Details

sample142.0ms

Algorithm

intervals

Results

47.0ms	367×	body	80	valid
37.0ms	320×	body	80	nan

simplify5.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	24
1	37	24
2	84	24
3	237	24
4	510	24
5	937	24
6	1858	24
7	3759	24
done	5000	24

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 0.5) (log x))
0.2b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.2b	(- (* (- x 0.5) (log x)) x)
4.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`log-prod`
12×	`associate--l+`
11×	`add-log-exp`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
8×	`add-exp-log` `associate-+l+` `add-cbrt-cube`
7×	`pow1`
5×	`associate-l`
4×	`associate-r`
3×	`associate-/r` `associate-/l`
2×	`sub-neg` `flip3--` `flip3-+` `diff-log` `associate-*l/` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `log-pow` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

37.0ms	(* (- x 0.5) (log x))
101.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
35.0ms	(- (* (- x 0.5) (log x)) x)
109.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series2.0s

Counts

4 → 12

Calls

4 calls:

426.0ms	(* (- x 0.5) (log x))
689.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
790.0ms	(- (* (- x 0.5) (log x)) x)
110.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify3.7s

Counts

110 → 110

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	213	1655
1	501	1589
2	1406	1469
3	4870	1419
done	5001	1419

prune688.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.6b	(* (cbrt x) (cbrt x))
4.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
22×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`times-frac`
8×	`add-exp-log` `pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-cbrt-cube`
4×	`add-log-exp` `unswap-sqr`
3×	`associate-/r` `associate-/l`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `flip3-+` `pow-plus` `div-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `flip-+` `div-inv`

Counts

4 → 91

Calls

4 calls:

3.0ms	(cbrt x)
1.0ms	(cbrt x)
11.0ms	(* (cbrt x) (cbrt x))
80.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.1s

Counts

4 → 12

Calls

4 calls:

324.0ms	(cbrt x)
307.0ms	(cbrt x)
308.0ms	(* (cbrt x) (cbrt x))
118.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify2.4s

Counts

103 → 103

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	132	1157
1	285	1039
2	840	967
3	2923	932
done	5000	929

prune801.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (log (cbrt x)) (- x 0.5)))
0.5b	(cbrt x)
0.5b	(cbrt x)
4.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

26×	`distribute-rgt-in` `distribute-lft-in`
24×	`associate-+l+` `log-prod`
22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`cbrt-prod`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-+r+` `flip3--` `associate-r/` `associate-l/` `frac-add` `flip--`
3×	`associate-/r` `associate-/l`
2×	`sub-neg` `flip3-+` `pow1/3` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 94

Calls

4 calls:

36.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (log (cbrt x)) (- x 0.5)))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
77.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series2.2s

Counts

4 → 12

Calls

4 calls:

1.4s	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (log (cbrt x)) (- x 0.5)))
302.0ms	(cbrt x)
324.0ms	(cbrt x)
137.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.3s

Counts

106 → 106

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	213	1920
1	579	1724
2	2045	1486
done	5001	1475

prune813.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.2b	(- (* (- x 0.5) (log x)) x)
0.3b	(/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))
4.1b	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
62×	`*-un-lft-identity`
60×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`associate-/r*`
17×	`add-exp-log`
12×	`log-prod` `associate--l+`
11×	`associate-/r/` `add-cbrt-cube` `add-log-exp`
8×	`associate-+l+` `div-exp`
6×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+` `div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv`
2×	`sub-neg` `rec-exp` `frac-2neg` `diff-log` `1-exp` `clear-num` `sum-log`
1×	`+-commutative` `associate-+l-` `flip3--` `pow-flip` `flip--` `distribute-lft-out` `inv-pow`

Counts

4 → 153

Calls

4 calls:

71.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
22.0ms	(- (* (- x 0.5) (log x)) x)
57.0ms	(/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))
47.0ms	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

series1.6s

Counts

4 → 12

Calls

4 calls:

676.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
636.0ms	(- (* (- x 0.5) (log x)) x)
121.0ms	(/ 1 (/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333)))
174.0ms	(/ x (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333))

simplify1.2s

Counts

165 → 165

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	305	3792
1	719	3526
2	1773	3252
done	5001	3148

prune702.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 1.2b

regimes630.0ms

Accuracy

56.2% (1.8b remaining)

Error of 3.7b against oracle of 1.8b and baseline of 6.0b

bsearch78.0ms

Steps

Iters	Range		Point
5	4.022397810881141e+88	1.1923880006824921e+89	1.176380466602636e+89

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	67
1	65	67
done	65	67

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.9s	11710×	body	80	nan
1.4s	11637×	body	80	valid