Details

Time bar (total: 19.2s)

sample69.0ms

Algorithm
intervals
Results
32.0ms274×body80valid
22.0ms86×body80nan

simplify195.0ms

Counts
1 → 1
Iterations
IterNodes
8152
7152
6151
5144
4132
3101
262
135
020

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.3b

localize204.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* (* 4 a) c))
2.5b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
21.7b
(sqrt (- (* b b) (* (* 4 a) c)))
21.7b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite74.0ms

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-cbrt-cube sqrt-div add-exp-log insert-posit16
3×flip3-- flip--
2×rem-sqrt-square sum-log sqrt-pow1 pow1/2 distribute-lft-out
1×neg-sub0 +-commutative sub-neg distribute-rgt-neg-in flip3-+ diff-log neg-log associate-+l- flip-+
Counts
4 → 61
Calls
4 calls:
15.0ms
(- (* b b) (* (* 4 a) c))
26.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series854.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* (* 4 a) c))
129.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
130.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
547.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.1s

Counts
73 → 73
Iterations
IterNodes
32749
2795
1247
095

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.2b

localize176.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* (* 4 a) c))
3.3b
(/ a (/ b c))
4.3b
(/ (* 2 (- (/ a (/ b c)) b)) (* 2 a))
21.7b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
48×add-sqr-sqrt
47×*-un-lft-identity add-cube-cbrt
21×add-cbrt-cube add-exp-log
14×associate-/r*
7×cbrt-undiv div-exp
6×div-inv add-log-exp
5×pow1
4×prod-exp cbrt-unprod insert-posit16 associate-/l*
3×flip3-- sqrt-prod flip--
2×clear-num frac-2neg sqrt-div associate-*r/ associate-/l/
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log associate-/r/
Counts
4 → 124
Calls
4 calls:
15.0ms
(- (* b b) (* (* 4 a) c))
12.0ms
(/ a (/ b c))
78.0ms
(/ (* 2 (- (/ a (/ b c)) b)) (* 2 a))
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series229.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* (* 4 a) c))
23.0ms
(/ a (/ b c))
49.0ms
(/ (* 2 (- (/ a (/ b c)) b)) (* 2 a))
108.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.7s

Counts
136 → 136
Iterations
IterNodes
22464
1679
0260

prune2.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.0b

localize113.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))))
0.3b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.4b
(- (* b b) (* (* 4 a) c))
21.7b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-cbrt-cube add-exp-log
7×associate-/r* times-frac add-cube-cbrt
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- insert-posit16 flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 80
Calls
4 calls:
45.0ms
(/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))))
14.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
7.0ms
(- (* b b) (* (* 4 a) c))
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series498.0ms

Counts
4 → 12
Calls
4 calls:
246.0ms
(/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))))
101.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
55.0ms
(- (* b b) (* (* 4 a) c))
96.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.1s

Counts
92 → 92
Iterations
IterNodes
34317
21201
1378
0152

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize171.0ms

Local error

Found 4 expressions with local error:

10.6b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
21.7b
(sqrt (- (* b b) (* (* 4 a) c)))
21.7b
(sqrt (- (* b b) (* (* 4 a) c)))
21.7b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div
4×add-cbrt-cube add-exp-log insert-posit16
3×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip--
2×sum-log
1×neg-sub0 +-commutative flip3-+ neg-log associate-+l- flip-+
Counts
4 → 62
Calls
4 calls:
16.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series409.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
86.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
107.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
99.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify837.0ms

Counts
74 → 74
Iterations
IterNodes
32296
2718
1232
087

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

regimes419.0ms

Accuracy

89.2% (1.5b remaining)

Error of 6.9b against oracle of 5.5b and baseline of 19.0b

bsearch327.0ms

Steps
ItersRangePoint
9
2.1762368803982262e+45
1.3534154308951418e+51
2.0167317209326723e+50
8
-1.7996802595953755e+64
-1.2634430355867738e+61
-1.665963569877209e+64

simplify11.0ms

Iterations
IterNodes
351
251
149
044

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.8s8733×body80valid
1.1s2882×body80nan