Details

sample124.0ms

Algorithm

intervals

Results

37.0ms	363×	body	80	valid
36.0ms	407×	body	80	nan

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	4181
4	921
3	265
2	92
1	40
0	20

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.5b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
23×	`add-cube-cbrt`
18×	`log-prod`
12×	`associate--l+`
11×	`associate-+l+` `add-log-exp`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
8×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`prod-diff`
5×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`associate-/r` `fma-def` `associate-/l`
2×	`sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `associate-*l/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `frac-2neg` `fma-neg` `div-exp` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `associate-+l-` `cbrt-unprod` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 116

Calls

4 calls:

19.0ms	(* (- x 0.5) (log x))
66.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
28.0ms	(- (* (- x 0.5) (log x)) x)
82.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series2.0s

Counts

4 → 12

Calls

4 calls:

399.0ms	(* (- x 0.5) (log x))
757.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
693.0ms	(- (* (- x 0.5) (log x)) x)
127.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.7s

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
2	2700
1	636
0	241

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.7b

localize66.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.3b	(fma (- x 0.5) (log x) (- 0.91893853320467 x))
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `associate-r` `associate-l` `prod-diff` `associate-/l`
2×	`flip3--` `associate-*l/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

11.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
41.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.0ms	(fma (- x 0.5) (log x) (- 0.91893853320467 x))
62.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series712.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* (+ y 0.0007936500793651) z) 0.0027777777777778)
71.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
477.0ms	(fma (- x 0.5) (log x) (- 0.91893853320467 x))
122.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.2s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	1757
1	459
0	193

prune856.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.6b

localize88.0ms

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)

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`cbrt-prod` `times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `pow1/3` `associate-/l`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv`

Counts

4 → 70

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
54.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series964.0ms

Counts

4 → 12

Calls

4 calls:

260.0ms	(cbrt x)
265.0ms	(cbrt x)
309.0ms	(cbrt x)
130.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify564.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	823
1	232
0	101

prune754.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.6b

localize71.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
4.9b	(pow (/ 1 x) -1/3)
5.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
13×	`unpow-prod-down`
11×	`add-exp-log`
6×	`cbrt-prod` `pow1` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-/r` `pow-pow` `div-exp` `associate-/l`
2×	`pow1/3` `div-inv` `associate-/l/`
1×	`pow-to-exp` `cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `flip3-+` `1-exp` `flip-+` `pow-flip` `inv-pow` `sqr-pow`

Counts

4 → 91

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
8.0ms	(pow (/ 1 x) -1/3)
66.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.2s

Counts

4 → 12

Calls

4 calls:

286.0ms	(cbrt x)
233.0ms	(cbrt x)
588.0ms	(pow (/ 1 x) -1/3)
109.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify572.0ms

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	1519
1	462
0	174

prune809.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.6b

regimes947.0ms

Accuracy

70.8% (1.6b remaining)

Error of 2.2b against oracle of 0.7b and baseline of 6.0b

bsearch121.0ms

Steps

Iters	Range		Point
7	5.8875098310894595e+81	1.23160676476912e+83	8.101543792246119e+82

simplify7.0ms

Iterations

Iter	Nodes
done	43
1	43
0	35

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.7s	11622×	body	80	valid
1.4s	11597×	body	80	nan