Details

Time bar (total: 23.0s)

sample90.0ms

Algorithm
intervals
Results
22.0ms184×body80valid
13.0ms31×body2560valid
12.0ms33×body1280valid
6.0ms90×body80nan
3.0ms12×body640valid
2.0ms9×body320valid
0.0ms1×body5120valid
0.0ms2×body160valid

simplify137.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
01217
12217
24216
38316
411216
512016
done12016

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b
(- (* b b) (* (* 3.0 a) c))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite216.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-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 neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
123.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
16.0ms
(- (* b b) (* (* 3.0 a) c))
53.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series512.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
78.0ms
(- (* b b) (* (* 3.0 a) c))
141.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
117.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.1s

Counts
102 → 102
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01671697
14451590
220861363
done50001354

prune817.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.7b

localize53.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.6b
(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
12.4b
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite395.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
124×*-un-lft-identity
90×times-frac
80×add-cube-cbrt
60×prod-diff
44×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
10×fma-neg
8×associate-/r* add-log-exp
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 232
Calls
4 calls:
56.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
175.0ms
(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
121.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series863.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
271.0ms
(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
325.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
124.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.9s

Counts
244 → 244
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
033410067
18487629
247426518
done50006518

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.6b

localize43.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.5b
(/ (/ (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
12.4b
(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite394.0ms

Algorithm
rewrite-expression-head
Rules
376×times-frac
233×add-sqr-sqrt
232×*-un-lft-identity
172×add-cube-cbrt
60×prod-diff
48×sqrt-prod
44×associate-/l*
36×distribute-rgt-neg-in
33×add-exp-log add-cbrt-cube
30×distribute-lft-out-- difference-of-squares
26×associate-/r/
21×distribute-lft-neg-in
18×div-inv
15×cbrt-undiv flip3-- div-exp flip--
10×fma-neg associate-/r*
8×add-log-exp
7×neg-mul-1
6×prod-exp cbrt-unprod
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×frac-2neg sqrt-div diff-log clear-num
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log associate-/l/
Counts
4 → 340
Calls
4 calls:
54.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
170.0ms
(/ (/ (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
109.0ms
(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
21.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series876.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
264.0ms
(/ (/ (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
342.0ms
(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
128.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.1s

Counts
352 → 352
Iterations

Useful iterations: done (1.0s)

IterNodesCost
057914652
1147212136
done500111029

prune2.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.6b

localize48.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.5b
(* (* a 3.0) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
2.5b
(/ (/ (* (* a 3.0) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) 3.0) a)
22.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite333.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
89×*-un-lft-identity
73×add-cube-cbrt
60×prod-diff
54×times-frac
41×add-exp-log add-cbrt-cube
37×sqrt-prod
27×associate-*r*
25×distribute-rgt-neg-in
21×distribute-lft-neg-in
15×cbrt-undiv div-exp
12×prod-exp cbrt-unprod
10×pow1 fma-neg
8×distribute-lft-out-- add-log-exp difference-of-squares
7×neg-mul-1 associate-/l*
6×div-inv
4×expm1-log1p-u log1p-expm1-u
3×flip3-- pow-prod-down associate-/r* flip--
2×sqrt-div diff-log associate-/r/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ associate-*l* neg-log clear-num *-commutative associate-/l/
Counts
4 → 212
Calls
4 calls:
55.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
145.0ms
(* (* a 3.0) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
84.0ms
(/ (/ (* (* a 3.0) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) 3.0) a)
31.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series807.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
293.0ms
(* (* a 3.0) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
246.0ms
(/ (/ (* (* a 3.0) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) 3.0) a)
127.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify833.0ms

Counts
224 → 224
Iterations

Useful iterations: done (817.0ms)

IterNodesCost
03708706
110226680
done50015499

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.6b

regimes385.0ms

Accuracy

88.7% (3.0b remaining)

Error of 8.4b against oracle of 5.4b and baseline of 31.8b

bsearch354.0ms

Steps
ItersRangePoint
8
1.1311204215935077e-37
1.5710948276089558e-34
3.593830924265355e-35
9
-3.913094050847411e-200
-3.3037963711260906e-206
-3.3528823044057167e-206
10
-6.623625638726693e+82
-6.4709084601913214e+72
-2.8920328608199634e+82

simplify13.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03667
14167
24367
34567
done4567

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.2s5794×body80valid
664.0ms1066×body2560valid
448.0ms910×body1280valid
387.0ms2980×body80nan
249.0ms450×body640valid
70.0ms121×body5120valid
53.0ms232×body320valid
24.0ms136×body160valid