Details

Time bar (total: 23.6s)

sample150.0ms

Algorithm
intervals
Results
31.0ms161×body160valid
29.0ms523×pre80true
24.0ms267×body80nan
14.0ms48×body320valid
4.0ms47×body80valid

simplify163.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01417
12417
24416
37916
49916
510716
done10716

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
40.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite228.0ms

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:
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
15.0ms
(- (* b b) (* (* 4.0 a) c))
141.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
53.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series535.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
86.0ms
(- (* b b) (* (* 4.0 a) c))
178.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
139.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.7s

Counts
82 → 82
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01541565
14191461
219261245
done50011239

prune606.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize65.0ms

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

rewrite391.0ms

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:
51.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(- (* b b) (* (* 4.0 a) c))
184.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
124.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series987.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
93.0ms
(- (* b b) (* (* 4.0 a) c))
359.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
377.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify3.3s

Counts
163 → 163
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
02475048
16594512
238214174
done50004174

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.4b
(/ (+ 0 (* (* 4.0 a) c)) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite356.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
15×add-sqr-sqrt *-un-lft-identity
10×add-log-exp
9×pow1
7×add-cube-cbrt associate-*r*
6×prod-exp cbrt-unprod
4×sub-neg flip3-- associate-*r/ flip-- distribute-lft-out-- difference-of-squares
3×cbrt-undiv times-frac diff-log div-exp pow-prod-down associate-/l*
2×distribute-rgt-in distribute-rgt-neg-in distribute-lft-in sqrt-prod 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 → 85
Calls
4 calls:
154.0ms
(* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
53.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(- (* b b) (* (* 4.0 a) c))
127.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series755.0ms

Counts
4 → 12
Calls
4 calls:
223.0ms
(* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
157.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
84.0ms
(- (* b b) (* (* 4.0 a) c))
291.0ms
(/ (+ 0 (* (* 4.0 a) c)) (* (* a 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify3.7s

Counts
97 → 97
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
01762262
15432068
243581760
done50011760

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize63.0ms

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
(/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b
(* (/ 1 (* a 2.0)) (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite418.0ms

Algorithm
rewrite-expression-head
Rules
131×add-exp-log
67×add-cbrt-cube
64×prod-exp
40×div-exp
28×add-sqr-sqrt cbrt-unprod
26×*-un-lft-identity
20×cbrt-undiv
17×times-frac
13×associate-*r*
10×add-cube-cbrt add-log-exp
8×rec-exp 1-exp distribute-lft-out-- difference-of-squares
7×associate-*l* associate-/r*
6×pow1
4×flip3-- distribute-rgt-neg-in sqrt-prod associate-/r/ flip--
3×diff-log div-inv
2×sub-neg
1×associate--l- neg-sub0 frac-times frac-2neg associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative associate-/l* unswap-sqr
Counts
4 → 136
Calls
4 calls:
41.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms
(- (* b b) (* (* 4.0 a) c))
104.0ms
(/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
247.0ms
(* (/ 1 (* a 2.0)) (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series809.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
87.0ms
(- (* b b) (* (* 4.0 a) c))
324.0ms
(/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
261.0ms
(* (/ 1 (* a 2.0)) (/ (* 4.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify730.0ms

Counts
148 → 148
Iterations

Useful iterations: done (721.0ms)

IterNodesCost
02574187
18593971
done50013087

prune918.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes381.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01725
12223
22323
done2323

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.3s16466×pre80true
1.1s4844×body160valid
945.0ms8466×body80nan
558.0ms1356×body320valid
160.0ms1800×body80valid