Details

sample36.0ms

Algorithm

intervals

Results

19.0ms

256×

body

valid

simplify45.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	62	11
1	154	11
2	503	11
3	1840	11
4	5003	11

prune13.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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

Merged error: 25.9b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.1b	(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.3b	(/ (- x 2.0) (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
25.1b	(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

128×	`times-frac`
96×	`add-sqr-sqrt` `*-un-lft-identity`
68×	`add-cube-cbrt`
16×	`associate-/r*`
14×	`distribute-lft-out--` `difference-of-squares`
11×	`add-exp-log` `add-cbrt-cube`
8×	`div-inv` `associate-/l*`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `fma-udef` `associate-/l/`
1×	`flip3--` `div-sub` `associate-/r/` `flip--`

Counts

4 → 152

Calls

4 calls:

1.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
1.0ms	(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
9.0ms	(/ (- x 2.0) (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
3.0ms	(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

series497.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
37.0ms	(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
266.0ms	(/ (- x 2.0) (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
168.0ms	(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

simplify93.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	674	2773
1	2618	2640
2	5001	2638

prune692.0ms

Filtered

164 candidates to 126 candidates (76.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	158	6	164
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	159	7	166

Merged error: 0.0b

Counts

166 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.1b	(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
3.0b	(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
25.3b	(/ (/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

652×	`times-frac`
372×	`add-sqr-sqrt` `*-un-lft-identity`
280×	`add-cube-cbrt`
46×	`distribute-lft-out--` `difference-of-squares`
36×	`div-inv`
28×	`add-exp-log`
24×	`associate-/l*`
18×	`add-cbrt-cube`
17×	`div-exp`
16×	`associate-/r*`
9×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`div-sub` `associate-/l/`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `fma-udef`
1×	`flip3--` `associate-/r/` `flip--`

Counts

4 → 366

Calls

4 calls:

1.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
1.0ms	(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
7.0ms	(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
17.0ms	(/ (/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
34.0ms	(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
86.0ms	(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
275.0ms	(/ (/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))

simplify135.0ms

Algorithm

egg-herbie

Counts

378 → 378

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1715	8615
1	5002	8178

prune1.2s

Filtered

378 candidates to 215 candidates (56.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	378	0	378
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	378	7	385

Merged error: 0.0b

Counts

385 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

9.5b	(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
14.6b	(/ (/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
14.6b	(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
25.0b	(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

2116×	`times-frac`
1176×	`add-sqr-sqrt`
1175×	`*-un-lft-identity`
885×	`add-cube-cbrt`
693×	`sqrt-prod`
145×	`distribute-lft-out--` `difference-of-squares`
61×	`div-inv`
45×	`associate-/l*`
31×	`associate-/r*`
20×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `div-sub` `clear-num` `associate-/l/`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--`

Counts

4 → 941

Calls

4 calls:

5.0ms	(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
27.0ms	(/ (/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
7.0ms	(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
4.0ms	(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

series829.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
290.0ms	(/ (/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))) (/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
156.0ms	(/ (- x 2.0) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
282.0ms	(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

simplify422.0ms

Algorithm

egg-herbie

Counts

953 → 953

Iterations

Useful iterations: 1 (60.0ms)

Iter	Nodes	Cost
0	3104	33067
1	5001	32249

prune2.7s

Filtered

953 candidates to 426 candidates (44.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	953	0	953
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	953	7	960

Merged error: 0.0b

Counts

960 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.3b	(/ (- x 2.0) (/ (fma (fma 43.3400022514 (pow x 2) (fma 263.505074721 x (pow x 3))) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
7.8b	(fma 43.3400022514 (pow x 2) (fma 263.505074721 x (pow x 3)))
25.1b	(/ (fma (fma 43.3400022514 (pow x 2) (fma 263.505074721 x (pow x 3))) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

128×	`times-frac`
96×	`add-sqr-sqrt` `*-un-lft-identity`
68×	`add-cube-cbrt`
16×	`associate-/r*`
14×	`distribute-lft-out--` `difference-of-squares`
11×	`add-exp-log` `add-cbrt-cube`
8×	`div-inv` `associate-/l*`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `fma-udef` `associate-/l/`
1×	`flip3--` `div-sub` `associate-/r/` `flip--`

Counts

4 → 152

Calls

4 calls:

1.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
9.0ms	(/ (- x 2.0) (/ (fma (fma 43.3400022514 (pow x 2) (fma 263.505074721 x (pow x 3))) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
1.0ms	(fma 43.3400022514 (pow x 2) (fma 263.505074721 x (pow x 3)))
3.0ms	(/ (fma (fma 43.3400022514 (pow x 2) (fma 263.505074721 x (pow x 3))) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

series483.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
272.0ms	(/ (- x 2.0) (/ (fma (fma 43.3400022514 (pow x 2) (fma 263.505074721 x (pow x 3))) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
26.0ms	(fma 43.3400022514 (pow x 2) (fma 263.505074721 x (pow x 3)))
158.0ms	(/ (fma (fma 43.3400022514 (pow x 2) (fma 263.505074721 x (pow x 3))) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

simplify93.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	664	2998
1	2638	2853
2	5002	2851

prune679.0ms

Filtered

164 candidates to 123 candidates (75.0%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	164	7	171

Merged error: 0.0b

Counts

171 → 7

regimes318.0ms

Accuracy

96.8% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 24.6b

bsearch247.0ms

Steps

Iters	Range		Point
8	1.8441495130057392e+61	2.911642662717668e+65	2.3624428090260776e+63
10	-4.865547021985336e+82	-4.3953033502493043e+71	-5.715916696131551e+71

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	16
1	42	16

end0.0ms

sample827.0ms

Algorithm

intervals

Results

636.0ms

8011×

body

valid

Details

sample36.0ms

simplify45.0ms

prune13.0ms

localize24.0ms

rewrite20.0ms

series497.0ms

simplify93.0ms

prune692.0ms

localize20.0ms

rewrite50.0ms

series420.0ms

simplify135.0ms

prune1.2s

localize22.0ms

rewrite134.0ms

series829.0ms

simplify422.0ms

prune2.7s

localize22.0ms

rewrite20.0ms

series483.0ms

simplify93.0ms

prune679.0ms

regimes318.0ms

bsearch247.0ms

simplify1.0ms

end0.0ms

sample827.0ms

Profiling