Details

sample31.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify6.1s

Counts

1 → 1

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	18	21
1	38	18
2	72	18
3	167	17
4	415	17
5	944	17
6	1502	17
7	1837	17
8	2224	17
9	2802	17
10	3764	17
done	5000	17

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.1b

localize24.0ms

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)
3.8b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
15.7b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite17.0ms

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)
14.0ms	(/ 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)

series305.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
30.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
81.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
173.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify2.5s

Counts

71 → 71

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	129	985
1	251	962
2	768	866
3	3365	855
done	5000	851

prune397.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

15.5b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.5b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.5b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.7b	(fma (* (/ 1 (* (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)) (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (/ y (cbrt (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

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

Counts

4 → 49

Calls

4 calls:

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

series538.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
158.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
152.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
111.0ms	(fma (* (/ 1 (* (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)) (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (/ y (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify2.5s

Counts

61 → 61

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	93	1190
1	197	1155
2	615	1008
3	2889	803
done	5001	797

prune423.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

15.5b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.5b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.5b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.7b	(fma (* (/ 1 (* (expm1 (log1p (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (/ y (cbrt (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

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

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(fma (* (/ 1 (* (expm1 (log1p (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (/ y (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series1.5s

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
114.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
151.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.1s	(fma (* (/ 1 (* (expm1 (log1p (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (/ y (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify2.5s

Counts

61 → 61

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	98	1224
1	215	1161
2	671	1015
3	3202	809
done	5001	802

prune471.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
5.4b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
18.9b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite241.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

31.0ms	(* (+ z 6.012459259764103) z)
47.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
88.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
73.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series347.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (+ z 6.012459259764103) z)
72.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
61.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
150.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify2.0s

Counts

108 → 108

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	198	1630
1	571	1386
2	2947	1238
done	5001	1227

prune418.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes195.0ms

Accuracy

99.6% (0.1b remaining)

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

bsearch229.0ms

Steps

Iters	Range		Point
9	112329.15105430307	120598577249.33295	459337941.87337846
9	-2.766418797691212e+17	-2793354732730.816	-1.3422508003615704e+17

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	25	44
1	31	36
done	31	36

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

8000×

body

valid