Details

sample23.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify90.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

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

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.9b

localize13.0ms

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)
2.4b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
17.2b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite4.0ms

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

series260.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
32.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
61.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
145.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify108.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	245	408
1	760	361
2	3482	358
3	5001	356

prune282.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))
15.7b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.7b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
17.2b	(fma (* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
58×	`times-frac`
38×	`*-un-lft-identity`
35×	`sqrt-prod`
32×	`add-cube-cbrt`
26×	`add-exp-log`
22×	`associate-r` `associate-l`
16×	`add-cbrt-cube`
15×	`unswap-sqr`
8×	`pow1` `div-exp` `prod-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `div-inv`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef`

Counts

4 → 125

Calls

4 calls:

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

series250.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))
59.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
58.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
89.0ms	(fma (* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify75.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	569	1489
1	2571	1300
2	5001	1177

prune461.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

1.9b	(exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))
2.4b	(/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304))))
16.3b	(log (fma (+ z 6.012459259764103) z 3.350343815022304))
17.2b	(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

2.0ms	(exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))
4.0ms	(/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304))))
1.0ms	(log (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series296.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))
61.0ms	(/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304))))
72.0ms	(log (fma (+ z 6.012459259764103) z 3.350343815022304))
142.0ms	(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify142.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (126.0ms)

Iter	Nodes	Cost
0	352	720
1	1070	618
2	4365	587
3	5001	583

prune523.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

16.3b	(log (fma (+ z 6.012459259764103) z 3.350343815022304))
17.2b	(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
17.2b	(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
17.2b	(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `fma-udef`
1×	`rem-log-exp` `log-pow`

Counts

4 → 44

Calls

4 calls:

1.0ms	(log (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
0.0ms	(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
0.0ms	(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series477.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(log (fma (+ z 6.012459259764103) z 3.350343815022304))
136.0ms	(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
134.0ms	(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
136.0ms	(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify47.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	167	482
1	405	416
2	1297	411
3	5001	396

prune295.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0b

regimes247.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.9b

bsearch163.0ms

Steps

Iters	Range		Point
10	449.39022747116985	4206327787051213.0	202926169.68211037
10	-4.7805415039378135e+20	-854233.3594044615	-3.359837486116857e+16

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	9
1	28	9

end0.0ms

sample534.0ms

Algorithm

intervals

Results

363.0ms

8000×

body

valid