Details

sample76.0ms

Algorithm

intervals

Results

45.0ms	274×	body	80	valid
12.0ms	88×	body	80	nan

simplify186.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	168
7	168
6	166
5	160
4	151
3	125
2	75
1	38
0	20

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.4b

localize147.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
21.0b	(sqrt (- (* b b) (* (* 4 a) c)))
21.0b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite54.0ms

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` `insert-posit16`
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 → 67

Calls

4 calls:

14.0ms	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
19.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
12.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series484.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
137.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
97.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
112.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify986.0ms

Counts

79 → 79

Iterations

Iter	Nodes
3	2437
2	760
1	248
0	102

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

localize211.0ms

Local error

Found 4 expressions with local error:

12.3b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
21.0b	(sqrt (- (* b b) (* (* 4 a) c)))
21.0b	(sqrt (- (* b b) (* (* 4 a) c)))
21.0b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`sqrt-div`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log` `difference-of-squares`

Counts

4 → 64

Calls

4 calls:

8.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
7.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
10.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
87.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
94.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
110.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify830.0ms

Counts

76 → 76

Iterations

Iter	Nodes
3	2124
2	658
1	224
0	91

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.3b

localize205.0ms

Local error

Found 4 expressions with local error:

21.0b	(sqrt (- (* b b) (* (* 4 a) c)))
21.8b	(cbrt (- (* b b) (* (* 4 a) c)))
21.8b	(cbrt (- (* b b) (* (* 4 a) c)))
21.8b	(cbrt (- (* b b) (* (* 4 a) c)))

rewrite24.0ms

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` `insert-posit16` `flip--` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

8.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

series520.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
138.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
121.0ms	(cbrt (- (* b b) (* (* 4 a) c)))
134.0ms	(cbrt (- (* b b) (* (* 4 a) c)))

simplify3.7s

Counts

70 → 70

Iterations

Iter	Nodes
4	6322
3	1876
2	580
1	200
0	89

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.3b

localize171.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
2.9b	(/ (* 2 c) (* (- (* (/ a b) c) b) 2))
4.9b	(* (/ a b) c)
21.0b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cbrt-cube` `add-exp-log`
17×	`*-un-lft-identity`
13×	`associate-l` `add-cube-cbrt`
11×	`times-frac`
8×	`add-log-exp`
7×	`pow1`
6×	`prod-exp` `cbrt-unprod`
5×	`cbrt-undiv` `div-exp`
4×	`sqrt-prod` `insert-posit16`
3×	`flip3--` `associate-r` `associate-*l/` `flip--`
2×	`sqrt-div` `diff-log` `associate-/r/` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `-commutative` `associate-/l*`

Counts

4 → 92

Calls

4 calls:

30.0ms	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
51.0ms	(/ (* 2 c) (* (- (* (/ a b) c) b) 2))
15.0ms	(* (/ a b) c)
7.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series332.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
74.0ms	(/ (* 2 c) (* (- (* (/ a b) c) b) 2))
33.0ms	(* (/ a b) c)
128.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify994.0ms

Counts

104 → 104

Iterations

Iter	Nodes
2	2143
1	523
0	202

prune1.6s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.3b

regimes425.0ms

Accuracy

93.1% (1.0b remaining)

Error of 6.5b against oracle of 5.5b and baseline of 19.7b

bsearch392.0ms

Steps

Iters	Range		Point
9	1.7155709022758137e+74	7.648947555279674e+80	5.909172052458495e+80
10	-1.0499721897563905e+163	-8.354690034354516e+151	-2.8096996975249965e+152

simplify12.0ms

Iterations

Iter	Nodes
2	49
1	49
0	41

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.3s	8721×	body	80	valid
499.0ms	2901×	body	80	nan