Details

sample147.0ms

Algorithm

intervals

Results

44.0ms	256×	body	80	valid
38.0ms	301×	body	80	nan

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	33
1	50	33
2	106	33
3	373	33
4	1497	33
done	5001	33

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.5b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
0.3b	(/ 2.0 (* t 3.0))
2.5b	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
7.1b	(/ (* z (sqrt (+ t a))) t)

rewrite322.0ms

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:

247.0ms	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
8.0ms	(/ 2.0 (* t 3.0))
45.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
16.0ms	(/ (* z (sqrt (+ t a))) t)

series483.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))
25.0ms	(/ 2.0 (* t 3.0))
270.0ms	(- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))
88.0ms	(/ (* z (sqrt (+ t a))) t)

simplify2.2s

Counts

131 → 131

Iterations

Useful iterations: 2 (822.0ms)

Iter	Nodes	Cost
0	341	3518
1	998	3261
2	4569	3129
done	5001	3129

prune938.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
1.2b	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
2.5b	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

rewrite151.0ms

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)
69.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
63.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

series949.0ms

Counts

4 → 12

Calls

4 calls:

242.0ms	(cbrt t)
219.0ms	(cbrt t)
151.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t)))
337.0ms	(- (* (/ z (* (cbrt t) (cbrt t))) (/ (sqrt (+ t a)) (cbrt t))) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))

simplify884.0ms

Counts

181 → 181

Iterations

Useful iterations: done (874.0ms)

Iter	Nodes	Cost
0	486	6783
1	1717	6293
done	5001	5978

prune1.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 0.6666666666666666 (/ c t))
1.2b	(- (+ (* 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))))
7.1b	(/ (* z (sqrt (+ t a))) t)

rewrite276.0ms

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:

20.0ms	(* 0.6666666666666666 (/ c t))
110.0ms	(- (+ (* 0.6666666666666666 (/ c t)) (* 0.8333333333333334 b)) (* 0.6666666666666666 (/ b t)))
115.0ms	(- (/ (* z (sqrt (+ t a))) t) (- (+ (* 0.6666666666666666 (/ c t)) (* 0.8333333333333334 b)) (* 0.6666666666666666 (/ b t))))
28.0ms	(/ (* z (sqrt (+ t a))) t)

series460.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* 0.6666666666666666 (/ c t))
68.0ms	(- (+ (* 0.6666666666666666 (/ c t)) (* 0.8333333333333334 b)) (* 0.6666666666666666 (/ b t)))
253.0ms	(- (/ (* z (sqrt (+ t a))) t) (- (+ (* 0.6666666666666666 (/ c t)) (* 0.8333333333333334 b)) (* 0.6666666666666666 (/ b t))))
108.0ms	(/ (* z (sqrt (+ t a))) t)

simplify1.5s

Counts

107 → 107

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	247	2238
1	683	2068
2	2503	1934
done	5000	1909

prune1.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* c (+ a 0.8333333333333334))
0.0b	(/ x (+ x (* y (exp (* 2.0 (- (* c (+ a 0.8333333333333334)) (* a b)))))))
0.0b	(* y (exp (* 2.0 (- (* c (+ a 0.8333333333333334)) (* a b)))))
1.8b	(- (* c (+ a 0.8333333333333334)) (* a b))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`associate-r`
10×	`add-cbrt-cube`
9×	`add-exp-log` `times-frac`
8×	`pow1` `distribute-rgt-in` `distribute-lft-in` `exp-sum`
6×	`associate-l` `associate--l+` `add-log-exp`
3×	`sub-neg` `associate-/r` `associate-/l`
2×	`flip3-+` `associate-r/` `pow-prod-down` `prod-exp` `associate-/r/` `-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `div-inv` `distribute-lft-out`

Counts

4 → 92

Calls

4 calls:

35.0ms	(* c (+ a 0.8333333333333334))
23.0ms	(/ x (+ x (* y (exp (* 2.0 (- (* c (+ a 0.8333333333333334)) (* a b)))))))
65.0ms	(* y (exp (* 2.0 (- (* c (+ a 0.8333333333333334)) (* a b)))))
21.0ms	(- (* c (+ a 0.8333333333333334)) (* a b))

series383.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* c (+ a 0.8333333333333334))
169.0ms	(/ x (+ x (* y (exp (* 2.0 (- (* c (+ a 0.8333333333333334)) (* a b)))))))
96.0ms	(* y (exp (* 2.0 (- (* c (+ a 0.8333333333333334)) (* a b)))))
66.0ms	(- (* c (+ a 0.8333333333333334)) (* a b))

simplify2.6s

Counts

104 → 104

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	181	1748
1	423	1669
2	1165	1533
3	4152	1531
done	5000	1531

prune427.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes422.0ms

Accuracy

11.2% (2.1b remaining)

Error of 2.4b against oracle of 0.3b and baseline of 2.7b

bsearch375.0ms

Steps

Iters	Range		Point
9	4.732469351843458e-247	2.1112207656587559e-240	9.548444342446725e-247
2	-1.0247148128888417e-243	-9.008756360082794e-244	-9.473153273384903e-244

simplify19.0ms

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	57	166
1	79	127
done	79	127

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.3s	8000×	body	80	valid
1.4s	7982×	body	80	nan