Details

sample88.0ms

Algorithm

intervals

Results

37.0ms	283×	body	80	valid
11.0ms	79×	body	80	nan

simplify127.0ms

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: 20.6b

localize176.0ms

Local error

Found 4 expressions with local error:

1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.6b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite86.0ms

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:

32.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
34.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
128.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
110.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
97.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify752.0ms

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
2	1036
1	254
0	100

prune655.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.7b

localize156.0ms

Local error

Found 4 expressions with local error:

1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.8b	(/ (* 2.0 c) (+ (* -2 b) (/ (* a 2.0) (/ b c))))
5.9b	(/ (* a 2.0) (/ b c))
24.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite103.0ms

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:

30.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
38.0ms	(/ (* 2.0 c) (+ (* -2 b) (/ (* a 2.0) (/ b c))))
17.0ms	(/ (* a 2.0) (/ b c))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series507.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
243.0ms	(/ (* 2.0 c) (+ (* -2 b) (/ (* a 2.0) (/ b c))))
48.0ms	(/ (* a 2.0) (/ b c))
99.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

111 → 111

Iterations

Iter	Nodes
done	5001
2	3945
1	686
0	240

prune836.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.7b

localize148.0ms

Local error

Found 4 expressions with local error:

1.8b	(/ (* 2.0 c) (+ (* -2 b) (/ (* a 2.0) (/ b c))))
2.2b	(/ (- (/ (* 2.0 a) (/ b c)) (* 2 b)) (* 2.0 a))
5.9b	(/ (* 2.0 a) (/ b c))
5.9b	(/ (* a 2.0) (/ b c))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

68×	`times-frac`
38×	`add-cbrt-cube` `add-exp-log`
36×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
30×	`associate-/r*`
16×	`cbrt-undiv` `div-exp`
8×	`div-inv`
6×	`prod-exp` `cbrt-unprod` `associate-/l*`
4×	`pow1` `clear-num` `frac-2neg` `associate-/r/` `add-log-exp`
2×	`associate-/l/`
1×	`flip3-+` `flip3--` `div-sub` `flip-+` `flip--`

Counts

4 → 139

Calls

4 calls:

35.0ms	(/ (* 2.0 c) (+ (* -2 b) (/ (* a 2.0) (/ b c))))
89.0ms	(/ (- (/ (* 2.0 a) (/ b c)) (* 2 b)) (* 2.0 a))
23.0ms	(/ (* 2.0 a) (/ b c))
23.0ms	(/ (* a 2.0) (/ b c))

series472.0ms

Counts

4 → 12

Calls

4 calls:

297.0ms	(/ (* 2.0 c) (+ (* -2 b) (/ (* a 2.0) (/ b c))))
103.0ms	(/ (- (/ (* 2.0 a) (/ b c)) (* 2 b)) (* 2.0 a))
36.0ms	(/ (* 2.0 a) (/ b c))
36.0ms	(/ (* a 2.0) (/ b c))

simplify525.0ms

Counts

151 → 151

Iterations

Iter	Nodes
done	5001
1	847
0	273

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize208.0ms

Local error

Found 4 expressions with local error:

5.9b	(/ (* 2.0 a) (/ b c))
18.7b	(cbrt (* (/ a (/ b c)) 2.0))
18.7b	(cbrt (* (/ a (/ b c)) 2.0))
18.7b	(cbrt (* (/ a (/ b c)) 2.0))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
18×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
13×	`associate-/r*`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `add-log-exp`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `associate-*l/` `div-inv`
2×	`prod-exp` `cbrt-unprod`
1×	`clear-num` `frac-2neg` `associate-/r/` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

26.0ms	(/ (* 2.0 a) (/ b c))
17.0ms	(cbrt (* (/ a (/ b c)) 2.0))
17.0ms	(cbrt (* (/ a (/ b c)) 2.0))
17.0ms	(cbrt (* (/ a (/ b c)) 2.0))

series545.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (* 2.0 a) (/ b c))
169.0ms	(cbrt (* (/ a (/ b c)) 2.0))
155.0ms	(cbrt (* (/ a (/ b c)) 2.0))
170.0ms	(cbrt (* (/ a (/ b c)) 2.0))

simplify1.1s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	2132
1	394
0	160

prune798.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

regimes461.0ms

Accuracy

93% (1.2b remaining)

Error of 6.6b against oracle of 5.4b and baseline of 21.9b

bsearch296.0ms

Steps

Iters	Range		Point
9	2.1340360609407003e+79	6.102484722804822e+84	2.6205431397402643e+84
9	-3.845605078781637e+76	-1.2146338677939432e+68	-7.943482039519134e+75

simplify10.0ms

Iterations

Iter	Nodes
done	69
1	69
0	57

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.1s	8696×	body	80	valid
830.0ms	2886×	body	80	nan