Details

analyze5.4s (19%)

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
4.3%	95.4%	0.3%	13
6.6%	93.1%	0.3%	14

Compiler

Compiled 25 to 19 computations (24% saved)

sample4.6s (16.3%)

Symmetry

(sort M D)

Results

2.8s	8256×	body	128	valid
1.7s	4637×	body	128	invalid

Compiler

Compiled 74 to 56 computations (24.3% saved)

simplify37.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

645×	`distribute-neg-frac_binary64`
581×	`distribute-rgt-neg-in_binary64`
418×	`associate-/l*_binary64`
372×	`cancel-sign-sub-inv_binary64`
263×	`associate-/l/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	27
1	42	27
2	111	27
3	723	27
4	2855	27
5	4994	27

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

11.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	11.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))

Compiler

Compiled 72 to 54 computations (25% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.9b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
✓	3.5b	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
✓	4.6b	(/.f64 (.f64 M D) (.f64 2 d))
✓	8.1b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))

series1.5s (5.5%)

Counts

4 → 204

Calls

4 calls:

681.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
449.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
381.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))
33.0ms	(/.f64 (.f64 M D) (.f64 2 d))

rewrite71.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64`
38×	`add-sqr-sqrt_binary64`
27×	`prod-exp_binary64`
23×	`add-cbrt-cube_binary64`
19×	`associate-r_binary64`

Counts

4 → 124

Calls

4 calls:

19.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))
12.0ms	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))
9.0ms	(/.f64 (.f64 M D) (.f64 2 d))
8.0ms	(sqrt.f64 (-.f64 1 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) (/.f64 h l))))

simplify396.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

517×	`times-frac_binary64`
399×	`associate-l_binary64`
365×	`associate-/l*_binary64`
342×	`associate-/r*_binary64`
258×	`associate-*r/_binary64`

Counts

328 → 314

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	516	11209
1	1262	10441
2	4988	10441

prune650.0ms (2.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	305	9	314
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	306	9	315

Error

3.4b

Counts

315 → 9

Alt Table

Status	Error	Program
	61.2b	(.f64 w0 (.f64 -1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 l (pow.f64 d 2)))))) M)))
	60.7b	(.f64 -1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 (pow.f64 d 2) l))))) (.f64 w0 M)))
	12.3b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 (*.f64 (/.f64 M 2) (/.f64 D d)) 2) (/.f64 h l)))))
	11.6b	w0
	61.4b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	11.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) (cbrt.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))) (cbrt.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))
	61.2b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	59.0b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
▶	9.0b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) h) l))))

Compiler

Compiled 12118 to 7295 computations (39.8% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.5b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)))
✓	4.3b	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)
	4.6b	(/.f64 (.f64 M D) (.f64 2 d))
✓	5.0b	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)

series1.1s (3.7%)

Counts

3 → 156

Calls

3 calls:

442.0ms	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)
345.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)))
265.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)

rewrite53.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-exp-log_binary64`
22×	`prod-exp_binary64`
19×	`add-sqr-sqrt_binary64`
16×	`div-exp_binary64`
12×	`*-un-lft-identity_binary64`

Counts

3 → 84

Calls

3 calls:

14.0ms	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)))
12.0ms	(.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h)
12.0ms	(/.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (*.f64 2 d)) 2) h) l)

simplify296.0ms (1%)

Algorithm

1×	egg-herbie

Rules

315×	`fma-def_binary64`
298×	`unswap-sqr_binary64`
288×	`distribute-neg-frac_binary64`
241×	`cancel-sign-sub-inv_binary64`
191×	`times-frac_binary64`

Counts

240 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	334	7367
1	764	6748
2	2985	6661
3	4995	6661

prune575.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	227	2	229
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	229	9	238

Error

3.0b

Counts

238 → 9

Alt Table

Status	Error	Program
	61.2b	(.f64 w0 (.f64 -1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 l (pow.f64 d 2)))))) M)))
	60.7b	(.f64 -1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 (pow.f64 d 2) l))))) (.f64 w0 M)))
	11.6b	w0
	61.4b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	11.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) (cbrt.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))) (cbrt.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))
	61.2b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 (.f64 M M) h) (.f64 l (*.f64 d d))) -1/4))))
	9.7b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) h) l))))
	59.0b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
▶	7.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)) l))))

Compiler

Compiled 7937 to 5023 computations (36.7% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.5b	(sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h)) l)))
✓	4.3b	(/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (.f64 2 d)) h)) l)
	4.6b	(/.f64 (.f64 M D) (.f64 2 d))
✓	4.9b	(.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)

series840.0ms (3%)

Counts

3 → 156

Calls

3 calls:

449.0ms

(/.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)) l)

333.0ms

(sqrt.f64 (-.f64 1 (/.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)) l)))

58.0ms

(*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)

rewrite142.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

226×	`add-cbrt-cube_binary64`
226×	`add-exp-log_binary64`
108×	`cbrt-unprod_binary64`
108×	`prod-exp_binary64`
79×	`cbrt-undiv_binary64`

Counts

3 → 135

Calls

3 calls:

32.0ms

(/.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)) l)

17.0ms

(sqrt.f64 (-.f64 1 (/.f64 (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) (*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)) l)))

13.0ms

(*.f64 (/.f64 (*.f64 M D) (*.f64 2 d)) h)

simplify359.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

584×	`associate-/l*_binary64`
484×	`associate-l_binary64`
455×	`associate-/r*_binary64`
414×	`associate-*l/_binary64`
390×	`associate-*r/_binary64`

Counts

291 → 254

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	458	9762
1	1205	8761
2	4703	8697
3	4996	8697

prune743.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	330	2	332
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	332	9	341

Error

2.7b

Counts

341 → 9

Alt Table

Status	Error	Program
	61.2b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 h (.f64 D D)) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
	61.4b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	11.6b	w0
	60.7b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 M (.f64 M h)) (.f64 l (*.f64 d d))) -1/4))))
	11.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l))) (cbrt.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))) (cbrt.f64 (.f64 (pow.f64 (/.f64 (.f64 M D) (.f64 2 d)) 2) (/.f64 h l)))))))
▶	9.7b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) h) l))))
	59.0b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
	60.7b	(.f64 -1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 (pow.f64 d 2) l))))) (.f64 w0 M)))
✓	7.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)) l))))

Compiler

Compiled 13216 to 7172 computations (45.7% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.5b	(sqrt.f64 (-.f64 1 (/.f64 (*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) h) l)))
✓	4.3b	(/.f64 (*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) h) l)
✓	5.0b	(/.f64 M (/.f64 2 (/.f64 D d)))
✓	5.0b	(*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) h)

series911.0ms (3.2%)

Counts

4 → 192

Calls

4 calls:

381.0ms	(/.f64 (*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) h) l)
277.0ms	(sqrt.f64 (-.f64 1 (/.f64 (*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) h) l)))
226.0ms	(*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) h)
26.0ms	(/.f64 M (/.f64 2 (/.f64 D d)))

rewrite251.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

735×	`times-frac_binary64`
366×	`add-sqr-sqrt_binary64`
347×	`*-un-lft-identity_binary64`
344×	`add-cube-cbrt_binary64`
142×	`associate-l_binary64`

Counts

4 → 415

Calls

4 calls:

60.0ms	(*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) h)
44.0ms	(/.f64 (*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) h) l)
16.0ms	(/.f64 M (/.f64 2 (/.f64 D d)))
16.0ms	(sqrt.f64 (-.f64 1 (/.f64 (*.f64 (pow.f64 (/.f64 M (/.f64 2 (/.f64 D d))) 2) h) l)))

simplify617.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

542×	`associate-/r/_binary64`
406×	`associate-/l/_binary64`
335×	`associate-/l*_binary64`
296×	`sqr-pow_binary64`
264×	`times-frac_binary64`

Counts

607 → 800

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	980	15547
1	2379	14776
2	4828	14772
3	4996	14772

prune1.7s (6.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	797	3	800
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	799	10	809

Error

2.2b

Counts

809 → 10

Alt Table

Status	Error	Program
	37.5b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (.f64 (/.f64 M (/.f64 2 (/.f64 D d))) (sqrt.f64 h)) (.f64 (/.f64 M (/.f64 2 (/.f64 D d))) (sqrt.f64 h))) l))))
	60.7b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (/.f64 (.f64 M (.f64 M h)) (.f64 l (*.f64 d d))) -1/4))))
	61.2b	(.f64 w0 (.f64 (sqrt.f64 (.f64 (/.f64 (.f64 h (.f64 D D)) (.f64 l (*.f64 d d))) -1/4)) (neg.f64 M)))
	61.4b	(/.f64 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) (.f64 h (pow.f64 M 2))) l)))) w0) d)
	59.5b	(.f64 w0 (.f64 D (sqrt.f64 (.f64 (.f64 (pow.f64 (/.f64 M d) 2) (/.f64 h l)) -1/4))))
	60.7b	(.f64 -1 (.f64 (sqrt.f64 (neg.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 D 2) h) (.f64 (pow.f64 d 2) l))))) (.f64 w0 M)))
	11.6b	w0
	9.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (pow.f64 (.f64 (.f64 (cbrt.f64 (/.f64 D d)) (cbrt.f64 (/.f64 D d))) (/.f64 M (/.f64 2 (cbrt.f64 (/.f64 D d))))) 2) h) l))))
	59.0b	(.f64 (sqrt.f64 (.f64 (.f64 (/.f64 h l) (pow.f64 (/.f64 D d) 2)) -1/4)) (neg.f64 (.f64 M w0)))
✓	7.8b	(.f64 w0 (sqrt.f64 (-.f64 1 (/.f64 (.f64 (/.f64 (.f64 M D) (.f64 2 d)) (.f64 (/.f64 (.f64 M D) (*.f64 2 d)) h)) l))))

Compiler

Compiled 26966 to 15694 computations (41.8% saved)

regimes7.5s (26.6%)

Accuracy

Total 5.2b remaining (58.7%)

Threshold costs 0b (0%)

Counts

222 → 4

Compiler

Compiled 102364 to 74687 computations (27% saved)

bsearch10.0ms (0%)

Compiler: Compiled 24 to 18 computations (25% saved)

simplify11.0ms (0%)

Algorithm

1×	egg-herbie

Rules

38×	`*-commutative_binary64`
24×	`+-commutative_binary64`
24×	`sub-neg_binary64`
21×	`neg-sub0_binary64`
20×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	224
1	102	224
2	139	224
3	182	224
4	222	224
5	242	224
6	250	224
7	251	224
8	249	224

end365.0ms (1.3%)

Compiler: Compiled 864 to 559 computations (35.3% saved)

Iter	Nodes	Cost
0	66	224
1	102	224
2	139	224
3	182	224
4	222	224
5	242	224
6	250	224
7	251	224
8	249	224

Iter	Nodes	Cost
0	66	224
1	102	224
2	139	224
3	182	224
4	222	224
5	242	224
6	250	224
7	251	224
8	249	224

Details

analyze5.4s (19%)

sample4.6s (16.3%)

simplify37.0ms (0.1%)

prune4.0ms (0%)

localize25.0ms (0.1%)

series1.5s (5.5%)

rewrite71.0ms (0.3%)

simplify396.0ms (1.4%)

prune650.0ms (2.3%)

localize28.0ms (0.1%)

series1.1s (3.7%)

rewrite53.0ms (0.2%)

simplify296.0ms (1%)

prune575.0ms (2%)

localize30.0ms (0.1%)

series840.0ms (3%)

rewrite142.0ms (0.5%)

simplify359.0ms (1.3%)

prune743.0ms (2.6%)

localize24.0ms (0.1%)

series911.0ms (3.2%)

rewrite251.0ms (0.9%)

simplify617.0ms (2.2%)

prune1.7s (6.1%)

regimes7.5s (26.6%)

bsearch10.0ms (0%)

simplify11.0ms (0%)

end365.0ms (1.3%)

Profiling

Iter	Nodes	Cost
0	66	224
1	102	224
2	139	224
3	182	224
4	222	224
5	242	224
6	250	224
7	251	224
8	249	224