Details

sample135.0ms

Algorithm

intervals

Results

56.0ms	380×	body	80	valid
32.0ms	387×	body	80	nan

simplify3.2s

Counts

1 → 1

Iterations

Useful iterations: 4 (207.0ms)

Iter	Nodes	Cost
0	20	24
1	40	23
2	92	23
3	265	23
4	934	22
5	4335	22
done	5000	22

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.7b

localize40.0ms

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)
4.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite319.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`add-cube-cbrt`
18×	`log-prod`
12×	`associate--l+`
11×	`associate-+l+` `add-log-exp`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`prod-diff`
5×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`fma-def` `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` `fma-neg` `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 → 116

Calls

4 calls:

36.0ms	(* (- x 0.5) (log x))
142.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
41.0ms	(- (* (- x 0.5) (log x)) x)
95.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series2.1s

Counts

4 → 12

Calls

4 calls:

492.0ms	(* (- x 0.5) (log x))
770.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
742.0ms	(- (* (- x 0.5) (log x)) x)
122.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify3.0s

Counts

128 → 128

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	238	1852
1	624	1686
2	2579	1560
done	5000	1537

prune926.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.5b

localize49.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(cbrt x)
4.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod` `times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-/r` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 70

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
87.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.0s

Counts

4 → 12

Calls

4 calls:

281.0ms	(cbrt x)
324.0ms	(cbrt x)
296.0ms	(cbrt x)
129.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify647.0ms

Counts

82 → 82

Iterations

Useful iterations: done (645.0ms)

Iter	Nodes	Cost
0	101	939
1	232	870
2	822	794
done	5000	768

prune529.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.8b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
4.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
5.1b	(pow (/ 1 x) -1/3)

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
13×	`unpow-prod-down`
11×	`add-exp-log`
6×	`pow1` `cbrt-prod` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-pow` `div-exp` `associate-/r` `associate-/l`
2×	`pow1/3` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `rec-exp` `pow-flip` `frac-2neg` `flip3-+` `1-exp` `clear-num` `flip-+` `inv-pow` `sqr-pow`

Counts

4 → 91

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
56.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
18.0ms	(pow (/ 1 x) -1/3)

series888.0ms

Counts

4 → 12

Calls

4 calls:

289.0ms	(cbrt x)
242.0ms	(cbrt x)
127.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
229.0ms	(pow (/ 1 x) -1/3)

simplify785.0ms

Counts

103 → 103

Iterations

Useful iterations: done (782.0ms)

Iter	Nodes	Cost
0	174	1209
1	461	1081
2	1511	995
done	5000	965

prune816.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.8b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* (* 2 (log (cbrt x))) (- x 0.5)) (* (log (cbrt x)) (- x 0.5)))
0.5b	(cbrt x)
0.5b	(cbrt x)
4.3b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
36×	`prod-diff`
22×	`distribute-rgt-in` `associate-+l+` `associate-+r+` `distribute-lft-in`
9×	`times-frac`
8×	`associate-*r/`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `sub-neg` `flip3--` `frac-add` `flip--` `log1p-expm1-u`
3×	`associate-/r` `associate-/l`
2×	`flip3-+` `pow1/3` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-out` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 120

Calls

4 calls:

76.0ms	(+ (* (* 2 (log (cbrt x))) (- x 0.5)) (* (log (cbrt x)) (- x 0.5)))
1.0ms	(cbrt x)
2.0ms	(cbrt x)
107.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.8s

Counts

4 → 12

Calls

4 calls:

1.1s	(+ (* (* 2 (log (cbrt x))) (- x 0.5)) (* (log (cbrt x)) (- x 0.5)))
271.0ms	(cbrt x)
297.0ms	(cbrt x)
127.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify2.5s

Counts

132 → 132

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	256	2569
1	738	2190
2	3633	1698
done	5000	1674

prune948.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.8b

regimes753.0ms

Accuracy

82% (0.4b remaining)

Error of 4.1b against oracle of 3.7b and baseline of 6.0b

bsearch110.0ms

Steps

Iters	Range		Point
5	3.12352244899542e+65	7.4876636978344635e+65	3.166124874515622e+65

simplify10.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	80
1	62	80
done	62	80

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.7s	11772×	body	80	valid
1.5s	11664×	body	80	nan