Details

sample23.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify101.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	38	7
1	72	7
2	167	6
3	354	6
4	646	6
5	921	6
6	1060	6
7	1331	6
8	1792	6
9	1860	6
10	1861	6
11	1861	6

prune10.0ms

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: 16.6b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
4.3b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
16.8b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

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 (+ z 6.012459259764103) z 3.350343815022304)
1.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
3.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series257.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
27.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
66.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
140.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify113.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (105.0ms)

Iter	Nodes	Cost
0	244	408
1	754	361
2	3433	358
3	5002	356

prune216.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	66	5	71
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	67	6	73

Merged error: 0b

Counts

73 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma z 6.012459259764103 (fma z z 3.350343815022304))
0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
4.3b	(/ y (fma z 6.012459259764103 (fma z z 3.350343815022304)))
16.8b	(fma (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite6.0ms

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 z 6.012459259764103 (fma z z 3.350343815022304))
1.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
3.0ms	(/ y (fma z 6.012459259764103 (fma z z 3.350343815022304)))
1.0ms	(fma (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series271.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(fma z 6.012459259764103 (fma z z 3.350343815022304))
28.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
70.0ms	(/ y (fma z 6.012459259764103 (fma z z 3.350343815022304)))
149.0ms	(fma (/ y (fma z 6.012459259764103 (fma z z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify114.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	242	404
1	788	360
2	3510	357
3	5002	355

prune201.0ms

Filtered

71 candidates to 57 candidates (80.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	71	6	77

Merged error: 0b

Counts

77 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
0.6b	(/ 1 (fma z 6.012459259764103 (fma z z 3.350343815022304)))
4.2b	(* y (/ 1 (fma z 6.012459259764103 (fma z z 3.350343815022304))))
16.8b	(fma (* y (/ 1 (fma z 6.012459259764103 (fma z z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
22×	`add-cube-cbrt`
20×	`times-frac`
17×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
9×	`associate-*r/`
7×	`pow1` `associate-/l*`
6×	`associate-/r*`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `clear-num` `un-div-inv` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `frac-2neg` `1-exp` `cbrt-unprod` `fma-udef` `div-inv`
1×	`pow-flip` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 101

Calls

4 calls:

1.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
3.0ms	(/ 1 (fma z 6.012459259764103 (fma z z 3.350343815022304)))
10.0ms	(* y (/ 1 (fma z 6.012459259764103 (fma z z 3.350343815022304))))
1.0ms	(fma (* y (/ 1 (fma z 6.012459259764103 (fma z z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series291.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
45.0ms	(/ 1 (fma z 6.012459259764103 (fma z z 3.350343815022304)))
71.0ms	(* y (/ 1 (fma z 6.012459259764103 (fma z z 3.350343815022304))))
146.0ms	(fma (* y (/ 1 (fma z 6.012459259764103 (fma z z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify54.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	370	651
1	1482	560
2	5002	527

prune258.0ms

Filtered

113 candidates to 73 candidates (64.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	114	5	119

Merged error: 0b

Counts

119 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.8b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
20.6b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

253×	`*-un-lft-identity`
119×	`distribute-lft-out`
100×	`associate-l`
96×	`times-frac`
68×	`add-sqr-sqrt`
62×	`associate-r`
48×	`add-cube-cbrt`
16×	`associate-/l*`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1` `*-commutative` `unswap-sqr`
6×	`associate-/r*`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `associate-r/` `associate-l/` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `distribute-lft-in` `div-exp` `associate-/r/` `associate-/l/`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 215

Calls

4 calls:

6.0ms	(* (+ z 6.012459259764103) z)
11.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
19.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
38.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series300.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (+ z 6.012459259764103) z)
68.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
57.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
131.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify108.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	667	2200
1	3030	1971
2	5001	1946

prune355.0ms

Filtered

227 candidates to 123 candidates (54.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	227	5	232

Merged error: 0b

Counts

232 → 5

regimes200.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.0b

bsearch119.0ms

Steps

Iters	Range		Point
6	55266295.648746796	418884803.12646145	230627903.7052228
9	-3.532745445146559e+20	-21436759175312.676	-104844522695889.77

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	9
1	27	9

end0.0ms

sample498.0ms

Algorithm

intervals

Results

329.0ms

8000×

body

valid