Details

Time bar (total: 21.9s)

sample60.0ms

Algorithm
intervals
Results
14.0ms36×body2560valid
10.0ms179×body80valid
7.0ms28×body1280valid
4.0ms79×body80nan
3.0ms15×body640valid
1.0ms3×body5120valid
1.0ms8×body320valid
0.0ms2×body160valid

simplify86.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01217
12117
24116
37516
48816
59616
done9616

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.6b
(- (* b b) (* (* 3.0 a) c))
21.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 *-un-lft-identity add-log-exp
9×add-exp-log add-cbrt-cube
7×add-sqr-sqrt
6×add-cube-cbrt
3×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×flip3-- sqrt-div sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 diff-log associate-*l* neg-log *-commutative flip-+
Counts
4 → 60
Calls
4 calls:
29.0ms
(* (* 3.0 a) c)
45.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
8.0ms
(- (* b b) (* (* 3.0 a) c))
9.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series309.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (* 3.0 a) c)
110.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
70.0ms
(- (* b b) (* (* 3.0 a) c))
105.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify4.3s

Counts
72 → 72
Iterations

Useful iterations: done (4.3s)

IterNodesCost
01221001
1303907
21072805
34081795
done5000793

prune346.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.5b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
0.6b
(- (* b b) (* (* 3.0 a) c))
21.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-exp-log add-cbrt-cube
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod
3×flip3-- associate-*r* pow-prod-down prod-exp flip-- cbrt-unprod
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
20.0ms
(* (* 3.0 a) c)
80.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
16.0ms
(- (* b b) (* (* 3.0 a) c))
19.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series313.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* (* 3.0 a) c)
96.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
80.0ms
(- (* b b) (* (* 3.0 a) c))
111.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.7s

Counts
72 → 72
Iterations

Useful iterations: done (3.7s)

IterNodesCost
01201001
1276903
2929825
33449821
done5000815

prune275.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* c 3.0) a)
0.5b
(+ (- b) (sqrt (- (* b b) (* (* c 3.0) a))))
0.6b
(- (* b b) (* (* c 3.0) a))
21.8b
(sqrt (- (* b b) (* (* c 3.0) a)))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 *-un-lft-identity add-log-exp
9×add-exp-log add-cbrt-cube
7×add-sqr-sqrt
6×add-cube-cbrt
3×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×flip3-- sqrt-div sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 diff-log associate-*l* neg-log *-commutative flip-+
Counts
4 → 60
Calls
4 calls:
43.0ms
(* (* c 3.0) a)
42.0ms
(+ (- b) (sqrt (- (* b b) (* (* c 3.0) a))))
16.0ms
(- (* b b) (* (* c 3.0) a))
21.0ms
(sqrt (- (* b b) (* (* c 3.0) a)))

series315.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (* c 3.0) a)
136.0ms
(+ (- b) (sqrt (- (* b b) (* (* c 3.0) a))))
68.0ms
(- (* b b) (* (* c 3.0) a))
90.0ms
(sqrt (- (* b b) (* (* c 3.0) a)))

simplify4.3s

Counts
72 → 72
Iterations

Useful iterations: done (4.3s)

IterNodesCost
01231001
1309907
21057805
33940795
done5000793

prune384.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.2b

localize47.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (pow b 2) (* 3.0 (* a c)))
21.8b
(sqrt (- (pow b 2) (* 3.0 (* a c))))
21.8b
(sqrt (- (pow b 2) (* 3.0 (* a c))))
21.8b
(sqrt (* (sqrt (- (pow b 2) (* 3.0 (* a c)))) (sqrt (- (pow b 2) (* 3.0 (* a c))))))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
24×sqrt-pow1 sqrt-div
22×pow1
11×pow1/2
9×flip3-- flip--
8×add-sqr-sqrt
7×sqrt-prod
6×add-cube-cbrt *-un-lft-identity add-log-exp
5×pow-prod-up
4×add-exp-log frac-times add-cbrt-cube
3×rem-sqrt-square pow-prod-down pow-sqr
2×associate-*r/ associate-*l/
1×pow2 sub-neg pow-plus diff-log
Counts
4 → 74
Calls
4 calls:
31.0ms
(- (pow b 2) (* 3.0 (* a c)))
18.0ms
(sqrt (- (pow b 2) (* 3.0 (* a c))))
14.0ms
(sqrt (- (pow b 2) (* 3.0 (* a c))))
54.0ms
(sqrt (* (sqrt (- (pow b 2) (* 3.0 (* a c)))) (sqrt (- (pow b 2) (* 3.0 (* a c))))))

series359.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(- (pow b 2) (* 3.0 (* a c)))
91.0ms
(sqrt (- (pow b 2) (* 3.0 (* a c))))
97.0ms
(sqrt (- (pow b 2) (* 3.0 (* a c))))
113.0ms
(sqrt (* (sqrt (- (pow b 2) (* 3.0 (* a c)))) (sqrt (- (pow b 2) (* 3.0 (* a c))))))

simplify2.2s

Counts
86 → 86
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01121657
12051217
25141169
318721153
done50011150

prune388.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.2b

regimes351.0ms

Accuracy

96.8% (0.7b remaining)

Error of 12.8b against oracle of 12.1b and baseline of 34.8b

bsearch344.0ms

Steps
ItersRangePoint
8
2.1675125417143413e+135
9.311977249963738e+138
2.270344858826678e+135
6
1.230628501312938e-151
7.040558363340882e-151
1.934433159970908e-151
10
-1.646508010505952e+112
-1.5729262717800982e+102
-4.170863269453545e+104

simplify22.0ms

Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
047104
157103
265103
373103
475103
done75103

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.3s5914×body80valid
546.0ms1022×body2560valid
277.0ms870×body1280valid
216.0ms2919×body80nan
194.0ms469×body640valid
78.0ms236×body320valid
55.0ms125×body5120valid
12.0ms107×body160valid