Details

sample28.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	2529
11	2529
10	2182
9	1689
8	1203
7	1037
6	864
5	633
4	359
3	162
2	70
1	38
0	18

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.1b	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
2.8b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
16.8b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) x)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `fma-udef` `associate-/l`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 63

Calls

4 calls:

0.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.0ms	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
8.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) x)

series343.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
34.0ms	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
76.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
206.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) x)

simplify2.0s

Counts

75 → 75

Iterations

Iter	Nodes
done	5003
3	2593
2	743
1	270
0	137

prune494.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))
0.1b	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
3.0b	(* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304)))
16.8b	(fma (* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) x)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`times-frac` `add-cube-cbrt`
17×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-l` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `fma-udef` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 95

Calls

4 calls:

4.0ms	(/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
25.0ms	(* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304)))
1.0ms	(fma (* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) x)

series333.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))
37.0ms	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
80.0ms	(* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304)))
165.0ms	(fma (* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) x)

simplify1.9s

Counts

107 → 107

Iterations

Iter	Nodes
done	5001
3	3108
2	1056
1	383
0	176

prune647.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* z 0.0692910599291889) 0.4917317610505968)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
3.4b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
19.5b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `unswap-sqr` `associate-/l/`
1×	`distribute-rgt-in` `+-commutative` `clear-num` `sum-log` `fma-def` `frac-2neg` `distribute-lft-in` `div-inv` `associate-/l*`

Counts

4 → 91

Calls

4 calls:

6.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
29.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
64.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
48.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series404.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (* z 0.0692910599291889) 0.4917317610505968)
126.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
69.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
161.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify2.0s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	1985
1	534
0	187

prune598.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

15.6b	(* (/ y (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
15.9b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.9b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.9b	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite301.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
28×	`times-frac`
25×	`add-exp-log`
24×	`associate-r`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`cbrt-prod` `cbrt-div`
18×	`add-cbrt-cube`
15×	`associate-l`
10×	`flip3-+` `associate-/r/` `flip-+`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `unswap-sqr`
5×	`frac-times`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-l/` `associate-r/`
2×	`div-inv`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 120

Calls

4 calls:

275.0ms	(* (/ y (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
12.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
7.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
7.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series640.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(* (/ y (* (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
151.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
150.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
142.0ms	(cbrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify2.6s

Counts

132 → 132

Iterations

Iter	Nodes
done	5000
2	2754
1	709
0	233

prune1.0s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes342.0ms

Accuracy

96.4% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 16.1b

bsearch197.0ms

Steps

Iters	Range		Point
8	6.0329627772416755e-24	8.874871730790149e-20	8.728612712058619e-20
8	-1019421082.415905	-2300368.468387598	-248713679.72383326

simplify33.0ms

Iterations

Iter	Nodes
done	40
1	40
0	28

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.3s

8000×

body

valid