Details

sample135.0ms

Algorithm

intervals

Results

51.0ms	383×	body	80	valid
32.0ms	354×	body	80	nan

simplify6.6s

Counts

1 → 1

Iterations

Useful iterations: 4 (196.0ms)

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.5b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite261.0ms

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:

110.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
35.0ms	(- (* (- x 0.5) (log x)) x)
30.0ms	(* (- x 0.5) (log x))
81.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series2.0s

Counts

4 → 12

Calls

4 calls:

707.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
734.0ms	(- (* (- x 0.5) (log x)) x)
370.0ms	(* (- x 0.5) (log x))
147.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.6s

Counts

128 → 128

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	238	1852
1	574	1682
2	1604	1549
done	5000	1485

prune866.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.0b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite106.0ms

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` `expm1-log1p-u` `log1p-expm1-u` `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 → 70

Calls

4 calls:

2.0ms	(cbrt x)
2.0ms	(cbrt x)
2.0ms	(cbrt x)
98.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series1.1s

Counts

4 → 12

Calls

4 calls:

317.0ms	(cbrt x)
320.0ms	(cbrt x)
302.0ms	(cbrt x)
150.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify1.5s

Counts

82 → 82

Iterations

Useful iterations: 3 (623.0ms)

Iter	Nodes	Cost
0	101	939
1	225	870
2	630	794
3	1990	767
done	5000	767

prune502.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
4.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
5.0b	(pow (/ 1 x) -1/3)

rewrite124.0ms

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×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u` `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 → 91

Calls

4 calls:

2.0ms	(cbrt x)
2.0ms	(cbrt x)
103.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
12.0ms	(pow (/ 1 x) -1/3)

series950.0ms

Counts

4 → 12

Calls

4 calls:

305.0ms	(cbrt x)
266.0ms	(cbrt x)
130.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
249.0ms	(pow (/ 1 x) -1/3)

simplify1.8s

Counts

103 → 103

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	174	1209
1	376	1081
2	886	995
3	2572	964
done	5002	962

prune712.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
4.1b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
5.0b	(pow (/ 1 x) -1/3)

rewrite136.0ms

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×	`expm1-log1p-u` `pow-exp` `log1p-expm1-u` `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 → 91

Calls

4 calls:

2.0ms	(cbrt x)
2.0ms	(cbrt x)
104.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
23.0ms	(pow (/ 1 x) -1/3)

series973.0ms

Counts

4 → 12

Calls

4 calls:

300.0ms	(cbrt x)
263.0ms	(cbrt x)
146.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)
263.0ms	(pow (/ 1 x) -1/3)

simplify1.9s

Counts

103 → 103

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	174	1209
1	376	1081
2	886	995
3	2572	964
done	5002	962

prune573.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.0b

regimes440.0ms

Accuracy

85.8% (0.3b remaining)

Error of 4.1b against oracle of 3.8b and baseline of 6.1b

bsearch139.0ms

Steps

Iters	Range		Point
10	7.771179902837788e+37	5.093761388576683e+47	2.5817537965028714e+45

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	62
1	49	62
done	49	62

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.8s	12000×	body	80	nan
1.3s	11741×	body	80	valid