 (pow.f64 d 2) c0) (.f64 (pow.f64 D 2) (.f64 w h)))))
	38.9b	(.f64 1/4 (/.f64 (pow.f64 D 2) (/.f64 d (/.f64 (exp.f64 (log.f64 (.f64 (*.f64 M M) h))) d))))
	41.9b	(.f64 1/4 (.f64 (.f64 (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h d)) (*.f64 (sqrt.f64 D) M)) (/.f64 (sqrt.f64 D) (/.f64 (cbrt.f64 d) (/.f64 M (cbrt.f64 d))))))
	60.1b	(exp.f64 (+.f64 (log.f64 1/4) (-.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (.f64 (log.f64 M) 2) (log.f64 h))) (*.f64 (log.f64 d) 2))))
	57.9b	(.f64 1/4 (/.f64 (exp.f64 (+.f64 (.f64 (log.f64 D) 2) (+.f64 (*.f64 (log.f64 M) 2) (log.f64 h)))) (pow.f64 d 2)))
	33.0b	(.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 M (.f64 M h))) (pow.f64 d 2)))
	26.9b	(.f64 1/4 (/.f64 (.f64 (.f64 (/.f64 D (cbrt.f64 d)) h) (/.f64 D (/.f64 (cbrt.f64 d) (/.f64 (.f64 M M) (cbrt.f64 d))))) d))
	21.6b	(.f64 1/4 (.f64 (.f64 (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h d)) (/.f64 (.f64 (cbrt.f64 D) (cbrt.f64 D)) (/.f64 (cbrt.f64 (.f64 (cbrt.f64 d) (cbrt.f64 d))) (/.f64 M (cbrt.f64 (*.f64 (cbrt.f64 d) (cbrt.f64 d))))))) (/.f64 (cbrt.f64 D) (/.f64 (cbrt.f64 (cbrt.f64 d)) (/.f64 M (cbrt.f64 (cbrt.f64 d)))))))
	60.1b	(.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)))))
	36.3b	(.f64 1/4 (.f64 (log.f64 (exp.f64 (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h d)))) (/.f64 D (/.f64 (cbrt.f64 d) (/.f64 (.f64 M M) (cbrt.f64 d))))))
	29.4b	(.f64 1/4 (.f64 (.f64 D h) (/.f64 D (.f64 d (/.f64 d (*.f64 M M))))))
	22.8b	(.f64 1/4 (.f64 (.f64 (/.f64 D (cbrt.f64 d)) (/.f64 h d)) (.f64 (.f64 (.f64 (cbrt.f64 D) (cbrt.f64 D)) M) (/.f64 (cbrt.f64 D) (/.f64 (cbrt.f64 d) (/.f64 M (cbrt.f64 d)))))))

Compiler

Compiled 37638 to 7414 computations (80.3% saved)

regimes5.0s (18%)

Accuracy

Total 4.0b remaining (21.2%)

Threshold costs 0b (0%)

Counts

345 → 5

Compiler

Compiled 128742 to 75443 computations (41.4% saved)

bsearch22.0ms (0.1%)

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

simplify13.0ms (0%)

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary64`
4×	`+-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	65	588
1	88	588
2	95	588
3	99	588
4	101	588
5	99	588

end419.0ms (1.5%)

Compiler: Compiled 1674 to 723 computations (56.8% saved)

Details

analyze2.7s (9.7%)

sample9.0s (32.5%)

simplify45.0ms (0.2%)

prune4.0ms (0%)

localize18.0ms (0.1%)

series1.3s (4.8%)

rewrite164.0ms (0.6%)

simplify308.0ms (1.1%)

prune488.0ms (1.8%)

localize10.0ms (0%)

series327.0ms (1.2%)

rewrite50.0ms (0.2%)

simplify139.0ms (0.5%)

prune401.0ms (1.4%)

localize15.0ms (0.1%)

series355.0ms (1.3%)

rewrite81.0ms (0.3%)

simplify438.0ms (1.6%)

prune1.1s (3.8%)

localize15.0ms (0.1%)

series2.3s (8.3%)

rewrite204.0ms (0.7%)

simplify439.0ms (1.6%)

prune2.4s (8.7%)

regimes5.0s (18%)

bsearch22.0ms (0.1%)

simplify13.0ms (0%)

end419.0ms (1.5%)

Profiling