Details

sample26.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify93.0ms

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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.4b

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)
4.1b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
15.8b	(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)

series246.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
29.0ms	(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)

simplify104.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (98.0ms)

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

prune259.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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)
0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
4.1b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
17.9b	(* (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))

rewrite18.0ms

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:

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

series341.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(+ (* (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) x)
25.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
62.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
109.0ms	(* (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))

simplify51.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (40.0ms)

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

prune330.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize12.0ms

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)
0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
0.2b	(* y (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)))
14.9b	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

rewrite18.0ms

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:

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

series359.0ms

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)
31.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
112.0ms	(* y (/ (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))

simplify57.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (40.0ms)

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

prune312.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* y (/ (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))
14.3b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
14.3b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
14.3b	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

268×	`times-frac`
171×	`add-sqr-sqrt`
145×	`add-cube-cbrt` `*-un-lft-identity`
143×	`sqrt-prod`
136×	`associate-r`
15×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `div-inv`
7×	`unswap-sqr`
6×	`associate-/r*`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 235

Calls

4 calls:

38.0ms	(* y (/ (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))
1.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
2.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
4.0ms	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* y (/ (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))
60.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
53.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
139.0ms	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))

simplify111.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	969	2936
1	4586	2557
2	5003	2544

prune663.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes128.0ms

Accuracy

97.7% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 15.8b

bsearch115.0ms

Steps

Iters	Range		Point
8	6.998959319022454e-10	4.5131138850246713e-07	4.469388652929308e-07
7	-1.2975233664675797e+155	-3.253945601927041e+153	-1.2713952720505764e+154

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	15
1	33	15

end0.0ms

sample505.0ms

Algorithm

intervals

Results

338.0ms

8000×

body

valid