Details

Time bar (total: 6.2s)

sample61.0ms

Algorithm
intervals
Results
15.0ms161×body160valid
10.0ms297×body80nan
9.0ms553×pre80true
3.0ms31×body320valid
2.0ms64×body80valid

simplify11.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059
done1059

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b
(- (* b b) (* (* 4.0 a) c))
39.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite107.0ms

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:
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
68.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(- (* b b) (* (* 4.0 a) c))
21.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series313.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
110.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
45.0ms
(- (* b b) (* (* 4.0 a) c))
83.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify46.0ms

Counts
82 → 82
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0405779
11563685
25002674
done5002674

prune200.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
82×add-sqr-sqrt *-un-lft-identity
38×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
11×distribute-rgt-neg-in sqrt-prod
10×add-log-exp
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 151
Calls
4 calls:
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
58.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
89.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series473.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms
(- (* b b) (* (* 4.0 a) c))
188.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
157.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify114.0ms

Counts
163 → 163
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
06422664
131752400
250022388
done50022388

prune560.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
0.5b
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
0.7b
(pow (- (* b b) (* (* 4.0 a) c)) 3)

rewrite274.0ms

Algorithm
rewrite-expression-head
Rules
166×add-sqr-sqrt
138×times-frac
96×*-un-lft-identity
60×difference-of-squares
56×add-cube-cbrt
52×cbrt-prod
50×sqrt-prod
42×associate-/l*
20×distribute-lft-out--
19×add-exp-log add-cbrt-cube
16×unpow-prod-down cube-prod
12×associate-/r* sqr-pow
10×distribute-rgt-neg-in
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×cube-div div-inv add-log-exp
3×pow-unpow associate-/l/
2×cube-mult cbrt-div frac-2neg unpow3 prod-exp clear-num cbrt-unprod
1×pow-to-exp pow-pow flip3-+ pow1/3 pow-exp rem-cbrt-cube flip-+ rem-cube-cbrt
Counts
4 → 209
Calls
4 calls:
95.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
146.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
10.0ms
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
11.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

series472.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
147.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
48.0ms
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
94.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

simplify149.0ms

Counts
221 → 221
Iterations

Useful iterations: 2 (116.0ms)

IterNodesCost
08564206
144263827
250013808
done50013808

prune571.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 4.0 (* a c)) a)
0.1b
(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(/ (/ (* 4.0 (* a c)) a) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.2b
(- (* b b) (* (* 4.0 a) c))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
126×times-frac
90×*-un-lft-identity
56×add-sqr-sqrt add-cube-cbrt
32×distribute-lft-neg-in distribute-rgt-neg-in
27×add-exp-log add-cbrt-cube
17×distribute-lft-out
15×associate-/r* div-inv
10×cbrt-undiv div-exp
8×neg-mul-1 associate-/l* add-log-exp
6×prod-exp cbrt-unprod
4×pow1
2×frac-2neg flip3-+ clear-num associate-/r/ flip-+ distribute-neg-frac
1×+-commutative sub-neg flip3-- diff-log sum-log flip-- associate-/l/
Counts
4 → 171
Calls
4 calls:
20.0ms
(/ (* 4.0 (* a c)) a)
15.0ms
(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms
(/ (/ (* 4.0 (* a c)) a) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms
(- (* b b) (* (* 4.0 a) c))

series284.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(/ (* 4.0 (* a c)) a)
79.0ms
(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
149.0ms
(/ (/ (* 4.0 (* a c)) a) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
45.0ms
(- (* b b) (* (* 4.0 a) c))

simplify104.0ms

Counts
183 → 183
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
08112685
142952456
250032436
done50032436

prune433.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes119.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04327
14427
24427
done4427

end0.0ms

sample1.5s

Algorithm
intervals
Results
321.0ms4854×body160valid
282.0ms16492×pre80true
269.0ms8492×body80nan
139.0ms1348×body320valid
63.0ms1798×body80valid