Details

analyze784.0ms (20.9%)

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
1.6%	98.2%	0.2%	8
19.1%	80.7%	0.2%	9
22%	77.8%	0.2%	10
34.5%	65.3%	0.2%	11
44.2%	55.7%	0.2%	12
53.3%	45.5%	1.2%	13
55.8%	42.7%	1.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.1s (28.8%)

Results

910.0ms	8256×	body	128	valid
72.0ms	669×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify116.0ms (3.1%)

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

prune1.0ms (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

2.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	2.6b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
✓	2.4b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

series52.0ms (1.4%)

Counts

2 → 84

Calls

2 calls:

32.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
20.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

rewrite28.0ms (0.7%)

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:

12.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
6.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

simplify128.0ms (3.4%)

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

prune128.0ms (3.4%)

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
▶	10.5b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
✓	2.6b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	10.6b	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))
	50.8b	(.f64 (/.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 y))) (.f64 (/.f64 (-.f64 x y) (-.f64 (sqrt.f64 z) (sqrt.f64 y))) t))
	35.3b	(.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 1) (.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y)) t))
	18.5b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 z y)) 3)) t)
	22.5b	(.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
	13.2b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))

Compiler

Compiled 4642 to 1347 computations (71% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 z y))
✓	10.4b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))

series54.0ms (1.4%)

Counts

2 → 72

Calls

2 calls:

34.0ms	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
17.0ms	(/.f64 t (-.f64 z y))

rewrite19.0ms (0.5%)

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:

9.0ms	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
3.0ms	(/.f64 t (-.f64 z y))

simplify104.0ms (2.8%)

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

prune91.0ms (2.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	159	8	167

Error

Counts

167 → 8

Alt Table

Status	Error	Program
✓	10.5b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
✓	2.6b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
▶	10.6b	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))
	50.8b	(.f64 (/.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 y))) (.f64 (/.f64 (-.f64 x y) (-.f64 (sqrt.f64 z) (sqrt.f64 y))) t))
	35.3b	(.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 1) (.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y)) t))
	18.5b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 z y)) 3)) t)
	22.5b	(.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
	13.2b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))

Compiler

Compiled 3551 to 1032 computations (70.9% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 z y))
✓	0.2b	(*.f64 (/.f64 1 (-.f64 z y)) t)
✓	10.4b	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))

series57.0ms (1.5%)

Counts

3 → 108

Calls

3 calls:

32.0ms	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))
17.0ms	(*.f64 (/.f64 1 (-.f64 z y)) t)
8.0ms	(/.f64 1 (-.f64 z y))

rewrite32.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
31×	`add-exp-log_binary64`
26×	`associate-l_binary64`

Counts

3 → 119

Calls

3 calls:

10.0ms	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))
8.0ms	(*.f64 (/.f64 1 (-.f64 z y)) t)
4.0ms	(/.f64 1 (-.f64 z y))

simplify124.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

827×	`fma-def_binary64`
337×	`distribute-rgt-in_binary64`
289×	`cancel-sign-sub-inv_binary64`
283×	`fma-neg_binary64`
207×	`sub-neg_binary64`

Counts

227 → 221

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	260	4516
1	675	4300
2	2529	3660
3	4920	3660
4	5052	3660

prune137.0ms (3.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	221	8	229

Error

Counts

229 → 8

Alt Table

Status	Error	Program
✓	10.5b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
✓	2.6b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
✓	10.6b	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))
	50.8b	(.f64 (/.f64 1 (+.f64 (sqrt.f64 z) (sqrt.f64 y))) (.f64 (/.f64 (-.f64 x y) (-.f64 (sqrt.f64 z) (sqrt.f64 y))) t))
	35.3b	(.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 1) (.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y)) t))
	18.5b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (-.f64 z y)) 3)) t)
	22.5b	(.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
▶	13.2b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))

Compiler

Compiled 4716 to 1878 computations (60.2% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	12.5b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))

series34.0ms (0.9%)

Counts

1 → 36

Calls

1 calls:

34.0ms

(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
5×	`associate-/r*_binary64`

Counts

1 → 31

Calls

1 calls:

7.0ms

(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))

simplify76.0ms (2%)

Algorithm

1×	egg-herbie

Rules

885×	`times-frac_binary64`
530×	`fma-def_binary64`
372×	`fma-neg_binary64`
257×	`cancel-sign-sub-inv_binary64`
230×	`distribute-rgt-in_binary64`

Counts

67 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	158	2010
1	469	1929
2	1795	1586
3	4975	1584
4	5232	1584

prune45.0ms (1.2%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	2	2	4
Picked	0	1	1
Done	0	3	3
Total	79	7	86

Error

Counts

86 → 7

Alt Table

Status	Error	Program
✓	10.5b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
✓	2.6b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	35.3b	(.f64 (/.f64 (sqrt.f64 (-.f64 x y)) 1) (.f64 (/.f64 (sqrt.f64 (-.f64 x y)) (-.f64 z y)) t))
	2.4b	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))
✓	10.6b	(.f64 (-.f64 x y) (.f64 (/.f64 1 (-.f64 z y)) t))
	22.5b	(.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (.f64 (sqrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
✓	13.2b	(/.f64 (*.f64 t (-.f64 x y)) (-.f64 z y))

Compiler

Compiled 1843 to 611 computations (66.8% saved)

regimes537.0ms (14.3%)

Accuracy

Total 1.0b remaining (98.9%)

Threshold costs 1.0b (98.9%)

Counts

89 → 1

Compiler

Compiled 11398 to 6051 computations (46.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	49
1	20	49
2	26	49
3	28	49
4	29	49
5	29	49

end78.0ms (2.1%)

Compiler: Compiled 181 to 92 computations (49.2% saved)

Details

analyze784.0ms (20.9%)

sample1.1s (28.8%)

simplify116.0ms (3.1%)

prune1.0ms (0%)

localize6.0ms (0.2%)

series52.0ms (1.4%)

rewrite28.0ms (0.7%)

simplify128.0ms (3.4%)

prune128.0ms (3.4%)

localize9.0ms (0.2%)

series54.0ms (1.4%)

rewrite19.0ms (0.5%)

simplify104.0ms (2.8%)

prune91.0ms (2.4%)

localize8.0ms (0.2%)

series57.0ms (1.5%)

rewrite32.0ms (0.9%)

simplify124.0ms (3.3%)

prune137.0ms (3.7%)

localize6.0ms (0.2%)

series34.0ms (0.9%)

rewrite9.0ms (0.2%)

simplify76.0ms (2%)

prune45.0ms (1.2%)

regimes537.0ms (14.3%)

simplify3.0ms (0.1%)

end78.0ms (2.1%)

Profiling