Details

sample128.0ms

Algorithm

intervals

Results

45.0ms	256×	body	80	valid
29.0ms	260×	body	80	nan

simplify979.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	33
1	50	33
2	106	33
3	374	33
4	1789	33
done	5001	33

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2.0 (* t 3.0))
0.4b	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
2.2b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
5.6b	(/ (* z (sqrt (+ t a))) t)

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

26×	`frac-sub`
17×	`flip3--` `*-un-lft-identity` `flip--`
16×	`add-exp-log` `add-sqr-sqrt` `frac-times` `add-cbrt-cube`
10×	`add-cube-cbrt` `associate-*r/`
7×	`flip3-+` `flip-+`
6×	`pow1` `distribute-rgt-in` `distribute-lft-in` `times-frac` `associate-r` `associate--r+` `add-log-exp`
5×	`sub-neg` `associate-l`
4×	`cbrt-undiv` `div-exp` `associate-l/` `associate--l+` `associate-/r` `associate-/l*`
3×	`prod-exp` `cbrt-unprod` `distribute-lft-out--`
2×	`frac-2neg` `sqrt-div` `clear-num` `div-inv` `associate-/l/` `difference-of-squares`
1×	`diff-log` `pow-prod-down` `*-commutative` `distribute-lft-out` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

8.0ms	(/ 2.0 (* t 3.0))
206.0ms	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
42.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
15.0ms	(/ (* z (sqrt (+ t a))) t)

series432.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ 2.0 (* t 3.0))
72.0ms	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
224.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
117.0ms	(/ (* z (sqrt (+ t a))) t)

simplify645.0ms

Counts

131 → 131

Iterations

Useful iterations: done (636.0ms)

Iter	Nodes	Cost
0	341	3518
1	1037	3261
done	5000	3149

prune966.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize36.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
2.2b	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
2.3b	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
60×	`frac-sub`
58×	`times-frac`
47×	`*-un-lft-identity`
46×	`associate-r`
39×	`frac-times`
35×	`add-cube-cbrt`
31×	`cbrt-prod`
28×	`sqrt-prod`
27×	`associate-*r/`
25×	`add-exp-log` `flip3--` `flip--`
21×	`associate-*l/`
18×	`add-cbrt-cube`
10×	`unswap-sqr`
9×	`flip3-+` `flip-+`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp` `associate-l`
6×	`pow1` `distribute-lft-out` `associate--r+` `add-log-exp`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
2×	`pow1/3` `associate--l+` `div-inv`
1×	`diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 169

Calls

4 calls:

1.0ms	(cbrt t)
1.0ms	(cbrt t)
88.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
82.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))

series1.1s

Counts

4 → 12

Calls

4 calls:

285.0ms	(cbrt t)
274.0ms	(cbrt t)
333.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
158.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))

simplify805.0ms

Counts

181 → 181

Iterations

Useful iterations: done (793.0ms)

Iter	Nodes	Cost
0	486	6783
1	1855	6317
done	5002	5987

prune1.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
5.7b	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (log (exp (cbrt t))))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
12.0b	(log (exp (cbrt t)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

60×	`frac-sub`
38×	`frac-times`
26×	`associate-*r/`
25×	`flip3--` `flip--`
20×	`associate-*l/`
9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `flip-+`
7×	`log-pow`
6×	`exp-prod` `associate--r+` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube`
3×	`distribute-rgt-in` `sub-neg` `log-prod` `distribute-lft-in`
2×	`pow1/3` `associate--l+`
1×	`diff-log` `rem-log-exp`

Counts

4 → 100

Calls

4 calls:

1.0ms	(cbrt t)
1.0ms	(cbrt t)
91.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (log (exp (cbrt t))))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
6.0ms	(log (exp (cbrt t)))

series1.1s

Counts

4 → 12

Calls

4 calls:

293.0ms	(cbrt t)
272.0ms	(cbrt t)
282.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (log (exp (cbrt t))))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
277.0ms	(log (exp (cbrt t)))

simplify608.0ms

Counts

112 → 112

Iterations

Useful iterations: done (601.0ms)

Iter	Nodes	Cost
0	350	5244
1	1338	4709
done	5000	4518

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 0.6666666666666666 (/ c t))
1.4b	(- (+ (* 0.6666666666666666 (/ c t)) (* 0.8333333333333334 b)) (* 0.6666666666666666 (/ b t)))
1.6b	(- (/ (* z (sqrt (+ t a))) t) (- (+ (* 0.6666666666666666 (/ c t)) (* 0.8333333333333334 b)) (* 0.6666666666666666 (/ b t))))
5.6b	(/ (* z (sqrt (+ t a))) t)

rewrite338.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
18×	`add-log-exp`
16×	`*-un-lft-identity`
14×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
13×	`times-frac` `associate-r`
8×	`frac-sub`
7×	`diff-log` `associate-*r/`
6×	`pow1`
3×	`cbrt-undiv` `sub-neg` `flip3--` `flip3-+` `div-exp` `associate-l` `prod-exp` `associate-/r*` `flip--` `cbrt-unprod` `flip-+` `associate--r+`
2×	`sqrt-div` `associate--l+` `sum-log` `div-inv` `associate-/l/` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l` `distribute-lft-out--` `associate--r-` `difference-of-squares`

Counts

4 → 95

Calls

4 calls:

28.0ms	(* 0.6666666666666666 (/ c t))
98.0ms	(- (+ (* 0.6666666666666666 (/ c t)) (* 0.8333333333333334 b)) (* 0.6666666666666666 (/ b t)))
175.0ms	(- (/ (* z (sqrt (+ t a))) t) (- (+ (* 0.6666666666666666 (/ c t)) (* 0.8333333333333334 b)) (* 0.6666666666666666 (/ b t))))
30.0ms	(/ (* z (sqrt (+ t a))) t)

series488.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* 0.6666666666666666 (/ c t))
77.0ms	(- (+ (* 0.6666666666666666 (/ c t)) (* 0.8333333333333334 b)) (* 0.6666666666666666 (/ b t)))
269.0ms	(- (/ (* z (sqrt (+ t a))) t) (- (+ (* 0.6666666666666666 (/ c t)) (* 0.8333333333333334 b)) (* 0.6666666666666666 (/ b t))))
113.0ms	(/ (* z (sqrt (+ t a))) t)

simplify2.3s

Counts

107 → 107

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	247	2238
1	715	2072
2	3580	1948
done	5001	1941

prune645.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes693.0ms

Accuracy

70.5% (4.5b remaining)

Error of 5.1b against oracle of 0.6b and baseline of 15.9b

bsearch621.0ms

Steps

Iters	Range		Point
6	8.511240283969747e+23	1.2393392759021717e+25	2.592927404032905e+24
10	-1.6049711026790853e-55	-7.338351173601763e-68	-1.5886461827511773e-55

simplify36.0ms

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	60	170
1	82	129
done	82	129

end2.0ms

sample4.3s

Algorithm

intervals

Results

1.5s	7863×	body	80	nan
1.5s	8000×	body	80	valid