Details

sample22.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify84.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

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

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.4b

localize12.0ms

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)
5.0b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
17.5b	(fma (/ y (fma (+ z 6.012459259764103) 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) 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)

series241.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
28.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
59.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
134.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify101.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (94.0ms)

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

prune265.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
0.2b	(/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))
5.1b	(* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304)))
17.5b	(fma (* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite15.0ms

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 (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
3.0ms	(/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))
8.0ms	(* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304)))
1.0ms	(fma (* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series263.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
39.0ms	(/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))
60.0ms	(* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304)))
137.0ms	(fma (* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify47.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	364	632
1	1472	543
2	5001	514

prune290.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
4.6b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
19.8b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
11×	`add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`fma-def` `times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 90

Calls

4 calls:

11.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
7.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
10.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
15.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series437.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
64.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
56.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
122.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify74.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	559	834
1	2525	723
2	5002	684

prune312.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* y (/ (* (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) 1) (fma (+ z 6.012459259764103) z 3.350343815022304))))
0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
0.1b	(* y (/ (* (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) 1) (fma (+ z 6.012459259764103) z 3.350343815022304)))
16.8b	(/ (* (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) 1) (fma (+ z 6.012459259764103) z 3.350343815022304))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
18×	`add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`prod-exp`
7×	`associate-r`
6×	`pow1` `times-frac` `div-exp` `add-log-exp`
5×	`cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `associate-l` `associate-/r*`
2×	`1-exp` `div-inv`
1×	`+-commutative` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+` `fma-udef` `associate-/l*` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

3.0ms	(+ x (* y (/ (* (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) 1) (fma (+ z 6.012459259764103) z 3.350343815022304))))
1.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
7.0ms	(* y (/ (* (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) 1) (fma (+ z 6.012459259764103) z 3.350343815022304)))
5.0ms	(/ (* (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) 1) (fma (+ z 6.012459259764103) z 3.350343815022304))

series361.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(+ x (* y (/ (* (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) 1) (fma (+ z 6.012459259764103) z 3.350343815022304))))
26.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
112.0ms	(* y (/ (* (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) 1) (fma (+ z 6.012459259764103) z 3.350343815022304)))
75.0ms	(/ (* (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) 1) (fma (+ z 6.012459259764103) z 3.350343815022304))

simplify55.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	410	742
1	1568	631
2	5001	623

prune274.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes124.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.2b

bsearch148.0ms

Steps

Iters	Range		Point
9	221841.602123724	1128751172469.6636	25166529335.741985
9	-2.7172054798100347e+70	-4.331403552570957e+63	-1.5803111416356161e+69

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	11
1	38	11
2	38	11

end0.0ms

sample488.0ms

Algorithm

intervals

Results

324.0ms

8000×

body

valid