Details

Time bar (total: 24.1s)

sample96.0ms

Algorithm
intervals
Results
17.0ms184×body80valid
17.0ms31×body2560valid
14.0ms33×body1280valid
8.0ms90×body80nan
4.0ms12×body640valid
2.0ms9×body320valid
1.0ms1×body5120valid
0.0ms2×body160valid

simplify151.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
01417
12417
24416
37916
49916
510716
done10716

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite204.0ms

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:
133.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
14.0ms
(- (* b b) (* (* 4.0 a) c))
37.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series593.0ms

Counts
4 → 12
Calls
4 calls:
218.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
88.0ms
(- (* b b) (* (* 4.0 a) c))
158.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
128.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts
82 → 82
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01541565
14211461
219321245
done50001239

prune693.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.7b

localize58.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.5b
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.5b
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite373.0ms

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:
48.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
180.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
113.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series922.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
283.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
357.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
144.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.2s

Counts
166 → 166
Iterations

Useful iterations: 2 (997.0ms)

IterNodesCost
02545113
16604543
237204219
done50014219

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.6b

localize48.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.5b
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))) (* 2.0 a))
12.6b
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite454.0ms

Algorithm
rewrite-expression-head
Rules
153×times-frac
122×add-exp-log
80×add-sqr-sqrt
79×*-un-lft-identity
63×div-exp
58×add-cbrt-cube
45×associate-/l*
43×add-cube-cbrt
34×prod-exp
27×cbrt-undiv
18×distribute-lft-out-- difference-of-squares
14×cbrt-unprod
12×sqrt-prod
10×div-inv
9×distribute-rgt-neg-in
8×rec-exp 1-exp add-log-exp
5×pow1
3×flip3-- flip-- associate-/l/
2×frac-2neg sqrt-div diff-log clear-num associate-/r* associate-/r/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 div-sub neg-log
Counts
4 → 191
Calls
4 calls:
45.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
212.0ms
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))) (* 2.0 a))
152.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series763.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
260.0ms
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))) (* 2.0 a))
218.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))
137.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.0s

Counts
203 → 203
Iterations

Useful iterations: done (1.0s)

IterNodesCost
03926102
111575697
done50014974

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.6b

localize53.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.5b
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 a)) c)) (* 2.0 a))
3.0b
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 a)) c)
22.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite524.0ms

Algorithm
rewrite-expression-head
Rules
723×times-frac
302×add-sqr-sqrt
301×*-un-lft-identity
209×add-cube-cbrt
127×associate-/l*
122×add-exp-log
77×div-exp
58×add-cbrt-cube
46×distribute-lft-out-- difference-of-squares
33×cbrt-undiv
32×div-inv
26×sqrt-prod
23×distribute-rgt-neg-in
20×prod-exp
8×rec-exp 1-exp cbrt-unprod add-log-exp
5×pow1
4×associate-/r*
2×flip3-- frac-2neg sqrt-div diff-log div-sub clear-num associate-/r/ flip-- associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 378
Calls
4 calls:
58.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
214.0ms
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 a)) c)) (* 2.0 a))
164.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 a)) c)
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series792.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
256.0ms
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 a)) c)) (* 2.0 a))
219.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 a)) c)
148.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts
390 → 390
Iterations

Useful iterations: done (1.9s)

IterNodesCost
074112808
1211712129
done500111068

prune2.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.6b

regimes487.0ms

Accuracy

88.9% (3.0b remaining)

Error of 8.4b against oracle of 5.4b and baseline of 32.6b

bsearch935.0ms

Steps
ItersRangePoint
8
1.1311204215935077e-37
1.5710948276089558e-34
3.593830924265355e-35
9
-3.913094050847411e-200
-3.3037963711260906e-206
-3.3528823044057167e-206
10
-6.623625638726693e+82
-6.4709084601913214e+72
-1.6581383089037873e+81

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03770
14670
done4670

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.3s1065×body2560valid
673.0ms5800×body80valid
583.0ms908×body1280valid
439.0ms2982×body80nan
174.0ms452×body640valid
149.0ms122×body5120valid
110.0ms231×body320valid
24.0ms133×body160valid