Details

analyze99.0ms (5.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	50%	6.3%	6
43.7%	43.7%	12.6%	7
59.3%	26.5%	14.1%	8
59.3%	22.6%	18%	9
67.1%	13.7%	19.2%	10
67.1%	11.5%	21.4%	11
71%	6.9%	22%	12
71%	5.8%	23.2%	13
73%	3.5%	23.5%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample748.0ms (38.4%)

Results

699.0ms	8256×	body	128	valid
13.0ms	178×	body	128	invalid

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	8	7
2	8	7

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

22.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	22.5b	(sqrt.f64 (fma.f64 x x y))

Compiler

Compiled 27 to 15 computations (44.4% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	20.9b	(sqrt.f64 (fma.f64 x x y))

series17.0ms (0.9%)

Counts

1 → 16

Calls

1 calls:

17.0ms

(sqrt.f64 (fma.f64 x x y))

rewrite1.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`sqrt-prod_binary64`
3×	`add-sqr-sqrt_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-cube-cbrt_binary64`
2×	`pow1_binary64`

Counts

1 → 15

Calls

1 calls:

1.0ms

(sqrt.f64 (fma.f64 x x y))

simplify55.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

653×	`times-frac_binary64`
423×	`associate-/l*_binary64`
423×	`cancel-sign-sub-inv_binary64`
379×	`unswap-sqr_binary64`
345×	`fma-neg_binary64`

Counts

31 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	471
1	174	463
2	445	436
3	1589	434
4	4455	434
5	5259	434

prune26.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	42	3	45
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	42	4	46

Error

Counts

46 → 4

Alt Table

Status	Error	Program
▶	23.1b	(*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x y))) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
✓	22.5b	(sqrt.f64 (fma.f64 x x y))
	40.3b	(-.f64 (.f64 (/.f64 y x) (+.f64 (.f64 (/.f64 y x) (/.f64 1/8 x)) -1/2)) x)
	42.2b	x

Compiler

Compiled 649 to 331 computations (49% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (cbrt.f64 (fma.f64 x x y)))
✓	0.3b	(*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x y))) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
✓	21.8b	(cbrt.f64 (fma.f64 x x y))

series96.0ms (4.9%)

Counts

3 → 72

Calls

3 calls:

41.0ms	(*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x y))) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
27.0ms	(cbrt.f64 (fma.f64 x x y))
27.0ms	(sqrt.f64 (cbrt.f64 (fma.f64 x x y)))

rewrite14.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-sqr-sqrt_binary64`
26×	`cbrt-prod_binary64`
22×	`sqrt-prod_binary64`
15×	`unswap-sqr_binary64`
12×	`fabs-mul_binary64`

Counts

3 → 84

Calls

3 calls:

6.0ms	(*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x y))) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
1.0ms	(sqrt.f64 (cbrt.f64 (fma.f64 x x y)))
1.0ms	(cbrt.f64 (fma.f64 x x y))

simplify162.0ms (8.3%)

Algorithm

1×	egg-herbie

Rules

619×	`times-frac_binary64`
382×	`cancel-sign-sub-inv_binary64`
343×	`associate-r_binary64`
290×	`fma-neg_binary64`
267×	`unswap-sqr_binary64`

Counts

156 → 200

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	294	4986
1	799	4590
2	2535	4254
3	4698	3777
4	4957	3777
5	4934	3777

prune114.0ms (5.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	239	4	243

Error

Counts

243 → 4

Alt Table

Status	Error	Program
✓	23.1b	(*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x y))) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
✓	22.5b	(sqrt.f64 (fma.f64 x x y))
▶	40.3b	(-.f64 (.f64 (/.f64 y x) (+.f64 (.f64 (/.f64 y x) (/.f64 1/8 x)) -1/2)) x)
	42.2b	x

Compiler

Compiled 6468 to 2836 computations (56.2% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (/.f64 y x) (+.f64 (.f64 (/.f64 y x) (/.f64 1/8 x)) -1/2)) x)
✓	0.1b	(.f64 (/.f64 y x) (+.f64 (.f64 (/.f64 y x) (/.f64 1/8 x)) -1/2))
✓	0.2b	(*.f64 (/.f64 y x) (/.f64 1/8 x))

series77.0ms (3.9%)

Counts

3 → 72

Calls

3 calls:

29.0ms	(.f64 (/.f64 y x) (+.f64 (.f64 (/.f64 y x) (/.f64 1/8 x)) -1/2))
28.0ms	(*.f64 (/.f64 y x) (/.f64 1/8 x))
19.0ms	(-.f64 (.f64 (/.f64 y x) (+.f64 (.f64 (/.f64 y x) (/.f64 1/8 x)) -1/2)) x)

rewrite34.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
32×	`times-frac_binary64`
27×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`
26×	`associate-l_binary64`

Counts

3 → 114

Calls

3 calls:

10.0ms	(-.f64 (.f64 (/.f64 y x) (+.f64 (.f64 (/.f64 y x) (/.f64 1/8 x)) -1/2)) x)
9.0ms	(.f64 (/.f64 y x) (+.f64 (.f64 (/.f64 y x) (/.f64 1/8 x)) -1/2))
8.0ms	(*.f64 (/.f64 y x) (/.f64 1/8 x))

simplify108.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

724×	`fma-def_binary64`
307×	`fma-neg_binary64`
291×	`times-frac_binary64`
285×	`associate-/r*_binary64`
219×	`associate-l_binary64`

Counts

186 → 197

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	3277
1	677	3046
2	2966	3013
3	4634	3013
4	4891	3013

prune93.0ms (4.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	197	4	201

Error

Counts

201 → 4

Alt Table

Status	Error	Program
✓	23.1b	(*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x y))) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
✓	22.5b	(sqrt.f64 (fma.f64 x x y))
✓	40.3b	(-.f64 (.f64 (/.f64 y x) (+.f64 (.f64 (/.f64 y x) (/.f64 1/8 x)) -1/2)) x)
▶	42.2b	x

Compiler

Compiled 4641 to 2195 computations (52.7% saved)

localize1.0ms (0%)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	3	3
Total	4	4

Error

Counts

4 → 4

Alt Table

Status	Error	Program
✓	23.1b	(*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x x y))) (sqrt.f64 (cbrt.f64 (fma.f64 x x y))))
✓	22.5b	(sqrt.f64 (fma.f64 x x y))
✓	40.3b	(-.f64 (.f64 (/.f64 y x) (+.f64 (.f64 (/.f64 y x) (/.f64 1/8 x)) -1/2)) x)
✓	42.2b	x

Compiler

Compiled 42 to 23 computations (45.2% saved)

regimes206.0ms (10.6%)

Accuracy

Total 0.1b remaining (94.4%)

Threshold costs 0.1b (94.4%)

Counts

28 → 3

Compiler

Compiled 1639 to 956 computations (41.7% saved)

bsearch13.0ms (0.7%)

Steps

Iters	Range		Point
5	5.200113852364843e+118	1.6897313327594673e+125	1.1157196809697832e+125
2	-1.1671965581043208e+149	-1.1990725939032492e+147	-3.787085724672916e+148

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	40
1	23	40
2	28	40
3	30	40
4	31	40
5	31	40

end55.0ms (2.8%)

Compiler: Compiled 102 to 59 computations (42.2% saved)

Details

analyze99.0ms (5.1%)

sample748.0ms (38.4%)

simplify6.0ms (0.3%)

prune2.0ms (0.1%)

localize3.0ms (0.2%)

series17.0ms (0.9%)

rewrite1.0ms (0.1%)

simplify55.0ms (2.8%)

prune26.0ms (1.3%)

localize7.0ms (0.3%)

series96.0ms (4.9%)

rewrite14.0ms (0.7%)

simplify162.0ms (8.3%)

prune114.0ms (5.8%)

localize7.0ms (0.4%)

series77.0ms (3.9%)

rewrite34.0ms (1.7%)

simplify108.0ms (5.5%)

prune93.0ms (4.8%)

localize1.0ms (0%)

prune2.0ms (0.1%)

regimes206.0ms (10.6%)

bsearch13.0ms (0.7%)

simplify3.0ms (0.2%)

end55.0ms (2.8%)

Profiling