Details

sample38.0ms

Algorithm

intervals

Results

26.0ms

256×

body

valid

simplify85.0ms

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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.9b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b

(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)

4.8b

(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))

19.0b

(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

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

Counts

3 → 49

Calls

3 calls:

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)

series225.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms

(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)

60.0ms

(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))

137.0ms

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

simplify103.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	232	361
1	733	322
2	3221	319
3	5002	317

prune234.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) x)
0.0b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
4.8b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
20.8b	(* (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

4.0ms	(+ (* (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) x)
0.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
2.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
8.0ms	(* (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))

series350.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(+ (* (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) x)
26.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
65.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
111.0ms	(* (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))

simplify52.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	430	759
1	1711	687
2	5003	684

prune348.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))) x)
0.0b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
0.1b	(* y (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)))
18.3b	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

4.0ms	(+ (* y (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))) x)
0.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
8.0ms	(* y (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)))
2.0ms	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

series360.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(+ (* y (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))) x)
26.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
120.0ms	(* y (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)))
72.0ms	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

simplify58.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	383	809
1	1529	730
2	5002	727

prune317.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y (sqrt (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))))
0.3b	(* (* y (sqrt (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)))) (sqrt (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))))
18.3b	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))
18.3b	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
37×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
32×	`associate-r`
28×	`sqrt-prod`
15×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
6×	`associate-/r` `associate-/l`
5×	`sqrt-div`
4×	`expm1-log1p-u` `associate-r/` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`unswap-sqr`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `*-commutative`
1×	`frac-times` `associate-*l/`

Counts

4 → 130

Calls

4 calls:

10.0ms	(* y (sqrt (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))))
24.0ms	(* (* y (sqrt (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)))) (sqrt (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))))
2.0ms	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))
2.0ms	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

series470.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(* y (sqrt (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))))
113.0ms	(* (* y (sqrt (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)))) (sqrt (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))))
73.0ms	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))
73.0ms	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

simplify73.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	481	1521
1	2082	1336
2	5002	1325

prune535.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes132.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.3b

bsearch161.0ms

Steps

Iters	Range		Point
8	32150385.06631287	1401143461023.1116	318335141.94349515
10	-1.6468299066896495e+28	-7.192008941699975e+16	-1.2169530213485977e+27

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	10
1	31	10

end0.0ms

sample910.0ms

Algorithm

intervals

Results

740.0ms

8000×

body

valid