Details

Time bar (total: 6.1s)

sample41.0ms

Algorithm
intervals
Results
8.0ms36×body2560valid
7.0ms187×body80valid
5.0ms26×body1280valid
3.0ms19×body640valid
3.0ms73×body80nan
1.0ms5×body320valid
0.0ms1×body5120valid
0.0ms2×body160valid

simplify11.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059
done1059

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b
(- (* b b) (* 4.0 (* a c)))
21.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite104.0ms

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:
65.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
20.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms
(- (* b b) (* 4.0 (* a c)))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series491.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
76.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
48.0ms
(- (* b b) (* 4.0 (* a c)))
259.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0403779
11514685
25002674
done5002674

prune218.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

localize15.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
7.9b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
21.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 154
Calls
4 calls:
22.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
85.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
58.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series462.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
141.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
175.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify93.0ms

Counts
166 → 166
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
06402692
129442439
250012426
done50012426

prune379.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.6b

localize19.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.2b
(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a))
7.8b
(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
21.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
41×add-sqr-sqrt
34×*-un-lft-identity
30×add-cbrt-cube
27×associate-*r*
24×times-frac
17×add-cube-cbrt prod-exp
16×div-exp
9×cbrt-undiv cbrt-unprod
8×distribute-lft-out-- add-log-exp difference-of-squares
7×pow1 sqrt-prod
6×associate-/l/
4×frac-times distribute-rgt-neg-in flip3-+ associate-*l/ flip-+
3×rec-exp flip3-- 1-exp associate-*l* flip-- unswap-sqr
2×sqrt-div diff-log associate-*r/ associate-/r/ un-div-inv div-inv
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down neg-log clear-num associate-/r* *-commutative associate-/l*
Counts
4 → 122
Calls
4 calls:
22.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
38.0ms
(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a))
94.0ms
(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series492.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
145.0ms
(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))) (* 2.0 a))
200.0ms
(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify162.0ms

Counts
134 → 134
Iterations

Useful iterations: 2 (148.0ms)

IterNodesCost
07151779
143361453
250021429
done50021429

prune313.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.6b

localize17.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.3b
(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
7.9b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
21.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite214.0ms

Algorithm
rewrite-expression-head
Rules
68×add-sqr-sqrt
62×*-un-lft-identity
51×add-exp-log
46×times-frac
30×add-cube-cbrt
27×associate-*l* add-cbrt-cube
20×prod-exp
16×div-exp distribute-lft-out-- difference-of-squares
11×sqrt-prod
8×cbrt-undiv distribute-rgt-neg-in cbrt-unprod add-log-exp
7×pow1 associate-*r* associate-/r*
4×rec-exp flip3-- 1-exp associate-/r/ flip--
3×div-inv associate-/l*
2×sqrt-div diff-log associate-/l/ unswap-sqr
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 149
Calls
4 calls:
23.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
118.0ms
(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
59.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
9.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series479.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
147.0ms
(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ 1 (* 2.0 a)))
182.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify121.0ms

Counts
161 → 161
Iterations

Useful iterations: 2 (103.0ms)

IterNodesCost
07322415
137222081
250012074
done50012074

prune369.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.6b

regimes252.0ms

Accuracy

88% (3.1b remaining)

Error of 8.6b against oracle of 5.5b and baseline of 31.7b

bsearch162.0ms

Steps
ItersRangePoint
6
1.4800420954007604e+99
6.083502279918113e+99
3.314242005915538e+99
7
-1.0239697416173795e-228
-3.8766937197960597e-230
-3.9143071953980664e-230
10
-4.9909276054097234e+78
-4.785667473127655e+65
-4.287313385232319e+78

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04636
14836
24836
done4836

end0.0ms

sample1.3s

Algorithm
intervals
Results
254.0ms1107×body2560valid
244.0ms5758×body80valid
175.0ms913×body1280valid
107.0ms2871×body80nan
71.0ms488×body640valid
35.0ms105×body5120valid
25.0ms222×body320valid
8.0ms110×body160valid