Details

Time bar (total: 16.5s)

sample89.0ms

Algorithm
intervals
Results
22.0ms33×body2560valid
14.0ms181×body80valid
10.0ms27×body1280valid
7.0ms92×body80nan
4.0ms13×body640valid
2.0ms4×body5120valid
2.0ms9×body320valid
1.0ms6×body160valid

simplify127.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01417
12417
24416
37916
49916
510716
done10716

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b
(- (* b b) (* (* 4.0 a) c))
1.6b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite127.0ms

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:
81.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(- (* b b) (* (* 4.0 a) c))
27.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series395.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
56.0ms
(- (* b b) (* (* 4.0 a) c))
86.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
107.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
82 → 82
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01541565
14211461
219321245
done50001239

prune271.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize17.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0b
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.2b
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite269.0ms

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:
44.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
116.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
87.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series742.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
215.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
285.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
134.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts
166 → 166
Iterations

Useful iterations: 2 (604.0ms)

IterNodesCost
02545113
16604543
237204219
done50014219

prune609.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize36.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0b
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))) (* 2.0 a))
9.5b
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite289.0ms

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:
22.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
144.0ms
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))) (* 2.0 a))
94.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series590.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
187.0ms
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))) (* 2.0 a))
179.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))
102.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify745.0ms

Counts
203 → 203
Iterations

Useful iterations: done (731.0ms)

IterNodesCost
03926102
111575697
done50014974

prune717.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.1b

localize40.0ms

Local error

Found 4 expressions with local error:

1.1b
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 a)) c)
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0b
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 a)) c)) (* 2.0 a))
23.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite420.0ms

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:
112.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 a)) c)
42.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
218.0ms
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 a)) c)) (* 2.0 a))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series607.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 a)) c)
121.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
187.0ms
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 a)) c)) (* 2.0 a))
122.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
390 → 390
Iterations

Useful iterations: done (1.4s)

IterNodesCost
074112808
1212012129
done500011054

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.1b

regimes414.0ms

Accuracy

88.7% (3.1b remaining)

Error of 8.5b against oracle of 5.4b and baseline of 32.9b

bsearch572.0ms

Steps
ItersRangePoint
2
2.9557653966214617e-29
3.491579857798755e-29
3.4246030501515935e-29
9
6.995428276738912e-281
4.047248354420239e-273
7.134363685689718e-281
8
-1.2658565361216573e+102
-2.0194296793555897e+99
-6.953668671676068e+101

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03982
14782
done4782

end0.0ms

sample3.5s

Algorithm
intervals
Results
911.0ms5893×body80valid
852.0ms1092×body2560valid
416.0ms848×body1280valid
364.0ms3047×body80nan
180.0ms463×body640valid
106.0ms96×body5120valid
53.0ms235×body320valid
17.0ms105×body160valid