Details

sample108.0ms

Algorithm

intervals

Results

35.0ms	367×	body	80	valid
28.0ms	320×	body	80	nan

simplify5.7s

Counts

1 → 1

Iterations

Useful iterations: 4 (271.0ms)

Iter	Nodes	Cost
0	20	24
1	40	23
2	92	23
3	263	23
4	576	22
5	1144	22
6	2010	22
7	4222	22
done	5000	22

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.5b

localize28.0ms

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)
4.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite314.0ms

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-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`prod-diff`
5×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`fma-def` `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` `fma-neg` `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 → 116

Calls

4 calls:

48.0ms	(* (- x 0.5) (log x))
109.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
44.0ms	(- (* (- x 0.5) (log x)) x)
105.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series2.1s

Counts

4 → 12

Calls

4 calls:

488.0ms	(* (- x 0.5) (log x))
698.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
759.0ms	(- (* (- x 0.5) (log x)) x)
139.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.4s

Counts

128 → 128

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	238	1852
1	574	1682
2	1606	1549
done	5001	1485

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.1b	(fma (log x) (- x 0.5) (- x))
0.2b	(+ (+ (fma (log x) (- x 0.5) (- x)) (+ (- x) x)) 0.91893853320467)
4.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite474.0ms

Algorithm

rewrite-expression-head

Rules

36×	`*-un-lft-identity`
17×	`add-sqr-sqrt` `add-log-exp`
15×	`add-cube-cbrt`
14×	`distribute-lft-out`
9×	`times-frac` `sum-log`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `fma-def`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`associate-+l-` `distribute-rgt-neg-in` `flip3-+` `associate-*l/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+r-` `associate-+l+` `flip3--` `frac-2neg` `div-exp` `pow-prod-down` `neg-log` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `div-inv` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

48.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
0.0ms	(fma (log x) (- x 0.5) (- x))
316.0ms	(+ (+ (fma (log x) (- x 0.5) (- x)) (+ (- x) x)) 0.91893853320467)
107.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.0s

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z)
418.0ms	(fma (log x) (- x 0.5) (- x))
425.0ms	(+ (+ (fma (log x) (- x 0.5) (- x)) (+ (- x) x)) 0.91893853320467)
122.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.3s

Counts

103 → 103

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	202	1724
1	492	1551
2	1467	1348
done	5001	1311

prune710.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.6b	(* (cbrt x) (cbrt x))
4.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
22×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`times-frac`
8×	`add-exp-log` `pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `associate-/l`
2×	`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 → 99

Calls

4 calls:

2.0ms	(cbrt x)
2.0ms	(cbrt x)
24.0ms	(* (cbrt x) (cbrt x))
63.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series996.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(cbrt x)
312.0ms	(cbrt x)
319.0ms	(* (cbrt x) (cbrt x))
115.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify2.5s

Counts

111 → 111

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	138	1209
1	298	1041
2	884	973
3	3105	940
done	5002	937

prune951.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.6b	(* (cbrt x) (cbrt x))
4.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
5.1b	(pow (/ 1 x) -1/3)

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
19×	`cbrt-prod`
18×	`times-frac`
13×	`pow1` `add-exp-log` `unpow-prod-down`
7×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-unpow` `pow-pow` `div-exp` `associate-/r` `associate-/l`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `pow2` `pow-to-exp` `rec-exp` `pow-flip` `frac-2neg` `flip3-+` `pow-plus` `1-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `flip-+` `inv-pow` `sqr-pow`

Counts

4 → 120

Calls

4 calls:

1.0ms	(cbrt x)
11.0ms	(* (cbrt x) (cbrt x))
77.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
13.0ms	(pow (/ 1 x) -1/3)

series1.0s

Counts

4 → 12

Calls

4 calls:

299.0ms	(cbrt x)
295.0ms	(* (cbrt x) (cbrt x))
145.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
277.0ms	(pow (/ 1 x) -1/3)

simplify2.5s

Counts

132 → 132

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	210	1479
1	447	1250
2	1133	1174
3	3688	1137
done	5002	1132

prune831.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.0b

regimes567.0ms

Accuracy

85.9% (0.3b remaining)

Error of 4.1b against oracle of 3.8b and baseline of 6.0b

bsearch147.0ms

Steps

Iters	Range		Point
9	18544.379693406936	380432113365.94904	7252182.273118808

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	63
1	46	63
done	46	63

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.8s	11637×	body	80	valid
1.5s	11710×	body	80	nan