Details

sample134.0ms

Algorithm

intervals

Results

42.0ms	418×	body	80	nan
39.0ms	379×	body	80	valid

simplify5.9s

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.0b

localize25.0ms

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))
6.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite248.0ms

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:

31.0ms	(- (* (- x 0.5) (log x)) x)
88.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
39.0ms	(* (- x 0.5) (log x))
86.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series2.0s

Counts

4 → 12

Calls

4 calls:

764.0ms	(- (* (- x 0.5) (log x)) x)
658.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
447.0ms	(* (- x 0.5) (log x))
109.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify3.3s

Counts

110 → 110

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	213	1655
1	501	1589
2	1405	1469
3	4873	1419
done	5000	1419

prune643.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.2b	(* (- x 0.5) (log x))
0.3b	(+ (* (- x 0.5) (log x)) (- 0.91893853320467 x))
6.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 103

Calls

4 calls:

66.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
42.0ms	(* (- x 0.5) (log x))
40.0ms	(+ (* (- x 0.5) (log x)) (- 0.91893853320467 x))
89.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.3s

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
365.0ms	(* (- x 0.5) (log x))
729.0ms	(+ (* (- x 0.5) (log x)) (- 0.91893853320467 x))
130.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.3s

Counts

115 → 115

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	256	1891
1	663	1825
2	2211	1666
done	5001	1664

prune620.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
6.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite82.0ms

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` `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 → 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)

series950.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(cbrt x)
283.0ms	(cbrt x)
285.0ms	(cbrt x)
139.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.1s

Counts

74 → 74

Iterations

Useful iterations: 3 (421.0ms)

Iter	Nodes	Cost
0	97	893
1	214	870
2	590	790
3	1830	761
done	5001	761

prune505.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.3b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* (* 2 (log (cbrt x))) (- x 0.5)) (* (log (cbrt x)) (- x 0.5)))
0.6b	(cbrt x)
0.6b	(cbrt x)
6.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

55.0ms	(+ (* (* 2 (log (cbrt x))) (- x 0.5)) (* (log (cbrt x)) (- x 0.5)))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
93.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series2.0s

Counts

4 → 12

Calls

4 calls:

1.3s	(+ (* (* 2 (log (cbrt x))) (- x 0.5)) (* (log (cbrt x)) (- x 0.5)))
300.0ms	(cbrt x)
275.0ms	(cbrt x)
129.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.1s

Counts

87 → 87

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	179	1569
1	507	1409
2	1870	1242
done	5002	1209

prune555.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.3b

regimes432.0ms

Accuracy

86.8% (0.3b remaining)

Error of 4.2b against oracle of 4.0b and baseline of 6.0b

bsearch120.0ms

Steps

Iters	Range		Point
9	38262912715953.914	3.3928674586328847e+18	52336596543435.78

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	76
1	47	76
done	47	76

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.9s	11398×	body	80	nan
1.2s	11564×	body	80	valid