Details

Time bar (total: 10.6s)

sample59.0ms

Algorithm
intervals
Results
11.0ms329×body80nan
11.0ms153×body160valid
11.0ms585×pre80true
7.0ms103×body80valid

simplify45.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12417
24416
37916
49216
510016
done10016

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
29.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite55.0ms

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:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(- (* b b) (* (* 4.0 a) c))
36.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series297.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms
(- (* b b) (* (* 4.0 a) c))
103.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify475.0ms

Counts
82 → 82
Iterations

Useful iterations: done (472.0ms)

IterNodesCost
01541565
14131461
214611245
done50001235

prune196.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.4b
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite110.0ms

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:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
50.0ms
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
38.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series450.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(- (* b b) (* (* 4.0 a) c))
148.0ms
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
181.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify1.1s

Counts
163 → 163
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02505760
16595251
226384489
done50014467

prune474.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4))))))
0.4b
(* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c)))
0.4b
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))
0.8b
(pow (* (* 4.0 a) c) 3)

rewrite315.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
58×*-un-lft-identity times-frac
36×difference-of-squares
34×add-cube-cbrt
23×add-exp-log add-cbrt-cube
21×sqr-pow
19×pow1
13×associate-/l*
12×distribute-lft-out--
11×associate-/r*
9×unpow-prod-down pow-prod-down prod-exp cbrt-unprod
8×sqrt-prod
4×distribute-rgt-neg-in associate-/r/ associate-/l/ add-log-exp
3×pow-unpow pow-pow flip3-+ associate-*r* pow-exp flip-+ rem-cube-cbrt
2×cbrt-undiv flip3-- frac-2neg associate-*r/ div-exp clear-num flip-- div-inv
1×distribute-rgt-in cube-mult pow-to-exp distribute-lft-in unpow3 div-sub cube-prod associate-*l* *-commutative
Counts
4 → 161
Calls
4 calls:
217.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4))))))
22.0ms
(* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c)))
64.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))
6.0ms
(pow (* (* 4.0 a) c) 3)

series551.0ms

Counts
4 → 12
Calls
4 calls:
282.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4))))))
76.0ms
(* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c)))
134.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* 4.0 (* a c)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))
59.0ms
(pow (* (* 4.0 a) c) 3)

simplify2.3s

Counts
173 → 173
Iterations

Useful iterations: done (2.3s)

IterNodesCost
03417766
18827344
240506750
done50006749

prune857.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
0.4b
(* (/ (+ 0 (* 4.0 (* a c))) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
332×times-frac
260×add-sqr-sqrt
234×*-un-lft-identity
144×add-cube-cbrt
85×associate-*r*
48×add-exp-log
44×distribute-lft-out-- difference-of-squares
30×add-cbrt-cube
27×associate-/l*
23×div-exp
22×distribute-rgt-neg-in sqrt-prod
14×associate-/r/
13×associate-*l*
12×cbrt-undiv
10×prod-exp div-inv add-log-exp
9×flip3-- flip--
8×unswap-sqr
6×pow1 cbrt-unprod
3×rec-exp diff-log 1-exp associate-/r*
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/
Counts
4 → 292
Calls
4 calls:
14.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0ms
(- (* b b) (* (* 4.0 a) c))
36.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
89.0ms
(* (/ (+ 0 (* 4.0 (* a c))) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series397.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(- (* b b) (* (* 4.0 a) c))
121.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
153.0ms
(* (/ (+ 0 (* 4.0 (* a c))) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify447.0ms

Counts
304 → 304
Iterations

Useful iterations: done (437.0ms)

IterNodesCost
04179274
112538224
done50017928

prune678.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

regimes196.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
02547
13345
23545
done3545

end0.0ms

sample1.4s

Algorithm
intervals
Results
318.0ms4500×body160valid
310.0ms16575×pre80true
292.0ms8575×body80nan
131.0ms3500×body80valid