Details

Time bar (total: 10.5s)

sample57.0ms

Algorithm
intervals
Results
12.0ms160×body160valid
11.0ms250×body80nan
9.0ms506×pre80true
5.0ms50×body320valid
2.0ms46×body80valid

simplify50.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
01417
12417
24416
37816
49016
59816
done9816

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.1b

localize11.0ms

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))
40.2b
(+ (- 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:
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* 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))))

series301.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms
(- (* b b) (* (* 4.0 a) c))
106.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify674.0ms

Counts
82 → 82
Iterations

Useful iterations: done (672.0ms)

IterNodesCost
01541565
14061461
213611245
done50001235

prune200.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

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

rewrite103.0ms

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))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
49.0ms
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
33.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series418.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms
(- (* b b) (* (* 4.0 a) c))
128.0ms
(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
166.0ms
(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify885.0ms

Counts
163 → 163
Iterations

Useful iterations: done (879.0ms)

IterNodesCost
02545790
16705273
223874513
done50004511

prune456.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
0.3b
(* (/ (- (* 4.0 (* a c)) 0) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
353×times-frac
284×add-sqr-sqrt
258×*-un-lft-identity
156×add-cube-cbrt
85×associate-*r*
52×add-exp-log
50×distribute-lft-out-- difference-of-squares
32×add-cbrt-cube
30×associate-/l*
25×distribute-rgt-neg-in div-exp sqrt-prod
16×associate-/r/
13×cbrt-undiv associate-*l*
11×div-inv
10×prod-exp associate-/r*
9×flip3-- flip--
8×unswap-sqr
7×pow1
6×cbrt-unprod add-log-exp
4×rec-exp 1-exp
2×frac-2neg clear-num
1×frac-times sub-neg pow-flip diff-log associate-*r/ pow-prod-down associate-*l/ *-commutative associate-/l/ inv-pow
Counts
4 → 323
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
21.0ms
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
38.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
99.0ms
(* (/ (- (* 4.0 (* a c)) 0) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series418.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* (* 4.0 a) c))
100.0ms
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
125.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
148.0ms
(* (/ (- (* 4.0 (* a c)) 0) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify1.3s

Counts
335 → 335
Iterations

Useful iterations: done (1.3s)

IterNodesCost
041610023
112318773
240688096
done50008093

prune698.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (- (* 4.0 (* a c)) 0) 2.0) (/ (/ 1 (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* c (* 4.0 a)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))))) a))
0.4b
(* (* c (* 4.0 a)) (+ (* b b) (* (* 4.0 a) c)))
0.4b
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* c (* 4.0 a)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))
0.8b
(pow (* (* 4.0 a) c) 3)

rewrite570.0ms

Algorithm
rewrite-expression-head
Rules
224×times-frac
214×add-sqr-sqrt
141×*-un-lft-identity
97×associate-*r*
95×add-cube-cbrt
56×add-exp-log
51×difference-of-squares
42×add-cbrt-cube
22×distribute-lft-out--
21×pow1 sqr-pow
19×prod-exp
18×div-exp sqrt-prod
15×cbrt-unprod
14×associate-*l*
10×cbrt-undiv pow-prod-down associate-/l*
9×unpow-prod-down distribute-rgt-neg-in
8×associate-/r/ unswap-sqr
6×div-inv
4×flip3-- flip-- add-log-exp
3×pow-unpow pow-pow associate-*r/ pow-exp associate-/r* rem-cube-cbrt
2×rec-exp flip3-+ 1-exp *-commutative flip-+ associate-/l/
1×distribute-rgt-in cube-mult frac-times pow-to-exp frac-2neg distribute-lft-in unpow3 div-sub cube-prod associate-*l/ clear-num
Counts
4 → 253
Calls
4 calls:
463.0ms
(* (/ (- (* 4.0 (* a c)) 0) 2.0) (/ (/ 1 (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* c (* 4.0 a)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))))) a))
22.0ms
(* (* c (* 4.0 a)) (+ (* b b) (* (* 4.0 a) c)))
64.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* c (* 4.0 a)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))
6.0ms
(pow (* (* 4.0 a) c) 3)

series473.0ms

Counts
4 → 12
Calls
4 calls:
220.0ms
(* (/ (- (* 4.0 (* a c)) 0) 2.0) (/ (/ 1 (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* c (* 4.0 a)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))))) a))
71.0ms
(* (* c (* 4.0 a)) (+ (* b b) (* (* 4.0 a) c)))
124.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* c (* 4.0 a)) (+ (* b b) (* (* 4.0 a) c))) (pow b 4)))
59.0ms
(pow (* (* 4.0 a) c) 3)

simplify627.0ms

Counts
265 → 265
Iterations

Useful iterations: done (612.0ms)

IterNodesCost
052012073
1158210993
done500010747

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes104.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03249
14047
done4047

end0.0ms

sample1.5s

Algorithm
intervals
Results
338.0ms4818×body160valid
304.0ms16455×pre80true
283.0ms8455×body80nan
147.0ms1399×body320valid
62.0ms1783×body80valid