Details

sample90.0ms

Algorithm

intervals

Results

36.0ms	271×	body	80	valid
15.0ms	102×	body	80	nan

simplify169.0ms

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.2b

localize172.0ms

Local error

Found 4 expressions with local error:

1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite96.0ms

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-cbrt-cube` `sqrt-div` `add-exp-log`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `sum-log` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `+-commutative` `sub-neg` `flip3-+` `associate-+l-` `flip-+`

Counts

4 → 63

Calls

4 calls:

27.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
36.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
113.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
113.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
128.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify673.0ms

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
2	1036
1	254
0	100

prune629.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.5b

localize142.0ms

Local error

Found 4 expressions with local error:

7.1b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.8b	(cbrt (- (* b b) (* (* 4.0 a) c)))
23.8b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

10.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series572.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
117.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
146.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
167.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify824.0ms

Counts

67 → 67

Iterations

Iter	Nodes
done	5001
2	1557
1	374
0	149

prune774.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.5b

localize221.0ms

Local error

Found 4 expressions with local error:

22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.8b	(cbrt (- (* b b) (* (* c 4.0) a)))
23.8b	(cbrt (- (* b b) (* (* c 4.0) a)))
23.8b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `flip--` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms	(cbrt (- (* b b) (* (* c 4.0) a)))
4.0ms	(cbrt (- (* b b) (* (* c 4.0) a)))
5.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
142.0ms	(cbrt (- (* b b) (* (* c 4.0) a)))
138.0ms	(cbrt (- (* b b) (* (* c 4.0) a)))
130.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify2.9s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
3	4859
2	939
1	277
0	116

prune895.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize149.0ms

Local error

Found 4 expressions with local error:

1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.4b	(/ (* 2.0 c) (+ (* -2 b) (/ (* a 2.0) (/ b c))))
6.3b	(/ (* a 2.0) (/ b c))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

16.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
36.0ms	(/ (* 2.0 c) (+ (* -2 b) (/ (* a 2.0) (/ b c))))
14.0ms	(/ (* a 2.0) (/ b c))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series546.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
281.0ms	(/ (* 2.0 c) (+ (* -2 b) (/ (* a 2.0) (/ b c))))
53.0ms	(/ (* a 2.0) (/ b c))
90.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts

111 → 111

Iterations

Iter	Nodes
done	5001
2	3945
1	686
0	240

prune775.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.5b

regimes503.0ms

Accuracy

92% (1.2b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 20.1b

bsearch416.0ms

Steps

Iters	Range		Point
9	6.258218916731328e+93	1.8883840965187804e+99	2.3494029304271108e+98
11	-2.5193242592864883e+168	-1.4178648401840193e+143	-3.2411871725505594e+147

simplify12.0ms

Iterations

Iter	Nodes
done	67
1	67
0	56

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.1s	8769×	body	80	valid
396.0ms	2946×	body	80	nan