Details

sample54.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify678.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
4	2001
3	641
2	119
1	36
0	15

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
586×	`*-un-lft-identity`
340×	`add-sqr-sqrt` `add-cube-cbrt`
123×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
13×	`add-log-exp`
10×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`sum-log`
4×	`pow1` `insert-posit16` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 469

Calls

4 calls:

131.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
315.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
447.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
225.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
161.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
203.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
113.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.5s

Counts

481 → 481

Iterations

Iter	Nodes
done	2005
2	2005
1	1435
0	606

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (+ (+ alpha beta) (* 2 1)))
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
586×	`*-un-lft-identity`
340×	`add-sqr-sqrt` `add-cube-cbrt`
123×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
13×	`add-log-exp`
10×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`sum-log`
4×	`pow1` `insert-posit16` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+r+`

Counts

4 → 469

Calls

4 calls:

80.0ms	(+ 1.0 (+ (+ alpha beta) (* 2 1)))
328.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
479.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))
273.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series558.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ 1.0 (+ (+ alpha beta) (* 2 1)))
226.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
211.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))
106.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.9s

Counts

481 → 481

Iterations

Iter	Nodes
done	2005
2	2005
1	1443
0	606

prune2.8s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) (* 2 1)))
0.0b	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1)))
0.1b	(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))
2.5b	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2 1))))

rewrite953.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
65×	`*-un-lft-identity`
54×	`add-exp-log`
49×	`add-sqr-sqrt`
42×	`add-cube-cbrt`
34×	`add-cbrt-cube`
24×	`div-exp`
18×	`associate-/r/`
15×	`associate-r`
14×	`cbrt-undiv`
13×	`flip3-+` `flip-+` `associate-/l*`
12×	`prod-exp`
11×	`distribute-lft-out`
10×	`associate-/r*`
9×	`div-inv`
7×	`pow1` `associate-/l/`
6×	`cbrt-unprod`
4×	`frac-times` `rec-exp` `1-exp` `associate-l` `associate-*l/` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `unswap-sqr`
2×	`associate-*r/` `un-div-inv`
1×	`pow-prod-down` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 185

Calls

4 calls:

46.0ms	(/ 1 (+ (+ alpha beta) (* 2 1)))
203.0ms	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1)))
367.0ms	(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))
333.0ms	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2 1))))

series639.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ 1 (+ (+ alpha beta) (* 2 1)))
213.0ms	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1)))
248.0ms	(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))
115.0ms	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2 1))))

simplify1.3s

Counts

197 → 197

Iterations

Iter	Nodes
done	2000
2	2000
1	850
0	288

prune1.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.8b

localize90.0ms

Local error

Found 4 expressions with local error:

1.1b	(/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) 1) (sqrt (+ (+ alpha beta) (* 2 1))))
2.7b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.7b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.7b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite358.0ms

Algorithm

rewrite-expression-head

Rules

63×	`times-frac`
43×	`*-un-lft-identity`
37×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`sqrt-prod`
18×	`add-exp-log`
12×	`cbrt-prod`
11×	`add-cbrt-cube`
9×	`div-exp`
8×	`div-inv`
7×	`associate-/l*`
6×	`cbrt-div` `associate-/r*`
5×	`cbrt-undiv`
4×	`pow1` `flip3-+` `flip-+` `insert-posit16` `add-log-exp`
3×	`pow1/3` `distribute-lft-out`
2×	`sqrt-div` `1-exp` `prod-exp` `associate-/r/`
1×	`clear-num` `frac-2neg` `cbrt-unprod` `associate-/l/`

Counts

4 → 122

Calls

4 calls:

163.0ms	(/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) 1) (sqrt (+ (+ alpha beta) (* 2 1))))
48.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
69.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
75.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series577.0ms

Counts

4 → 12

Calls

4 calls:

296.0ms	(/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) 1) (sqrt (+ (+ alpha beta) (* 2 1))))
89.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
100.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
91.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.4s

Counts

134 → 134

Iterations

Iter	Nodes
done	2001
3	2001
2	1727
1	658
0	271

prune1.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.8b

regimes129.0ms

Accuracy

53.7% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.6b

bsearch94.0ms

Steps

Iters	Range		Point
7	7.759695545517782e+161	7.872712566567013e+163	8.836463279649086e+162

simplify9.0ms

Iterations

Iter	Nodes
done	36
1	36
0	27

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.2s	8000×	body	80	valid
299.0ms	8000×	pre	80	true