Details

sample33.0ms

Algorithm

intervals

Results

16.0ms

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 (0.0%)

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: 23.7b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.0b	(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
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)))
22.9b	(/ (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))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 160

Calls

4 calls:

1.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
1.0ms	(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
11.0ms	(/ (- 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)))
4.0ms	(/ (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))

series572.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
61.0ms	(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
297.0ms	(/ (- 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)))
186.0ms	(/ (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))

simplify96.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	697	2838
1	2679	2705
2	5002	2703

prune685.0ms

Filtered

172 candidates to 132 candidates (23.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	167	5	172
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	169	5	174

Merged error: 0.0b

Counts

174 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
0.0b	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.0b	(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
22.9b	(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `fma-udef` `associate-/l`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 59

Calls

4 calls:

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

series400.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
27.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
60.0ms	(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
255.0ms	(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

simplify92.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	249	640
1	681	578
2	2808	578
3	5001	575

prune295.0ms

Filtered

71 candidates to 60 candidates (15.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	71	5	76

Merged error: 0.0b

Counts

76 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
0.2b	(/ (/ (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)) (- x 2.0))
0.3b	(/ 1 (/ (/ (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)) (- x 2.0)))
22.9b	(/ (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))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

790×	`times-frac`
484×	`*-un-lft-identity`
482×	`add-sqr-sqrt`
348×	`add-cube-cbrt`
90×	`associate-/r*`
67×	`distribute-lft-out--` `difference-of-squares`
40×	`associate-/r/` `associate-/l*`
34×	`div-inv`
32×	`add-exp-log`
20×	`add-cbrt-cube` `associate-/l/`
19×	`div-exp`
10×	`cbrt-undiv`
8×	`clear-num`
6×	`frac-2neg`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `remove-double-div` `add-log-exp`
3×	`rec-exp` `1-exp`
1×	`pow-flip` `fma-udef` `inv-pow`

Counts

4 → 496

Calls

4 calls:

1.0ms	(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
10.0ms	(/ (/ (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)) (- x 2.0))
26.0ms	(/ 1 (/ (/ (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)) (- x 2.0)))
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))

series777.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y)
220.0ms	(/ (/ (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)) (- x 2.0))
301.0ms	(/ 1 (/ (/ (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)) (- x 2.0)))
193.0ms	(/ (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))

simplify160.0ms

Algorithm

egg-herbie

Counts

508 → 508

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1494	10636
1	5001	10024

prune1.7s

Filtered

508 candidates to 306 candidates (39.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	507	1	508
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	508	5	513

Merged error: 0.0b

Counts

513 → 5

localize27.0ms

Local error

Found 4 expressions with local error:

7.3b	(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
7.3b	(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
18.7b	(/ (/ 1 (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)) (- x 2.0)))
22.9b	(/ (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))

rewrite532.0ms

Algorithm

rewrite-expression-head

Rules

9294×	`times-frac`
4602×	`add-sqr-sqrt`
4600×	`*-un-lft-identity`
3586×	`add-cube-cbrt`
2121×	`sqrt-prod`
507×	`distribute-lft-out--` `difference-of-squares`
258×	`div-inv`
133×	`associate-/r*`
88×	`associate-/r/`
59×	`associate-/l*`
45×	`add-exp-log`
31×	`div-exp`
27×	`add-cbrt-cube`
24×	`associate-/l/`
23×	`flip3--` `flip--`
16×	`cbrt-undiv`
6×	`pow1`
5×	`frac-2neg` `clear-num`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 2845

Calls

4 calls:

1.0ms	(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
2.0ms	(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
90.0ms	(/ (/ 1 (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)) (- x 2.0)))
5.0ms	(/ (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))

series851.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
111.0ms	(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
311.0ms	(/ (/ 1 (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)) (- x 2.0)))
315.0ms	(/ (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))

simplify1.6s

Algorithm

egg-herbie

Counts

2857 → 2857

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5001	118896

prune11.7s

Filtered

2857 candidates to 1520 candidates (46.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	2857	0	2857
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	2857	5	2862

Merged error: 0.0b

Counts

2862 → 5

regimes178.0ms

Accuracy

97.6% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 24.7b

bsearch254.0ms

Steps

Iters	Range		Point
8	1.762913208951331e+54	6.029997523963933e+57	4.0051275836208615e+55
10	-4.213223813186294e+37	-1.457896030987712e+24	-4.1667266857959677e+37

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	15
1	39	15

end0.0ms

sample709.0ms

Algorithm

intervals

Results

528.0ms

8014×

body

valid