Details

Time bar (total: 19.3s)

sample82.0ms

Algorithm
intervals
Results
34.0ms273×body80valid
22.0ms93×body80nan

simplify203.0ms

Counts
1 → 1
Iterations
IterNodes
done158
7158
6157
5150
4138
3110
262
136
020

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.7b

localize164.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (* b b) (* (* 4.0 a) c))
2.0b
(- (* b b) (* (* 4.0 a) c))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×expm1-log1p-u flip3-- add-cbrt-cube sqrt-div add-exp-log log1p-expm1-u flip--
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 66
Calls
4 calls:
13.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(- (* b b) (* (* 4.0 a) c))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
27.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series375.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (* b b) (* (* 4.0 a) c))
61.0ms
(- (* b b) (* (* 4.0 a) c))
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
132.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts
78 → 78
Iterations
IterNodes
done5000
32176
2551
1177
071

prune752.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.7b

localize159.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (* b b) (* (* 4.0 a) c))
4.3b
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
5.2b
(/ (* a c) b)
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
14×add-cbrt-cube add-exp-log
10×add-sqr-sqrt
9×add-cube-cbrt
8×times-frac
6×associate-/l* add-log-exp
5×pow1
4×expm1-log1p-u cbrt-undiv associate-/r* div-exp log1p-expm1-u distribute-lft-out
3×sqrt-prod
2×clear-num distribute-rgt-neg-in frac-2neg flip3-- sqrt-div div-sub prod-exp cbrt-unprod div-inv flip-- associate-/l/
1×neg-sub0 rem-sqrt-square associate-+r- sub-neg sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff associate-+l- flip-+
Counts
4 → 87
Calls
4 calls:
7.0ms
(- (* b b) (* (* 4.0 a) c))
165.0ms
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
11.0ms
(/ (* a c) b)
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series303.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (* b b) (* (* 4.0 a) c))
107.0ms
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
21.0ms
(/ (* a c) b)
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
99 → 99
Iterations
IterNodes
done5001
21864
1479
0177

prune906.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.4b

localize162.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0b
(- (* b b) (* (* 4.0 a) c))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-cbrt-cube add-exp-log
7×associate-/r* neg-mul-1 times-frac
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- log1p-expm1-u flip--
3×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 → 156
Calls
4 calls:
51.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
29.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(- (* b b) (* (* 4.0 a) c))
25.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series601.0ms

Counts
4 → 12
Calls
4 calls:
278.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
106.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
83.0ms
(- (* b b) (* (* 4.0 a) c))
134.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts
168 → 168
Iterations
IterNodes
done5002
21757
1572
0235

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.9b

localize174.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 2.0 c) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0b
(- (* b b) (* (* 4.0 a) c))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
74×add-sqr-sqrt
73×*-un-lft-identity
61×prod-diff
57×add-cube-cbrt
37×sqrt-prod
27×associate-*r*
26×add-exp-log
25×distribute-rgt-neg-in
21×distribute-lft-neg-in times-frac
16×add-cbrt-cube
12×prod-exp
11×fma-neg
10×pow1 add-log-exp
8×distribute-lft-out-- difference-of-squares
7×neg-mul-1
6×cbrt-unprod
4×expm1-log1p-u flip3-- div-exp log1p-expm1-u 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 → 177
Calls
4 calls:
110.0ms
(* (* 2.0 c) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
26.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms
(- (* b b) (* (* 4.0 a) c))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series588.0ms

Counts
4 → 12
Calls
4 calls:
286.0ms
(* (* 2.0 c) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
123.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
65.0ms
(- (* b b) (* (* 4.0 a) c))
113.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts
189 → 189
Iterations
IterNodes
done5000
22063
1714
0272

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.9b

regimes423.0ms

Accuracy

92.6% (1.1b remaining)

Error of 6.9b against oracle of 5.8b and baseline of 20.9b

bsearch255.0ms

Steps
ItersRangePoint
5
6.972240796235003e+85
2.4695855038465726e+86
1.1138197438371946e+86
9
-6.117539429929052e+154
-3.6285784997486435e+148
-3.2516568688411723e+152

simplify11.0ms

Iterations
IterNodes
done55
155
046

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.6s8721×body80valid
413.0ms2954×body80nan