Details

Time bar (total: 25.8s)

sample169.0ms

Algorithm
intervals
Results
53.0ms527×pre80true
29.0ms151×body160valid
25.0ms271×body80nan
10.0ms105×body80valid

simplify145.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
01417
12417
24416
37916
49916
510716
done10716

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize41.0ms

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))
29.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite250.0ms

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:
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
164.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
17.0ms
(- (* b b) (* (* 4.0 a) c))
46.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series601.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
222.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
86.0ms
(- (* b b) (* (* 4.0 a) c))
157.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.6s

Counts
82 → 82
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01541565
14191461
219061245
done50001239

prune591.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite392.0ms

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:
183.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
50.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(- (* b b) (* (* 4.0 a) c))
130.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series926.0ms

Counts
4 → 12
Calls
4 calls:
296.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
162.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
88.0ms
(- (* b b) (* (* 4.0 a) c))
380.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify2.9s

Counts
163 → 163
Iterations

Useful iterations: 2 (914.0ms)

IterNodesCost
02475048
16544512
237824174
done50014174

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize54.0ms

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
(/ (+ 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))))) (/ 1 (* 2.0 a)))

rewrite430.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
61×*-un-lft-identity
51×add-exp-log
46×times-frac
29×add-cube-cbrt
27×associate-*l* add-cbrt-cube
20×prod-exp
16×div-exp distribute-lft-out-- difference-of-squares
10×add-log-exp
8×cbrt-undiv distribute-rgt-neg-in sqrt-prod cbrt-unprod
7×associate-*r* associate-/r*
6×pow1
4×rec-exp flip3-- 1-exp associate-/r/ flip--
3×diff-log div-inv associate-/l*
2×sub-neg associate-/l/ unswap-sqr
1×associate--l- neg-sub0 frac-times frac-2neg flip3-+ associate-*r/ pow-prod-down neg-log associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 146
Calls
4 calls:
50.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms
(- (* b b) (* (* 4.0 a) c))
105.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
244.0ms
(* (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

series898.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
101.0ms
(- (* b b) (* (* 4.0 a) c))
346.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
294.0ms
(* (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

simplify4.3s

Counts
158 → 158
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
02534638
17564068
248013604
done50003604

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ 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))))) (/ 1 (* 2.0 a)))
0.5b
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
0.7b
(pow (- (* b b) (* (* 4.0 a) c)) 3)

rewrite673.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
71×*-un-lft-identity
70×times-frac
52×add-exp-log
43×add-cube-cbrt
42×difference-of-squares
40×cbrt-prod
39×associate-*l*
35×sqrt-prod
28×add-cbrt-cube
20×prod-exp
16×div-exp
14×distribute-lft-out--
13×unpow-prod-down cube-prod
11×associate-/r*
9×sqr-pow
8×cbrt-undiv cbrt-unprod
7×pow1 distribute-rgt-neg-in associate-*r*
4×cube-div rec-exp flip3-- 1-exp associate-/r/ flip-- add-log-exp
3×pow-unpow div-inv associate-/l*
2×cube-mult cbrt-div unpow3 associate-/l/ unswap-sqr
1×frac-times pow-to-exp pow-pow frac-2neg flip3-+ pow1/3 associate-*r/ pow-prod-down associate-*l/ pow-exp clear-num un-div-inv *-commutative rem-cbrt-cube flip-+ rem-cube-cbrt
Counts
4 → 192
Calls
4 calls:
189.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
421.0ms
(* (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (/ 1 (* 2.0 a)))
21.0ms
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
23.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

series915.0ms

Counts
4 → 12
Calls
4 calls:
362.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
284.0ms
(* (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (/ 1 (* 2.0 a)))
90.0ms
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
179.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

simplify873.0ms

Counts
204 → 204
Iterations

Useful iterations: done (859.0ms)

IterNodesCost
03286712
110085443
done50004859

prune1.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes517.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02026
12526
done2526

end0.0ms

sample5.3s

Algorithm
intervals
Results
1.4s16755×pre80true
1.0s4469×body160valid
1.0s3531×body80valid
913.0ms8755×body80nan