Details

sample154.0ms

Algorithm

intervals

Results

41.0ms	383×	body	80	valid
35.0ms	356×	body	80	nan

simplify2.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	24
1	37	24
2	84	24
3	244	24
4	860	24
5	4090	24
done	5001	24

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.1b	(- (* (- x 0.5) (log x)) x)
0.2b	(* (- x 0.5) (log x))
6.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite202.0ms

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:

76.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
19.0ms	(- (* (- x 0.5) (log x)) x)
26.0ms	(* (- x 0.5) (log x))
75.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.8s

Counts

4 → 12

Calls

4 calls:

630.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
669.0ms	(- (* (- x 0.5) (log x)) x)
411.0ms	(* (- x 0.5) (log x))
124.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify984.0ms

Counts

110 → 110

Iterations

Useful iterations: done (980.0ms)

Iter	Nodes	Cost
0	213	1655
1	521	1589
2	1910	1479
done	5001	1476

prune790.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 5.7b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (* (- (log x)) 0.5) x) (* x (log x)))
0.1b	(+ (+ (- (* (- (log x)) 0.5) x) (* x (log x))) 0.91893853320467)
0.3b	(* x (log x))
6.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite385.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

56.0ms	(+ (- (* (- (log x)) 0.5) x) (* x (log x)))
212.0ms	(+ (+ (- (* (- (log x)) 0.5) x) (* x (log x))) 0.91893853320467)
9.0ms	(* x (log x))
103.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.8s

Counts

4 → 12

Calls

4 calls:

779.0ms	(+ (- (* (- (log x)) 0.5) x) (* x (log x)))
686.0ms	(+ (+ (- (* (- (log x)) 0.5) x) (* x (log x))) 0.91893853320467)
249.0ms	(* x (log x))
116.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.4s

Counts

103 → 103

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	203	1695
1	523	1621
2	2055	1388
done	5000	1376

prune647.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.7b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* (* 2 (log (cbrt x))) x) (* x (log (cbrt x))))
0.6b	(cbrt x)
0.6b	(cbrt x)
6.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

27.0ms	(+ (* (* 2 (log (cbrt x))) x) (* x (log (cbrt x))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
59.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.1s

Counts

4 → 12

Calls

4 calls:

530.0ms	(+ (* (* 2 (log (cbrt x))) x) (* x (log (cbrt x))))
231.0ms	(cbrt x)
258.0ms	(cbrt x)
123.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify978.0ms

Counts

86 → 86

Iterations

Useful iterations: done (974.0ms)

Iter	Nodes	Cost
0	161	1288
1	408	1229
2	1745	1058
done	5000	1047

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.7b

localize74.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
6.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite83.0ms

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)
79.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series859.0ms

Counts

4 → 12

Calls

4 calls:

299.0ms	(cbrt x)
223.0ms	(cbrt x)
225.0ms	(cbrt x)
112.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify606.0ms

Counts

74 → 74

Iterations

Useful iterations: done (602.0ms)

Iter	Nodes	Cost
0	97	893
1	224	870
2	902	792
done	5001	761

prune397.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.5b

regimes711.0ms

Accuracy

84.9% (0.3b remaining)

Error of 4.3b against oracle of 4.0b and baseline of 6.3b

bsearch59.0ms

Steps

Iters	Range		Point
4	1.1002106537292756e+46	1.7722746760900536e+46	1.1701312037307003e+46

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	75
1	56	75
done	56	75

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.6s	11775×	body	80	nan
1.4s	11830×	body	80	valid