Details

analyze1.5s (11.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
3.1%	96.7%	0.2%	8
19.9%	79.9%	0.2%	9
22.8%	77%	0.2%	10
35.1%	64.7%	0.2%	11
45%	54.8%	0.2%	12
53.8%	45.1%	1.2%	13
56.2%	42.4%	1.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample39.0ms (0.3%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
1.0ms	21×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify139.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1536×	`fma-neg_binary64`
909×	`div-sub_binary64`
615×	`times-frac_binary64`
547×	`fma-def_binary64`
362×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	18	13
2	29	13
3	67	13
4	136	13
5	250	13
6	551	13
7	1395	13
8	2791	13
9	2886	13
10	3210	13
11	3295	13
12	3304	13
13	3354	13
14	4929	13

prune3.0ms (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

3.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	3.0b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
✓	2.9b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

series123.0ms (0.9%)

Counts

2 → 84

Calls

2 calls:

80.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
42.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

rewrite57.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
70×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-l_binary64`
26×	`add-cube-cbrt_binary64`

Counts

2 → 106

Calls

2 calls:

21.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
17.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

simplify242.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

951×	`fma-def_binary64`
905×	`times-frac_binary64`
465×	`fma-neg_binary64`
154×	`associate-/l*_binary64`
144×	`+-commutative_binary64`

Counts

190 → 193

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	4749
1	800	4617
2	2672	4102
3	4971	4102
4	5241	4102

prune252.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	186	7	193
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	186	8	194

Error

Counts

194 → 8

Alt Table

Status	Error	Program
	12.3b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
	25.0b	(.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
	33.4b	(.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) (sqrt.f64 t)) (sqrt.f64 t))
▶	3.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
	10.9b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
	27.7b	(.f64 (sqrt.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)) (sqrt.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)))
	34.9b	(.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 1) (.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y)) t))
✓	3.0b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

Compiler

Compiled 4694 to 1343 computations (71.4% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t)
✓	0.4b	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))))
✓	0.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
✓	5.5b	(cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))

series2.7s (20.8%)

Counts

4 → 168

Calls

4 calls:

1.2s	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t)
954.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))))
408.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))
96.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))

rewrite264.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

304×	`*-un-lft-identity_binary64`
251×	`add-sqr-sqrt_binary64`
248×	`cbrt-prod_binary64`
205×	`times-frac_binary64`
96×	`distribute-lft-out--_binary64`

Counts

4 → 285

Calls

4 calls:

66.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))))
49.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
25.0ms	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t)
11.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))

simplify627.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

331×	`associate-r_binary64`
329×	`fma-def_binary64`
275×	`associate-+r+_binary64`
181×	`associate-/l*_binary64`
173×	`associate-*r/_binary64`

Counts

453 → 461

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1820	27927
1	5310	27927

prune1.8s (13.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	661	0	661
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	661	8	669

Error

Counts

669 → 8

Alt Table

Status	Error	Program
	12.3b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
	25.0b	(.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
	33.4b	(.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) (sqrt.f64 t)) (sqrt.f64 t))
✓	3.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
▶	10.9b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
	27.7b	(.f64 (sqrt.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)) (sqrt.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)))
	34.9b	(.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 1) (.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y)) t))
✓	3.0b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

Compiler

Compiled 54277 to 23980 computations (55.8% saved)

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 z y))
✓	10.8b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))

series109.0ms (0.8%)

Counts

2 → 72

Calls

2 calls:

72.0ms	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
37.0ms	(/.f64 t (-.f64 z y))

rewrite43.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

2 → 87

Calls

2 calls:

21.0ms	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
8.0ms	(/.f64 t (-.f64 z y))

simplify192.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

847×	`times-frac_binary64`
695×	`fma-def_binary64`
344×	`fma-neg_binary64`
282×	`cancel-sign-sub-inv_binary64`
204×	`sub-neg_binary64`

Counts

159 → 159

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	235	3780
1	617	3669
2	2394	3214
3	4765	3214
4	4978	3214

prune207.0ms (1.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	158	1	159
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	159	8	167

Error

Counts

167 → 8

Alt Table

Status	Error	Program
▶	12.3b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
	25.0b	(.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
	33.4b	(.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) (sqrt.f64 t)) (sqrt.f64 t))
✓	3.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
✓	10.9b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
	27.7b	(.f64 (sqrt.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)) (sqrt.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)))
✓	3.0b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	36.9b	(/.f64 (.f64 (-.f64 (.f64 x x) (.f64 y y)) t) (.f64 (+.f64 x y) (-.f64 z y)))

Compiler

Compiled 3571 to 1017 computations (71.5% saved)

localize22.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
✓	7.0b	(/.f64 (*.f64 t x) (-.f64 z y))
✓	10.7b	(/.f64 (*.f64 y t) (-.f64 z y))

series191.0ms (1.5%)

Counts

3 → 87

Calls

3 calls:

92.0ms	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
58.0ms	(/.f64 (*.f64 t x) (-.f64 z y))
40.0ms	(/.f64 (*.f64 y t) (-.f64 z y))

rewrite114.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`times-frac_binary64`
121×	`prod-diff_binary64`
113×	`*-un-lft-identity_binary64`
113×	`add-sqr-sqrt_binary64`
56×	`associate-/r/_binary64`

Counts

3 → 221

Calls

3 calls:

34.0ms	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
11.0ms	(/.f64 (*.f64 y t) (-.f64 z y))
10.0ms	(/.f64 (*.f64 t x) (-.f64 z y))

simplify483.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

435×	`fma-neg_binary64`
321×	`sub-neg_binary64`
215×	`associate-/l*_binary64`
197×	`unsub-neg_binary64`
172×	`associate-l_binary64`

Counts

308 → 343

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	386	12003
1	994	10068
2	3722	8341
3	4484	8341
4	4970	8341
5	4868	8341

prune542.0ms (4.2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	342	1	343
Fresh	2	2	4
Picked	0	1	1
Done	0	3	3
Total	344	7	351

Error

Counts

351 → 7

Alt Table

Status	Error	Program
✓	12.3b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
	11.5b	(-.f64 (/.f64 t (/.f64 (-.f64 z y) x)) (/.f64 (*.f64 y t) (-.f64 z y)))
	25.0b	(.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
✓	10.9b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
	27.7b	(.f64 (sqrt.f64 (.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)) (sqrt.f64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)))
✓	3.0b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
✓	3.7b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))

Compiler

Compiled 12881 to 2245 computations (82.6% saved)

regimes1.9s (14.5%)

Accuracy

Total 2.5b remaining (99.4%)

Threshold costs 0b (0%)

Counts

125 → 3

Compiler

Compiled 15206 to 8219 computations (45.9% saved)

bsearch51.0ms (0.4%)

Steps

Iters	Range		Point
8	-2.5632950690219472e-245	-3.7890568307004434e-249	-3.3018215432180023e-248
5	-1.4836781204626482e+116	-5.052206568205052e+115	-5.150743828419859e+115

Compiler

Compiled 5 to 4 computations (20% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
8×	`*-commutative_binary64`
7×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	67
1	44	67
2	59	67
3	68	67
4	73	67
5	74	67
6	74	67

end1.0ms (0%)

Compiler: Compiled 48 to 23 computations (52.1% saved)

sample1.3s (10.2%)

Algorithm

1×

intervals

Results

594.0ms	8000×	body	128	valid
58.0ms	622×	body	128	invalid

Compiler

Compiled 210 to 103 computations (51% saved)

Details

analyze1.5s (11.8%)

sample39.0ms (0.3%)

simplify139.0ms (1.1%)

prune3.0ms (0%)

localize13.0ms (0.1%)

series123.0ms (0.9%)

rewrite57.0ms (0.4%)

simplify242.0ms (1.9%)

prune252.0ms (1.9%)

localize19.0ms (0.1%)

series2.7s (20.8%)

rewrite264.0ms (2%)

simplify627.0ms (4.8%)

prune1.8s (13.7%)

localize13.0ms (0.1%)

series109.0ms (0.8%)

rewrite43.0ms (0.3%)

simplify192.0ms (1.5%)

prune207.0ms (1.6%)

localize22.0ms (0.2%)

series191.0ms (1.5%)

rewrite114.0ms (0.9%)

simplify483.0ms (3.7%)

prune542.0ms (4.2%)

regimes1.9s (14.5%)

bsearch51.0ms (0.4%)

simplify10.0ms (0.1%)

end1.0ms (0%)

sample1.3s (10.2%)

Profiling