Details

sample76.0ms

Algorithm

intervals

Results

27.0ms	382×	body	80	valid
22.0ms	381×	body	80	nan

simplify2.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	518
1	37	518
2	84	518
3	244	518
4	855	518
5	4006	518
done	5000	518

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.5b

localize53.0ms

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))
6.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite164.0ms

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:

21.0ms	(- (* (- x 0.5) (log x)) x)
61.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
18.0ms	(* (- x 0.5) (log x))
62.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.7s

Counts

4 → 12

Calls

4 calls:

600.0ms	(- (* (- x 0.5) (log x)) x)
601.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
400.0ms	(* (- x 0.5) (log x))
136.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.7s

Counts

110 → 110

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	216	35388
1	526	33084
2	1982	32519
done	5000	32319

prune996.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.2b

localize99.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
6.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite85.0ms

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)
78.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series926.0ms

Counts

4 → 12

Calls

4 calls:

240.0ms	(cbrt x)
275.0ms	(cbrt x)
288.0ms	(cbrt x)
124.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.2s

Counts

74 → 74

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	97	21113
1	224	19261
2	898	19023
done	5000	18383

prune786.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (+ (* (- x 0.5) (log (sqrt x))) (- (* (- x 0.5) (log (sqrt x))) x)) 0.91893853320467)
0.2b	(* (- x 0.5) (log (sqrt x)))
0.2b	(* (- x 0.5) (log (sqrt x)))
6.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite777.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

648.0ms	(+ (+ (* (- x 0.5) (log (sqrt x))) (- (* (- x 0.5) (log (sqrt x))) x)) 0.91893853320467)
32.0ms	(* (- x 0.5) (log (sqrt x)))
36.0ms	(* (- x 0.5) (log (sqrt x)))
56.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series640.0ms

Counts

4 → 12

Calls

4 calls:

238.0ms	(+ (+ (* (- x 0.5) (log (sqrt x))) (- (* (- x 0.5) (log (sqrt x))) x)) 0.91893853320467)
155.0ms	(* (- x 0.5) (log (sqrt x)))
133.0ms	(* (- x 0.5) (log (sqrt x)))
115.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify2.0s

Counts

131 → 131

Iterations

Useful iterations: 2 (620.0ms)

Iter	Nodes	Cost
0	219	48816
1	536	44439
2	2326	42816
done	5001	42816

prune931.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (- x 0.5) (log (sqrt x))) x)
0.2b	(* (- x 0.5) (log (sqrt x)))
0.2b	(* (- x 0.5) (log (sqrt x)))
6.2b	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
36×	`log-prod`
33×	`*-un-lft-identity`
28×	`add-cube-cbrt`
25×	`associate-r`
18×	`distribute-rgt-in` `distribute-lft-in` `sqrt-prod`
17×	`add-exp-log`
14×	`pow1`
13×	`add-cbrt-cube` `associate-l`
12×	`associate--l+`
11×	`times-frac`
6×	`associate-*l/` `prod-exp` `log-pow` `add-log-exp`
5×	`unswap-sqr`
4×	`cbrt-unprod`
3×	`flip3--` `pow-prod-down` `*-commutative` `flip--`
2×	`frac-times` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `rec-exp` `sub-neg` `diff-log` `1-exp` `associate-*r/` `un-div-inv` `div-inv`

Counts

4 → 138

Calls

4 calls:

16.0ms	(- (* (- x 0.5) (log (sqrt x))) x)
31.0ms	(* (- x 0.5) (log (sqrt x)))
23.0ms	(* (- x 0.5) (log (sqrt x)))
86.0ms	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

series648.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(- (* (- x 0.5) (log (sqrt x))) x)
118.0ms	(* (- x 0.5) (log (sqrt x)))
169.0ms	(* (- x 0.5) (log (sqrt x)))
143.0ms	(* (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) (/ 1 x))

simplify4.3s

Counts

150 → 150

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	230	54364
1	580	48540
2	3869	45689
done	5000	45689

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.0b

regimes849.0ms

Accuracy

83% (0.4b remaining)

Error of 4.4b against oracle of 4.0b and baseline of 6.4b

bsearch128.0ms

Steps

Iters	Range		Point
7	3.320593221623759e+22	4.50898369950121e+24	4.856018666852463e+22

simplify15.0ms

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	41	1469
1	55	1469
done	55	1469

end0.0ms

sample4.0s

Algorithm

intervals

Results

2.1s	11827×	body	80	valid
1.2s	11707×	body	80	nan