Details

sample83.0ms

Algorithm

intervals

Results

26.0ms	373×	body	80	valid
20.0ms	412×	body	80	nan

simplify3.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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: 6.0b

localize20.0ms

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)
5.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite151.0ms

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:

23.0ms	(* (- x 0.5) (log x))
18.0ms	(- (* (- x 0.5) (log x)) x)
57.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
51.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

256.0ms	(* (- x 0.5) (log x))
417.0ms	(- (* (- x 0.5) (log x)) x)
421.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
91.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify2.0s

Counts

110 → 110

Iterations

Useful iterations: 3 (997.0ms)

Iter	Nodes	Cost
0	213	1655
1	501	1589
2	1406	1469
3	4880	1419
done	5000	1419

prune383.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
5.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite56.0ms

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)
52.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series655.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(cbrt x)
187.0ms	(cbrt x)
186.0ms	(cbrt x)
92.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify762.0ms

Counts

74 → 74

Iterations

Useful iterations: 3 (317.0ms)

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

prune341.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt x))
0.6b	(cbrt (pow x 2/3))
5.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
6.0b	(pow x 2/3)

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`cbrt-prod`
9×	`times-frac`
7×	`add-exp-log`
6×	`unpow-prod-down` `add-cbrt-cube`
5×	`pow1`
4×	`add-log-exp`
3×	`pow-unpow` `associate-/r` `associate-/l`
2×	`pow1/3` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `flip3-+` `div-exp` `pow-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 75

Calls

4 calls:

1.0ms	(cbrt (cbrt x))
2.0ms	(cbrt (pow x 2/3))
52.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
3.0ms	(pow x 2/3)

series727.0ms

Counts

4 → 12

Calls

4 calls:

253.0ms	(cbrt (cbrt x))
195.0ms	(cbrt (pow x 2/3))
94.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
185.0ms	(pow x 2/3)

simplify1.1s

Counts

87 → 87

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	156	1061
1	324	1023
2	761	920
3	2221	891
done	5001	885

prune488.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

localize44.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cbrt 2/3) (cbrt 2/3))
2.9b	(pow x (* (cbrt 2/3) (cbrt 2/3)))
5.5b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
5.8b	(pow (pow x (* (cbrt 2/3) (cbrt 2/3))) (cbrt 2/3))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
25×	`add-cube-cbrt` `*-un-lft-identity`
19×	`cbrt-prod`
13×	`unpow-prod-down`
12×	`pow1`
11×	`add-exp-log`
9×	`times-frac`
7×	`pow-unpow`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-exp`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `associate-/r` `associate-/l` `sqr-pow`
2×	`pow-pow` `pow-prod-down` `pow-sqr` `pow-prod-up` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `flip3-+` `pow-plus` `div-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `flip-+` `div-inv`

Counts

4 → 110

Calls

4 calls:

11.0ms	(* (cbrt 2/3) (cbrt 2/3))
3.0ms	(pow x (* (cbrt 2/3) (cbrt 2/3)))
52.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
6.0ms	(pow (pow x (* (cbrt 2/3) (cbrt 2/3))) (cbrt 2/3))

series824.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(* (cbrt 2/3) (cbrt 2/3))
250.0ms	(pow x (* (cbrt 2/3) (cbrt 2/3)))
92.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
482.0ms	(pow (pow x (* (cbrt 2/3) (cbrt 2/3))) (cbrt 2/3))

simplify1.8s

Counts

120 → 120

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	183	1655
1	407	1475
2	1114	1358
3	3480	1290
done	5001	1230

prune659.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

regimes381.0ms

Accuracy

85.1% (0.3b remaining)

Error of 4.3b against oracle of 4.0b and baseline of 6.0b

bsearch63.0ms

Steps

Iters	Range		Point
6	254195247935743.44	2396706146367806.5	520673369551077.94

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	65
1	45	65
done	45	65

end0.0ms

sample1.8s

Algorithm

intervals

Results

598.0ms	11597×	body	80	valid
499.0ms	11507×	body	80	nan