Details

sample63.0ms

Algorithm

intervals

Results

27.0ms	283×	body	80	valid
7.0ms	96×	body	80	nan

simplify9.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.6b

localize153.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
2.0b	(+ (- 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)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `distribute-rgt-neg-in` `flip3-+` `diff-log` `neg-log` `flip-+`

Counts

4 → 57

Calls

4 calls:

10.0ms	(- (* b b) (* (* 4.0 a) c))
30.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (* b b) (* (* 4.0 a) c))
126.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
96.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
102.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify142.0ms

Counts: 69 → 69

prune437.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 10.4b

localize104.0ms

Local error

Found 4 expressions with local error:

2.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.2b	(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
5.6b	(/ (* a c) b)
24.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

27.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
22.0ms	(/ (* a c) b)
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
101.0ms	(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
25.0ms	(/ (* a c) b)
124.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify57.0ms

Counts: 93 → 93

prune529.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.7b

localize146.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
1.2b	(- (* b b) (* (* 4.0 a) c))
2.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

92.0ms	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.0ms	(- (* b b) (* (* 4.0 a) c))
40.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series656.0ms

Counts

4 → 12

Calls

4 calls:

372.0ms	(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
83.0ms	(- (* b b) (* (* 4.0 a) c))
91.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
110.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify37.0ms

Counts: 81 → 81

prune442.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.5b

localize115.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 c))
1.2b	(- (* b b) (* (* 4.0 a) c))
2.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

71.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 c))
8.0ms	(- (* b b) (* (* 4.0 a) c))
28.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 c))
49.0ms	(- (* b b) (* (* 4.0 a) c))
89.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
80.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify39.0ms

Counts: 82 → 82

prune337.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.7b

regimes361.0ms

Accuracy

91.5% (1.3b remaining)

Error of 6.9b against oracle of 5.6b and baseline of 21.3b

bsearch297.0ms

Steps

Iters	Range		Point
9	1.2073698495971617e+61	8.75865749938149e+67	4.620002785864607e+67
10	-2.3639790504379266e+162	-1.7004475472942417e+152	-1.333835582926585e+154

simplify71.0ms

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.4s	8706×	body	80	valid
321.0ms	2844×	body	80	nan