Details

sample41.0ms

Algorithm

intervals

Results

22.0ms

256×

body

valid

simplify4.1s

Counts

1 → 1

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	18	21
1	38	18
2	72	18
3	164	17
4	339	17
5	596	17
6	819	17
7	926	17
8	1192	17
9	1633	17
10	1697	17
11	1698	17
done	1698	17

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.7b

localize29.0ms

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)
6.6b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
15.5b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite8.0ms

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:

0.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
6.0ms	(/ 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)

series370.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
36.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
93.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
212.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify1.1s

Counts

71 → 71

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	129	985
1	246	962
2	572	857
3	1554	852
done	5000	849

prune357.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.1b	(fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525)
6.6b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
15.5b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

rewrite24.0ms

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 z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525)
20.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

series387.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
35.0ms	(fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525)
75.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
255.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

simplify1.1s

Counts

71 → 71

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	129	985
1	246	962
2	572	857
3	1554	852
done	5000	849

prune453.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525)
0.6b	(/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))
6.3b	(* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304)))
15.5b	(fma (* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

1.0ms	(fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525)
23.0ms	(/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))
28.0ms	(* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304)))
0.0ms	(fma (* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

series396.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525)
67.0ms	(/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))
92.0ms	(* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304)))
190.0ms	(fma (* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525) x)

simplify1.8s

Counts

103 → 103

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	170	1488
1	358	1308
2	800	1151
3	2085	1143
done	5000	1141

prune471.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

6.6b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
14.5b	(sqrt (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525))
14.5b	(sqrt (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525))
15.5b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (* (sqrt (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525)) (sqrt (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525))) x)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

8.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
2.0ms	(sqrt (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525))
2.0ms	(sqrt (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525))
0.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (* (sqrt (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525)) (sqrt (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525))) x)

series1.0s

Counts

4 → 12

Calls

4 calls:

492.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
163.0ms	(sqrt (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525))
140.0ms	(sqrt (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525))
236.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (* (sqrt (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525)) (sqrt (fma z (fma z 0.0692910599291889 0.4917317610505968) 0.279195317918525))) x)

simplify1.5s

Counts

81 → 81

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	153	1378
1	317	1180
2	806	1079
3	2124	1058
done	5000	1046

prune521.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes392.0ms

Accuracy

98.7% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 16.7b

bsearch218.0ms

Steps

Iters	Range		Point
10	1.0178730837508075e-23	7.806085722401822e-05	7.61910361890589e-05
11	-6291016968.746921	-5.960240395557237e-20	-220354992.6475145

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	28	47
1	40	39
done	40	39

end0.0ms

sample1.1s

Algorithm

intervals

Results

834.0ms

8000×

body

valid