Details

sample124.0ms

Algorithm

intervals

Results

49.0ms	392×	body	80	nan
36.0ms	357×	body	80	valid

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	4006
4	855
3	244
2	84
1	37
0	20

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.2b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (- x 0.5) (log x)) x)
0.2b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.2b	(* (- x 0.5) (log x))
4.8b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite151.0ms

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×	`associate-+l+` `add-cbrt-cube` `add-exp-log`
7×	`pow1`
5×	`associate-l`
4×	`associate-r`
3×	`associate-/r` `associate-/l`
2×	`sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `associate-*l/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `associate-+l-` `cbrt-unprod` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

13.0ms	(- (* (- x 0.5) (log x)) x)
47.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
28.0ms	(* (- x 0.5) (log x))
61.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.8s

Counts

4 → 12

Calls

4 calls:

691.0ms	(- (* (- x 0.5) (log x)) x)
636.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
374.0ms	(* (- x 0.5) (log x))
127.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.5s

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
2	1982
1	526
0	216

prune795.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize93.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
4.8b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`cbrt-prod` `times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`pow1` `add-log-exp`
3×	`associate-/r` `pow1/3` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv`

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
42.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series950.0ms

Counts

4 → 12

Calls

4 calls:

258.0ms	(cbrt x)
321.0ms	(cbrt x)
247.0ms	(cbrt x)
123.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify948.0ms

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
2	898
1	224
0	97

prune612.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize89.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
4.8b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
5.1b	(pow x 1/3)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-exp-log`
6×	`cbrt-prod` `add-cbrt-cube`
5×	`pow1`
4×	`add-log-exp`
3×	`pow-unpow` `associate-/r` `unpow-prod-down` `associate-/l`
2×	`pow1/3` `associate-/l/`
1×	`pow-to-exp` `cbrt-undiv` `clear-num` `pow-pow` `frac-2neg` `flip3-+` `unpow1/3` `div-exp` `pow-exp` `flip-+` `div-inv` `sqr-pow`

Counts

4 → 69

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
49.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
2.0ms	(pow x 1/3)

series909.0ms

Counts

4 → 12

Calls

4 calls:

312.0ms	(cbrt x)
235.0ms	(cbrt x)
100.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
261.0ms	(pow x 1/3)

simplify1.2s

Counts

81 → 81

Iterations

Iter	Nodes
done	5001
2	1239
1	313
0	124

prune751.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (- (* (+ (sqrt x) (sqrt 0.5)) (* (- (sqrt x) (sqrt 0.5)) (log x))) x) 0.91893853320467)
0.4b	(* (+ (sqrt x) (sqrt 0.5)) (* (- (sqrt x) (sqrt 0.5)) (log x)))
0.4b	(* (- (sqrt x) (sqrt 0.5)) (log x))
4.8b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite576.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 130

Calls

4 calls:

334.0ms	(+ (- (* (+ (sqrt x) (sqrt 0.5)) (* (- (sqrt x) (sqrt 0.5)) (log x))) x) 0.91893853320467)
119.0ms	(* (+ (sqrt x) (sqrt 0.5)) (* (- (sqrt x) (sqrt 0.5)) (log x)))
50.0ms	(* (- (sqrt x) (sqrt 0.5)) (log x))
68.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.1s

Counts

4 → 12

Calls

4 calls:

547.0ms	(+ (- (* (+ (sqrt x) (sqrt 0.5)) (* (- (sqrt x) (sqrt 0.5)) (log x))) x) 0.91893853320467)
322.0ms	(* (+ (sqrt x) (sqrt 0.5)) (* (- (sqrt x) (sqrt 0.5)) (log x)))
121.0ms	(* (- (sqrt x) (sqrt 0.5)) (log x))
119.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.6s

Counts

142 → 142

Iterations

Iter	Nodes
done	5001
1	1132
0	371

prune1.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes804.0ms

Accuracy

90.7% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 6.0b

bsearch340.0ms

Steps

Iters	Range		Point
8	1.2368744601631003e-16	5.304801808987539e-14	5.2562163192701693e-14
10	-1.822573667716502e+21	-1990274354.3986437	-1.8206639466674119e+19

simplify17.0ms

Iterations

Iter	Nodes
done	63
2	63
1	62
0	45

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.8s	11720×	body	80	nan
1.4s	11704×	body	80	valid