Details

sample145.0ms

Algorithm

intervals

Results

65.0ms	383×	body	80	valid
34.0ms	388×	body	80	nan

simplify6.1s

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 0.5) (log x))
0.1b	(- (* (- x 0.5) (log x)) x)
0.1b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
5.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite259.0ms

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:

39.0ms	(* (- x 0.5) (log x))
35.0ms	(- (* (- x 0.5) (log x)) x)
90.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
90.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series2.0s

Counts

4 → 12

Calls

4 calls:

420.0ms	(* (- x 0.5) (log x))
709.0ms	(- (* (- x 0.5) (log x)) x)
753.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
154.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify3.4s

Counts

110 → 110

Iterations

Useful iterations: 3 (1.7s)

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

prune515.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
5.2b	(/ (+ (* (- (* (+ 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:

2.0ms	(cbrt x)
2.0ms	(cbrt x)
2.0ms	(cbrt x)
74.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.0s

Counts

4 → 12

Calls

4 calls:

252.0ms	(cbrt x)
316.0ms	(cbrt x)
310.0ms	(cbrt x)
122.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.1s

Counts

74 → 74

Iterations

Useful iterations: 3 (462.0ms)

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

prune550.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
4.9b	(pow (/ 1 x) -1/3)
5.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite92.0ms

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×	`pow-exp` `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 → 83

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
8.0ms	(pow (/ 1 x) -1/3)
80.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.0s

Counts

4 → 12

Calls

4 calls:

289.0ms	(cbrt x)
305.0ms	(cbrt x)
309.0ms	(pow (/ 1 x) -1/3)
115.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.7s

Counts

95 → 95

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	168	1157
1	363	1075
2	841	985
3	2364	952
done	5002	950

prune666.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467)
0.2b	(- (* (log (sqrt x)) (- x 0.5)) x)
0.3b	(+ (* (log (sqrt x)) (- x 0.5)) (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467))
5.2b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite364.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

81.0ms	(+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467)
27.0ms	(- (* (log (sqrt x)) (- x 0.5)) x)
173.0ms	(+ (* (log (sqrt x)) (- x 0.5)) (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467))
79.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series787.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467)
209.0ms	(- (* (log (sqrt x)) (- x 0.5)) x)
238.0ms	(+ (* (log (sqrt x)) (- x 0.5)) (+ (- (* (log (sqrt x)) (- x 0.5)) x) 0.91893853320467))
128.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.4s

Counts

100 → 100

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	222	2307
1	643	2108
2	2200	2001
done	5000	1963

prune634.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.0b

regimes922.0ms

Accuracy

86.8% (0.3b remaining)

Error of 4.4b against oracle of 4.1b and baseline of 6.2b

bsearch3.0ms

simplify13.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	45	133
1	63	96
done	63	96

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.2s	11709×	body	80	valid
1.9s	11586×	body	80	nan