Details

sample71.0ms

Algorithm

intervals

Results

40.0ms	266×	body	80	valid
8.0ms	94×	body	80	nan

simplify163.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize171.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.7b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite82.0ms

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:

31.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
123.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
89.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
111.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
2	1036
1	254
0	100

prune666.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.1b

localize194.0ms

Local error

Found 4 expressions with local error:

21.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series464.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
128.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
107.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
103.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts

72 → 72

Iterations

Iter	Nodes
done	5002
3	3090
2	531
1	137
0	52

prune710.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 8.1b

localize211.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.2b	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
6.6b	(/ (* a c) b)
21.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

38.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
51.0ms	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
8.0ms	(/ (* a c) b)
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series459.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
233.0ms	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
22.0ms	(/ (* a c) b)
95.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
2	2570
1	479
0	179

prune883.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.3b

localize153.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.2b	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ a (/ b c))))))
3.5b	(/ a (/ b c))
21.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

Calls

4 calls:

29.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
32.0ms	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ a (/ b c))))))
10.0ms	(/ a (/ b c))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series515.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
265.0ms	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ a (/ b c))))))
39.0ms	(/ a (/ b c))
95.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts

141 → 141

Iterations

Iter	Nodes
done	5000
2	3595
1	743
0	284

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.3b

regimes449.0ms

Accuracy

84.3% (2.1b remaining)

Error of 8.6b against oracle of 6.5b and baseline of 20.0b

bsearch166.0ms

Steps

Iters	Range		Point
3	5.437233749566996e+22	6.419404774371196e+22	6.358019085320933e+22
8	-4.367569986683318e+31	-6.412561728939963e+28	-4.292636537496693e+31

simplify10.0ms

Iterations

Iter	Nodes
done	55
1	55
0	42

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.6s	8708×	body	80	valid
409.0ms	2942×	body	80	nan