Details

sample110.0ms

Algorithm

intervals

Results

36.0ms	407×	body	80	nan
30.0ms	408×	body	80	valid

simplify2.7s

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: 5.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 0.5) (log x))
0.1b	(- (* (- x 0.5) (log x)) x)
0.2b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite207.0ms

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:

30.0ms	(* (- x 0.5) (log x))
26.0ms	(- (* (- x 0.5) (log x)) x)
69.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
78.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series2.0s

Counts

4 → 12

Calls

4 calls:

460.0ms	(* (- x 0.5) (log x))
764.0ms	(- (* (- x 0.5) (log x)) x)
675.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
128.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.1s

Counts

110 → 110

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	213	1655
1	520	1589
2	1929	1479
done	5000	1476

prune778.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 0.5) (log (sqrt x)))
0.1b	(- (* (- x 0.5) (log (sqrt x))) x)
0.3b	(+ (* (- x 0.5) (log (sqrt x))) (+ (- (* (- x 0.5) (log (sqrt x))) x) 0.91893853320467))
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite360.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

27.0ms	(* (- x 0.5) (log (sqrt x)))
33.0ms	(- (* (- x 0.5) (log (sqrt x))) x)
194.0ms	(+ (* (- x 0.5) (log (sqrt x))) (+ (- (* (- x 0.5) (log (sqrt x))) x) 0.91893853320467))
98.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series750.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(* (- x 0.5) (log (sqrt x)))
242.0ms	(- (* (- x 0.5) (log (sqrt x))) x)
215.0ms	(+ (* (- x 0.5) (log (sqrt x))) (+ (- (* (- x 0.5) (log (sqrt x))) x) 0.91893853320467))
136.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify2.2s

Counts

133 → 133

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	276	2693
1	745	2478
2	3425	2332
done	5001	2304

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.0b

localize100.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(cbrt x)
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite119.0ms

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:

2.0ms	(cbrt x)
2.0ms	(cbrt x)
2.0ms	(cbrt x)
111.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series955.0ms

Counts

4 → 12

Calls

4 calls:

285.0ms	(cbrt x)
274.0ms	(cbrt x)
278.0ms	(cbrt x)
118.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify566.0ms

Counts

74 → 74

Iterations

Useful iterations: done (563.0ms)

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

prune646.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.5b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (sqrt (* (- x 0.5) (log (sqrt x)))) (sqrt (* (- x 0.5) (log (sqrt x))))) x)
0.3b	(+ (* (- x 0.5) (log (sqrt x))) (+ (- (* (sqrt (* (- x 0.5) (log (sqrt x)))) (sqrt (* (- x 0.5) (log (sqrt x))))) x) 0.91893853320467))
0.5b	(* (sqrt (* (- x 0.5) (log (sqrt x)))) (sqrt (* (- x 0.5) (log (sqrt x)))))
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

53×	`pow1`
28×	`sqrt-pow1`
23×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity` `pow-prod-down`
18×	`associate-*l/`
15×	`add-log-exp`
12×	`associate-+l+` `log-prod` `sqrt-div`
10×	`pow1/2` `sqrt-prod` `pow-prod-up`
9×	`flip3--` `times-frac` `flip--`
8×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-in` `distribute-lft-in` `pow-sqr`
5×	`sum-log`
4×	`frac-times` `flip3-+` `swap-sqr` `associate-r` `associate-l` `frac-add` `flip-+`
3×	`associate-/r` `associate-/l`
2×	`diff-log` `associate-*r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow2` `associate-+l-` `associate-+r-` `sub-neg` `associate-+r+` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv` `difference-of-squares` `unswap-sqr`

Counts

4 → 130

Calls

4 calls:

162.0ms	(- (* (sqrt (* (- x 0.5) (log (sqrt x)))) (sqrt (* (- x 0.5) (log (sqrt x))))) x)
1.2s	(+ (* (- x 0.5) (log (sqrt x))) (+ (- (* (sqrt (* (- x 0.5) (log (sqrt x)))) (sqrt (* (- x 0.5) (log (sqrt x))))) x) 0.91893853320467))
91.0ms	(* (sqrt (* (- x 0.5) (log (sqrt x)))) (sqrt (* (- x 0.5) (log (sqrt x)))))
87.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1000.0ms

Counts

4 → 12

Calls

4 calls:

238.0ms	(- (* (sqrt (* (- x 0.5) (log (sqrt x)))) (sqrt (* (- x 0.5) (log (sqrt x))))) x)
354.0ms	(+ (* (- x 0.5) (log (sqrt x))) (+ (- (* (sqrt (* (- x 0.5) (log (sqrt x)))) (sqrt (* (- x 0.5) (log (sqrt x))))) x) 0.91893853320467))
280.0ms	(* (sqrt (* (- x 0.5) (log (sqrt x)))) (sqrt (* (- x 0.5) (log (sqrt x)))))
127.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify2.8s

Counts

142 → 142

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	338	4027
1	954	2844
2	4802	2564
done	5000	2529

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.5b

regimes1.1s

Accuracy

85.6% (0.3b remaining)

Error of 4.1b against oracle of 3.7b and baseline of 5.9b

bsearch122.0ms

Steps

Iters	Range		Point
7	2.3827492464977967e+26	3.7617724825378538e+28	2.427234054502609e+26

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	44	85
1	59	85
done	59	85

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.1s	11784×	body	80	valid
1.7s	11987×	body	80	nan