Details

Time bar (total: 10.4s)

sample59.0ms

Algorithm
intervals
Results
13.0ms297×body80nan
11.0ms161×body160valid
10.0ms553×pre80true
4.0ms41×body320valid
2.0ms54×body80valid

simplify48.0ms

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: 44.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(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))
41.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite56.0ms

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))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series300.0ms

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))))

simplify492.0ms

Counts
82 → 82
Iterations

Useful iterations: done (490.0ms)

IterNodesCost
01541565
14131461
214611245
done50001235

prune195.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite112.0ms

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:
14.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
36.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* 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))

series459.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(- (* b b) (* (* 4.0 a) c))
188.0ms
(/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
147.0ms
(/ (/ (+ (* 4.0 (* a c)) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify1.3s

Counts
163 → 163
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02505760
16595251
226344489
done50004467

prune464.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
378×times-frac
207×add-sqr-sqrt *-un-lft-identity
119×add-cube-cbrt
66×associate-/r*
62×add-exp-log
44×distribute-lft-out-- difference-of-squares
36×add-cbrt-cube
35×div-exp
22×distribute-rgt-neg-in sqrt-prod
20×associate-/r/
18×cbrt-undiv
13×div-inv
8×flip3-- prod-exp flip--
7×associate-/l*
6×add-log-exp
5×pow1 rec-exp 1-exp
4×cbrt-unprod
3×frac-2neg clear-num
2×associate-/l/
1×sub-neg pow-flip flip3-+ diff-log flip-+ inv-pow
Counts
4 → 297
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
38.0ms
(/ 1 (/ (* 2.0 a) (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
28.0ms
(/ (* 2.0 a) (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
27.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series464.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
150.0ms
(/ 1 (/ (* 2.0 a) (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
86.0ms
(/ (* 2.0 a) (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
185.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify439.0ms

Counts
309 → 309
Iterations

Useful iterations: done (421.0ms)

IterNodesCost
040711792
1106710221
done50009961

prune621.0ms

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

rewrite299.0ms

Algorithm
rewrite-expression-head
Rules
4090×times-frac
2048×add-sqr-sqrt *-un-lft-identity
1344×add-cube-cbrt
689×sqrt-prod
352×distribute-lft-out-- difference-of-squares
225×associate-/r*
209×div-inv
176×distribute-rgt-neg-in
59×associate-/r/
51×add-exp-log add-cbrt-cube
30×cbrt-undiv div-exp
27×flip3-- flip--
10×add-log-exp
9×associate-/l*
6×prod-exp cbrt-unprod
4×pow1
3×diff-log
2×sub-neg frac-2neg clear-num
1×associate--l- neg-sub0 neg-log
Counts
4 → 1493
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
76.0ms
(/ (sqrt 1) (/ 2.0 (/ (/ (* c (* 4.0 a)) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
40.0ms
(/ 2.0 (/ (/ (* c (* 4.0 a)) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series419.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms
(- (* b b) (* (* 4.0 a) c))
175.0ms
(/ (sqrt 1) (/ 2.0 (/ (/ (* c (* 4.0 a)) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
120.0ms
(/ 2.0 (/ (/ (* c (* 4.0 a)) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify1.1s

Counts
1505 → 1505
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0145571221
1344264970
done500162470

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes104.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01825
12225
done2225

end0.0ms

sample1.5s

Algorithm
intervals
Results
341.0ms4850×body160valid
301.0ms16215×pre80true
275.0ms8215×body80nan
140.0ms1326×body320valid
64.0ms1824×body80valid