Details

Time bar (total: 22.5s)

sample135.0ms

Algorithm
intervals
Results
44.0ms184×body80valid
19.0ms31×body2560valid
17.0ms33×body1280valid
9.0ms90×body80nan
5.0ms12×body640valid
3.0ms9×body320valid
1.0ms1×body5120valid
0.0ms2×body160valid

simplify147.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
01417
12417
24416
37916
49916
510716
done10716

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize41.0ms

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)))

rewrite245.0ms

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:
148.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
17.0ms
(- (* b b) (* (* 4.0 a) c))
54.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series601.0ms

Counts
4 → 12
Calls
4 calls:
203.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
94.0ms
(- (* b b) (* (* 4.0 a) c))
153.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
151.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts
82 → 82
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01541565
14211461
219321245
done50001239

prune657.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.7b

localize52.0ms

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)))

rewrite399.0ms

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:
46.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
190.0ms
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
129.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series949.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(- (- 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))
378.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
146.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.1s

Counts
166 → 166
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
02545113
16604543
237204219
done50014219

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.6b

localize50.0ms

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)))

rewrite410.0ms

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:
42.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
185.0ms
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))) (* 2.0 a))
147.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series665.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
224.0ms
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))) (* 2.0 a))
185.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (* 4.0 a) c))
117.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify983.0ms

Counts
203 → 203
Iterations

Useful iterations: done (968.0ms)

IterNodesCost
03926102
111575697
done50014974

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.6b

localize54.0ms

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)))

rewrite534.0ms

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:
51.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
232.0ms
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 a)) c)) (* 2.0 a))
157.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 a)) c)
34.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series749.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
243.0ms
(/ (/ 1 (/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 a)) c)) (* 2.0 a))
217.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 4.0 a)) c)
143.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
390 → 390
Iterations

Useful iterations: done (1.8s)

IterNodesCost
074112808
1211712129
done500111068

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.6b

regimes418.0ms

Accuracy

88.9% (3.0b remaining)

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

bsearch851.0ms

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

sample3.8s

Algorithm
intervals
Results
975.0ms908×body1280valid
783.0ms1065×body2560valid
747.0ms5800×body80valid
313.0ms2982×body80nan
200.0ms452×body640valid
98.0ms122×body5120valid
58.0ms231×body320valid
20.0ms133×body160valid