Details

sample57.0ms

Algorithm

intervals

Results

23.0ms	286×	body	80	valid
14.0ms	79×	body	80	nan

simplify224.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize135.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite94.0ms

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:

47.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
105.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
90.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
127.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify710.0ms

Counts

75 → 75

Iterations

Useful iterations: done (706.0ms)

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

prune480.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.7b

localize171.0ms

Local error

Found 4 expressions with local error:

5.0b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite72.0ms

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:

25.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series598.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
101.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
181.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
170.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts

67 → 67

Iterations

Useful iterations: done (1.1s)

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

prune578.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.7b

localize153.0ms

Local error

Found 4 expressions with local error:

9.1b	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))
22.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite53.0ms

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` `add-cbrt-cube`
3×	`flip3--` `sqrt-prod` `flip--`
2×	`pow1/3` `sqrt-div` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 54

Calls

4 calls:

22.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
106.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
126.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
120.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts

66 → 66

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	146	1516
1	382	1425
2	1650	1235
done	5001	1203

prune578.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 6.7b

localize137.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.6b	(/ (* a c) b)
4.6b	(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(/ (* a c) b)
61.0ms	(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
38.0ms	(/ (* a c) b)
120.0ms	(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
100.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

86 → 86

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	173	1340
1	488	1252
2	2696	1090
done	5000	1082

prune429.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 6.3b

regimes249.0ms

Accuracy

88.6% (1.4b remaining)

Error of 8.4b against oracle of 7.0b and baseline of 19.4b

bsearch284.0ms

Steps

Iters	Range		Point
8	3932480935863.943	2020002846347102.2	929319867835151.5
9	-7.561250615295736e+156	-1.350243324689865e+150	-1.3130331840827711e+154

simplify25.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	47	132
1	59	132
done	59	132

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.5s	8765×	body	80	valid
418.0ms	2894×	body	80	nan