Details

sample104.0ms

Algorithm

intervals

Results

54.0ms	281×	body	80	valid
13.0ms	108×	body	80	nan

simplify206.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	20	38
1	35	38
2	66	37
3	116	37
4	150	37
5	164	37
6	166	37
done	166	37

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.0b

localize125.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-log-exp`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `sum-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate--l-` `associate-+l-` `sub-neg` `flip3-+` `flip-+`

Counts

4 → 63

Calls

4 calls:

43.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
31.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
116.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
100.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
111.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify738.0ms

Counts

75 → 75

Iterations

Useful iterations: done (736.0ms)

Iter	Nodes	Cost
0	100	1330
1	255	1186
2	1030	1089
done	5000	1074

prune485.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.4b

localize151.0ms

Local error

Found 4 expressions with local error:

6.7b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))
23.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--`
3×	`sqrt-prod`
2×	`pow1/3` `sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 55

Calls

4 calls:

13.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series531.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
131.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
137.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
140.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify940.0ms

Counts

67 → 67

Iterations

Useful iterations: done (936.0ms)

Iter	Nodes	Cost
0	149	1566
1	379	1475
2	1626	1275
done	5000	1259

prune531.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.4b

localize161.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.7b	(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
5.1b	(/ (* a c) b)
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite283.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
14×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt`
8×	`times-frac` `add-log-exp`
6×	`associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `div-exp` `associate-/r*` `sqrt-prod` `distribute-lft-out`
3×	`distribute-rgt-neg-in`
2×	`neg-sub0` `flip3--` `frac-2neg` `sqrt-div` `diff-log` `div-sub` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `associate-+l-` `associate-+r-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 83

Calls

4 calls:

42.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
207.0ms	(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
12.0ms	(/ (* a c) b)
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
120.0ms	(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
38.0ms	(/ (* a c) b)
105.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

95 → 95

Iterations

Useful iterations: 2 (404.0ms)

Iter	Nodes	Cost
0	187	1588
1	500	1449
2	2523	1291
done	5001	1291

prune614.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.6b

localize125.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `associate-/r*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

59.0ms	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.0ms	(- (* b b) (* (* 4.0 a) c))
50.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series615.0ms

Counts

4 → 12

Calls

4 calls:

305.0ms	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
71.0ms	(- (* b b) (* (* 4.0 a) c))
109.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
130.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts

88 → 88

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	149	1693
1	386	1585
2	1889	1419
done	5001	1399

prune448.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

regimes310.0ms

Accuracy

91.8% (1.2b remaining)

Error of 7.3b against oracle of 6.1b and baseline of 20.7b

bsearch713.0ms

Steps

Iters	Range		Point
6	1.9101351599902807e+102	2.525038855038462e+103	5.291645547718113e+102
9	-9.502057580036763e+144	-6.537164733756459e+138	-4.7395197774900957e+139

simplify11.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	47	117
1	57	117
done	57	117

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	8730×	body	80	valid
395.0ms	2902×	body	80	nan