Details

analyze300.0ms (11.6%)

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
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
49.9%	49.9%	0.2%	8
49.9%	49.9%	0.2%	9
49.9%	49.9%	0.2%	10
74.8%	24.9%	0.2%	11
74.8%	24.9%	0.2%	12
74.8%	24.9%	0.2%	13
74.8%	24.9%	0.2%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample903.0ms (34.9%)

Infinites

24.2% of outputs are infinite.

Results

789.0ms

8256×

body

128

valid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify64.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

783×	`fma-neg_binary64`
721×	`fma-def_binary64`
244×	`cancel-sign-sub-inv_binary64`
187×	`distribute-rgt-in_binary64`
138×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	17	13
2	39	13
3	98	13
4	258	11
5	542	11
6	1019	11
7	1302	11
8	1414	11
9	1470	11
10	1476	11
11	1481	11
12	1481	11
13	1408	11

prune3.0ms (0.1%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	5.2b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
▶	4.5b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 46 computations (39.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 z t))
✓	0.0b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	5.3b	(/.f64 (*.f64 y (-.f64 z t)) a)

series53.0ms (2.1%)

Counts

3 → 144

Calls

3 calls:

27.0ms	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
19.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
6.0ms	(*.f64 y (-.f64 z t))

rewrite28.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
39×	`prod-diff_binary64`
37×	`add-cube-cbrt_binary64`
15×	`times-frac_binary64`

Counts

3 → 121

Calls

3 calls:

8.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
6.0ms	(*.f64 y (-.f64 z t))
5.0ms	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

simplify131.0ms (5%)

Algorithm

1×	egg-herbie

Rules

753×	`fma-def_binary64`
746×	`times-frac_binary64`
299×	`exp-prod_binary64`
213×	`cancel-sign-sub-inv_binary64`
208×	`fma-neg_binary64`

Counts

265 → 195

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	268	3653
1	555	3282
2	2075	2974
3	4562	2896
4	4877	2896

prune118.0ms (4.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	191	4	195
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	191	6	197

Error

Counts

197 → 6

Alt Table

Status	Error	Program
▶	1.6b	(fma.f64 (/.f64 y a) (fma.f64 -1 z t) x)
	30.2b	(/.f64 y (/.f64 a (-.f64 t z)))
	36.4b	(-.f64 x (/.f64 (/.f64 (*.f64 y (-.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a)))
	4.6b	(-.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
	5.2b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
✓	4.5b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 3979 to 1006 computations (74.7% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.6b	(fma.f64 (/.f64 y a) (fma.f64 -1 z t) x)

series25.0ms (1%)

Counts

1 → 60

Calls

1 calls:

25.0ms

(fma.f64 (/.f64 y a) (fma.f64 -1 z t) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (/.f64 y a) (fma.f64 -1 z t) x)

simplify73.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

402×	`distribute-rgt-neg-out_binary64`
399×	`distribute-lft-neg-out_binary64`
377×	`distribute-rgt-in_binary64`
373×	`distribute-lft-in_binary64`
227×	`distribute-rgt-out_binary64`

Counts

70 → 33

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	875
1	79	750
2	165	733
3	440	733
4	2134	733
5	4825	733
6	5128	733

prune22.0ms (0.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	33	6	39

Error

Counts

39 → 6

Alt Table

Status	Error	Program
✓	1.6b	(fma.f64 (/.f64 y a) (fma.f64 -1 z t) x)
	30.2b	(/.f64 y (/.f64 a (-.f64 t z)))
	36.4b	(-.f64 x (/.f64 (/.f64 (*.f64 y (-.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a)))
▶	4.6b	(-.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
	5.2b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
✓	4.5b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 538 to 214 computations (60.2% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (-.f64 z t))
✓	0.0b	(-.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
✓	5.4b	(.f64 (.f64 y (-.f64 z t)) (/.f64 1 a))

series45.0ms (1.8%)

Counts

2 → 108

Calls

2 calls:

27.0ms	(-.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
18.0ms	(.f64 (.f64 y (-.f64 z t)) (/.f64 1 a))

rewrite15.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
13×	`associate-r_binary64`
12×	`prod-exp_binary64`
11×	`*-un-lft-identity_binary64`

Counts

2 → 64

Calls

2 calls:

9.0ms	(.f64 (.f64 y (-.f64 z t)) (/.f64 1 a))
3.0ms	(-.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))

simplify62.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

640×	`distribute-rgt-in_binary64`
634×	`distribute-lft-in_binary64`
446×	`fma-def_binary64`
168×	`distribute-rgt-neg-in_binary64`
153×	`cancel-sign-sub-inv_binary64`

Counts

172 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	151	2142
1	384	2076
2	1335	1918
3	5314	1918

prune131.0ms (5.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	191	6	197

Error

Counts

197 → 6

Alt Table

Status	Error	Program
✓	1.6b	(fma.f64 (/.f64 y a) (fma.f64 -1 z t) x)
	30.2b	(/.f64 y (/.f64 a (-.f64 t z)))
	36.4b	(-.f64 x (/.f64 (/.f64 (*.f64 y (-.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a)))
✓	4.6b	(-.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
▶	5.2b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
✓	4.5b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 3570 to 1328 computations (62.8% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) a)
✓	5.2b	(fma.f64 y (/.f64 (-.f64 t z) a) x)

series33.0ms (1.3%)

Counts

2 → 88

Calls

2 calls:

24.0ms	(fma.f64 y (/.f64 (-.f64 t z) a) x)
9.0ms	(/.f64 (-.f64 t z) a)

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/l*_binary64`

Counts

2 → 50

Calls

2 calls:

4.0ms	(/.f64 (-.f64 t z) a)
0.0ms	(fma.f64 y (/.f64 (-.f64 t z) a) x)

simplify89.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

696×	`distribute-rgt-in_binary64`
684×	`distribute-lft-in_binary64`
583×	`times-frac_binary64`
453×	`fma-def_binary64`
215×	`div-sub_binary64`

Counts

138 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	1607
1	238	1462
2	525	1460
3	1333	1460
4	4886	1460
5	4983	1460

prune42.0ms (1.6%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	78	6	84

Error

Counts

84 → 6

Alt Table

Status	Error	Program
✓	1.6b	(fma.f64 (/.f64 y a) (fma.f64 -1 z t) x)
	30.2b	(/.f64 y (/.f64 a (-.f64 t z)))
	36.4b	(-.f64 x (/.f64 (/.f64 (*.f64 y (-.f64 z t)) (sqrt.f64 a)) (sqrt.f64 a)))
✓	4.6b	(-.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 a)))
✓	5.2b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
✓	4.5b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 1131 to 313 computations (72.3% saved)

regimes335.0ms (13%)

Accuracy

Total 0.3b remaining (97%)

Threshold costs 0.3b (97%)

Counts

28 → 3

Compiler

Compiled 3655 to 2487 computations (32% saved)

bsearch1.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	56
1	30	56
2	43	56
3	57	56
4	69	56
5	83	56
6	89	56
7	85	56

end75.0ms (2.9%)

Compiler: Compiled 173 to 94 computations (45.7% saved)

Details

analyze300.0ms (11.6%)

sample903.0ms (34.9%)

simplify64.0ms (2.5%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series53.0ms (2.1%)

rewrite28.0ms (1.1%)

simplify131.0ms (5%)

prune118.0ms (4.6%)

localize7.0ms (0.3%)

series25.0ms (1%)

rewrite1.0ms (0%)

simplify73.0ms (2.8%)

prune22.0ms (0.9%)

localize7.0ms (0.3%)

series45.0ms (1.8%)

rewrite15.0ms (0.6%)

simplify62.0ms (2.4%)

prune131.0ms (5.1%)

localize6.0ms (0.2%)

series33.0ms (1.3%)

rewrite7.0ms (0.3%)

simplify89.0ms (3.4%)

prune42.0ms (1.6%)

regimes335.0ms (13%)

bsearch1.0ms (0%)

simplify5.0ms (0.2%)

end75.0ms (2.9%)

Profiling