Details

Time bar (total: 19.3s)

sample70.0ms

Algorithm
intervals
Results
37.0ms277×body80valid
12.0ms86×body80nan

simplify196.0ms

Counts
1 → 1
Iterations
IterNodes
done152
7152
6151
5144
4132
3101
262
135
020

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.5b

localize137.0ms

Local error

Found 4 expressions with local error:

0.9b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.2b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
23.5b
(sqrt (- (* b b) (* (* 4 a) c)))
23.5b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite67.0ms

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:
18.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
14.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
10.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
22.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series439.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
108.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
104.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
113.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.1s

Counts
79 → 79
Iterations
IterNodes
done2000
32000
2773
1250
0102

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.2b

localize181.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
4.8b
(/ (* 2 (- (/ a (/ b c)) b)) (* 2 a))
5.5b
(/ a (/ b c))
23.5b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
52×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
21×add-cbrt-cube add-exp-log
14×associate-/r*
8×add-log-exp
7×cbrt-undiv div-exp
6×div-inv
5×pow1
4×prod-exp sqrt-prod cbrt-unprod insert-posit16 associate-/l*
3×flip3-- flip--
2×clear-num frac-2neg sqrt-div diff-log associate-*r/ distribute-lft-out-- difference-of-squares associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square sub-neg distribute-rgt-neg-in sqrt-pow1 pow1/2 neg-log associate-/r/
Counts
4 → 130
Calls
4 calls:
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
69.0ms
(/ (* 2 (- (/ a (/ b c)) b)) (* 2 a))
11.0ms
(/ a (/ b c))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series330.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
69.0ms
(/ (* 2 (- (/ a (/ b c)) b)) (* 2 a))
23.0ms
(/ a (/ b c))
128.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.0s

Counts
142 → 142
Iterations
IterNodes
done2000
22000
1760
0285

prune2.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.2b

localize146.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))))
0.8b
(- (* b b) (* (* 4 a) c))
1.2b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
23.5b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite96.0ms

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:
48.0ms
(/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))))
7.0ms
(- (* b b) (* (* 4 a) c))
24.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series531.0ms

Counts
4 → 12
Calls
4 calls:
254.0ms
(/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))))
80.0ms
(- (* b b) (* (* 4 a) c))
94.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
102.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.2s

Counts
92 → 92
Iterations
IterNodes
done2007
32007
21283
1387
0152

prune1.9s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.2b

localize168.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 2 c) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))))
0.8b
(- (* b b) (* (* 4 a) c))
1.2b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
23.5b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
32×*-un-lft-identity
27×associate-*r*
26×add-exp-log
21×times-frac
16×add-cbrt-cube add-cube-cbrt
12×prod-exp
10×pow1 add-log-exp
8×distribute-lft-out-- difference-of-squares
7×sqrt-prod
6×cbrt-unprod
4×distribute-rgt-neg-in flip3-- div-exp insert-posit16 flip--
3×diff-log pow-prod-down
2×cbrt-undiv rec-exp sub-neg sqrt-div 1-exp associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* neg-log associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 101
Calls
4 calls:
88.0ms
(* (* 2 c) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))))
11.0ms
(- (* b b) (* (* 4 a) c))
32.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
20.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series500.0ms

Counts
4 → 12
Calls
4 calls:
206.0ms
(* (* 2 c) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))))
62.0ms
(- (* b b) (* (* 4 a) c))
114.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
118.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.4s

Counts
113 → 113
Iterations
IterNodes
done2024
32024
21721
1514
0189

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.2b

regimes525.0ms

Accuracy

92.6% (1.1b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 21.0b

bsearch407.0ms

Steps
ItersRangePoint
8
2.231296991249122e+66
2.5939819947174796e+69
2.559678284282607e+69
9
-2.2464591800446616e+91
-3.153507839293123e+86
-1.3599228730895225e+90

simplify19.0ms

Iterations
IterNodes
done56
156
046

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.7s8699×body80valid
910.0ms2954×body80nan