Details

Time bar (total: 19.0s)

sample74.0ms

Algorithm
intervals
Results
13.0ms184×body80valid
12.0ms31×body2560valid
11.0ms33×body1280valid
6.0ms90×body80nan
3.0ms12×body640valid
2.0ms9×body320valid
0.0ms1×body5120valid
0.0ms2×body160valid

simplify115.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
01217
12117
24116
37616
49616
510416
done10416

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0) a)
0.8b
(- (* b b) (* (* 3.0 a) c))
1.0b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
22.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite216.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
121×add-sqr-sqrt
94×*-un-lft-identity
68×add-cube-cbrt
26×difference-of-squares
22×associate-/l*
16×sqrt-prod
13×distribute-lft-out--
9×add-exp-log add-cbrt-cube
8×add-log-exp
5×pow1 div-inv
3×cbrt-undiv flip3-- div-exp associate-/r* flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 149
Calls
4 calls:
115.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0) a)
12.0ms
(- (* b b) (* (* 3.0 a) c))
64.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series463.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0) a)
70.0ms
(- (* b b) (* (* 3.0 a) c))
122.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
110.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.9s

Counts
161 → 161
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02814083
16863921
230613757
done50003755

prune935.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.8b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* a 3.0))
0.8b
(- (* b b) (* (* 3.0 a) c))
1.0b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
22.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 72
Calls
4 calls:
120.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* a 3.0))
13.0ms
(- (* b b) (* (* 3.0 a) c))
69.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series487.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* a 3.0))
68.0ms
(- (* b b) (* (* 3.0 a) c))
127.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
106.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.7s

Counts
84 → 84
Iterations

Useful iterations: 2 (328.0ms)

IterNodesCost
01551592
14021498
217591334
done50021334

prune575.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a) 3.0)
0.8b
(- (* b b) (* (* 3.0 a) c))
1.0b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
22.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite267.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
121×add-sqr-sqrt
94×*-un-lft-identity
68×add-cube-cbrt
26×difference-of-squares
22×associate-/l*
16×sqrt-prod
13×distribute-lft-out--
9×add-exp-log add-cbrt-cube
8×add-log-exp
5×pow1 div-inv
3×cbrt-undiv flip3-- div-exp associate-/r* flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 149
Calls
4 calls:
140.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a) 3.0)
14.0ms
(- (* b b) (* (* 3.0 a) c))
87.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
13.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series533.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a) 3.0)
77.0ms
(- (* b b) (* (* 3.0 a) c))
149.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
120.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.3s

Counts
161 → 161
Iterations

Useful iterations: 2 (658.0ms)

IterNodesCost
02794083
16853921
230683755
done50013755

prune997.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.8b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ 1 3.0) a)
0.8b
(- (* b b) (* (* 3.0 a) c))
1.0b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
22.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
52×add-sqr-sqrt
49×*-un-lft-identity
47×add-cube-cbrt
13×add-exp-log associate-/l*
9×add-cbrt-cube
8×add-log-exp
6×div-exp
5×pow1 div-inv
4×sqrt-prod
3×cbrt-undiv flip3-- associate-/r* flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square rec-exp frac-2neg sqrt-pow1 pow1/2 1-exp clear-num associate-/l/ distribute-lft-out--
Counts
4 → 114
Calls
4 calls:
23.0ms
(/ (/ 1 3.0) a)
16.0ms
(- (* b b) (* (* 3.0 a) c))
85.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
16.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series383.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(/ (/ 1 3.0) a)
79.0ms
(- (* b b) (* (* 3.0 a) c))
149.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
123.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.9s

Counts
126 → 126
Iterations

Useful iterations: 2 (525.0ms)

IterNodesCost
02321713
15401514
221651395
done50001395

prune770.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.8b

regimes539.0ms

Accuracy

82.7% (5.0b remaining)

Error of 10.5b against oracle of 5.5b and baseline of 34.7b

bsearch239.0ms

Steps
ItersRangePoint
8
7.520261887413394e-140
8.544177483477188e-136
2.4581158795060287e-136
10
-6.623625638726693e+82
-6.4709084601913214e+72
-2.8920328608199634e+82

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02844
13244
done3244

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.1s5794×body80valid
914.0ms1066×body2560valid
549.0ms910×body1280valid
340.0ms2980×body80nan
157.0ms450×body640valid
129.0ms121×body5120valid
62.0ms232×body320valid
23.0ms136×body160valid