Details

Time bar (total: 23.8s)

sample299.0ms

Algorithm
intervals
Results
75.0ms93×body160valid
35.0ms121×body320valid
24.0ms244×body80nan
20.0ms500×pre80true
9.0ms12×body640valid
3.0ms30×body80valid

simplify187.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
01417
12517
24616
38716
412016
512916
done12916

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.9b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.1b
(- (* b b) (* (* 4.0 a) c))
26.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite261.0ms

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:
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
145.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
18.0ms
(- (* b b) (* (* 4.0 a) c))
68.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series621.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
216.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
95.0ms
(- (* b b) (* (* 4.0 a) c))
168.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify2.6s

Counts
102 → 102
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01671697
14501588
221521361
done50011352

prune809.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite417.0ms

Algorithm
rewrite-expression-head
Rules
123×add-sqr-sqrt *-un-lft-identity
90×times-frac
79×add-cube-cbrt
61×prod-diff
41×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
11×fma-neg
10×add-log-exp
8×associate-/r*
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 expm1-log1p-u log1p-expm1-u 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 → 231
Calls
4 calls:
64.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms
(- (* b b) (* (* 4.0 a) c))
117.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
195.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series954.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
97.0ms
(- (* b b) (* (* 4.0 a) c))
343.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
370.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify845.0ms

Counts
243 → 243
Iterations

Useful iterations: done (825.0ms)

IterNodesCost
033910026
18577622
done50006606

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite396.0ms

Algorithm
rewrite-expression-head
Rules
181×prod-diff
132×add-sqr-sqrt *-un-lft-identity
124×add-cube-cbrt
92×sqrt-prod
62×distribute-rgt-in distribute-lft-in
59×distribute-rgt-neg-in
57×distribute-lft-neg-in
19×neg-mul-1
18×add-exp-log add-cbrt-cube
11×fma-neg
10×add-log-exp
9×pow1
7×associate-*r*
6×prod-exp cbrt-unprod
4×expm1-log1p-u sub-neg flip3-- associate-*r/ flip-- log1p-expm1-u distribute-lft-out-- difference-of-squares
3×cbrt-undiv times-frac diff-log div-exp pow-prod-down associate-/l*
2×associate-/r/ associate-/l/
1×associate--l- neg-sub0 frac-2neg flip3-+ associate-*l* neg-log clear-num associate-/r* *-commutative flip-+ div-inv
Counts
4 → 285
Calls
4 calls:
60.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
176.0ms
(* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
17.0ms
(- (* b b) (* (* 4.0 a) c))
110.0ms
(/ (+ 0 (* c (* 4.0 a))) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series789.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
210.0ms
(* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
88.0ms
(- (* b b) (* (* 4.0 a) c))
345.0ms
(/ (+ 0 (* c (* 4.0 a))) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify1.1s

Counts
297 → 297
Iterations

Useful iterations: done (1.0s)

IterNodesCost
036817588
1112511818
done50009508

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (cbrt (pow (- (pow b 2) (* 4.0 (* a c))) 3)))))
0.3b
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (cbrt (pow (- (pow b 2) (* 4.0 (* a c))) 3))))) (* 2.0 a))
0.5b
(cbrt (pow (- (pow b 2) (* 4.0 (* a c))) 3))
0.7b
(pow (- (pow b 2) (* 4.0 (* a c))) 3)

rewrite777.0ms

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 expm1-log1p-u log1p-expm1-u 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 → 217
Calls
4 calls:
266.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (cbrt (pow (- (pow b 2) (* 4.0 (* a c))) 3)))))
420.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (cbrt (pow (- (pow b 2) (* 4.0 (* a c))) 3))))) (* 2.0 a))
30.0ms
(cbrt (pow (- (pow b 2) (* 4.0 (* a c))) 3))
36.0ms
(pow (- (pow b 2) (* 4.0 (* a c))) 3)

series932.0ms

Counts
4 → 12
Calls
4 calls:
336.0ms
(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (cbrt (pow (- (pow b 2) (* 4.0 (* a c))) 3)))))
328.0ms
(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (cbrt (pow (- (pow b 2) (* 4.0 (* a c))) 3))))) (* 2.0 a))
94.0ms
(cbrt (pow (- (pow b 2) (* 4.0 (* a c))) 3))
174.0ms
(pow (- (pow b 2) (* 4.0 (* a c))) 3)

simplify886.0ms

Counts
229 → 229
Iterations

Useful iterations: done (866.0ms)

IterNodesCost
03488034
19526549
done50006169

prune2.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes428.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01825
12223
done2223

end0.0ms

sample6.3s

Algorithm
intervals
Results
1.4s3688×body320valid
1.4s16221×pre80true
1.4s8221×body80nan
727.0ms2937×body160valid
233.0ms493×body640valid
137.0ms882×body80valid