Details

Time bar (total: 8.6s)

sample58.0ms

Algorithm
intervals
Results
14.0ms570×pre80true
11.0ms314×body80nan
10.0ms137×body160valid
4.0ms119×body80valid

simplify47.0ms

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: 27.5b

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))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
27.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite57.0ms

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)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
37.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series291.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
43.0ms
(- (* b b) (* (* 4.0 a) c))
102.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify489.0ms

Counts
82 → 82
Iterations

Useful iterations: done (486.0ms)

IterNodesCost
01541565
14131461
214611245
done50001235

prune181.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite114.0ms

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:
3.0ms
(- (* b b) (* (* 4.0 a) c))
54.0ms
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
39.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series437.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 4.0 a) c))
141.0ms
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
176.0ms
(/ (+ (* 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
226344489
done50014467

prune446.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
353×times-frac
288×add-sqr-sqrt
262×*-un-lft-identity
156×add-cube-cbrt
85×associate-*r*
52×add-exp-log distribute-lft-out-- difference-of-squares
32×add-cbrt-cube
30×associate-/l*
26×distribute-rgt-neg-in sqrt-prod
25×div-exp
16×associate-/r/
13×cbrt-undiv associate-*l*
11×div-inv
10×prod-exp associate-/r*
9×flip3-- flip--
8×add-log-exp unswap-sqr
7×pow1
6×cbrt-unprod
4×rec-exp 1-exp
2×frac-2neg diff-log clear-num
1×associate--l- neg-sub0 frac-times sub-neg pow-flip associate-*r/ pow-prod-down neg-log associate-*l/ *-commutative associate-/l/ inv-pow
Counts
4 → 329
Calls
4 calls:
22.0ms
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
40.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
91.0ms
(* (/ (+ 0 (* 4.0 (* a c))) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series432.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
116.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
146.0ms
(* (/ (+ 0 (* 4.0 (* a c))) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify475.0ms

Counts
341 → 341
Iterations

Useful iterations: done (461.0ms)

IterNodesCost
041410224
112229118
done50028768

prune711.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
518×times-frac
320×add-sqr-sqrt *-un-lft-identity
172×add-cube-cbrt
74×distribute-lft-out-- difference-of-squares
62×associate-/l*
42×div-inv
38×add-exp-log add-cbrt-cube
37×distribute-rgt-neg-in sqrt-prod
19×cbrt-undiv div-exp
10×associate-/r* associate-/r/ add-log-exp
7×flip3-- flip--
6×prod-exp cbrt-unprod
4×pow1
3×diff-log
2×sub-neg frac-2neg clear-num associate-/l/
1×associate--l- neg-sub0 neg-log
Counts
4 → 358
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
54.0ms
(/ (/ (/ (* (* 4.0 a) c) 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
29.0ms
(/ (/ (* (* 4.0 a) c) 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series452.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (* b b) (* (* 4.0 a) c))
146.0ms
(/ (/ (/ (* (* 4.0 a) c) 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
75.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
183.0ms
(/ (/ (* (* 4.0 a) c) 2.0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify395.0ms

Counts
370 → 370
Iterations

Useful iterations: done (379.0ms)

IterNodesCost
049313321
1127912780
done500012720

prune864.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes128.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: done (2.0ms)

IterNodesCost
02148
12746
done2744

end0.0ms

sample1.5s

Algorithm
intervals
Results
344.0ms4461×body160valid
319.0ms16802×pre80true
319.0ms8802×body80nan
135.0ms3538×body80valid
0.0ms1×body320valid