Details

Time bar (total: 25.4s)

sample68.0ms

Algorithm
intervals
Results
14.0ms35×body2560valid
12.0ms190×body80valid
9.0ms29×body1280valid
5.0ms92×body80nan
4.0ms16×body640valid
1.0ms7×body320valid
0.0ms3×body160valid
0.0ms1×body5120valid

simplify119.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
01217
12117
24116
37516
48816
59616
done9616

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.2b
(- (* b b) (* (* 3.0 a) c))
1.1b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
22.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite409.0ms

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:
22.0ms
(* (* 3.0 a) c)
13.0ms
(- (* b b) (* (* 3.0 a) c))
361.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
10.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series313.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (* 3.0 a) c)
61.0ms
(- (* b b) (* (* 3.0 a) c))
115.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
104.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.6s

Counts
72 → 72
Iterations

Useful iterations: done (3.6s)

IterNodesCost
01201001
1276903
2928825
33466821
done5000815

prune202.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.4b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)
4.4b
(/ (/ (/ (- 0 (* (* 3.0 a) c)) (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)) 3.0) a)
8.1b
(/ (- 0 (* (* 3.0 a) c)) (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b))
22.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite371.0ms

Algorithm
rewrite-expression-head
Rules
546×times-frac
327×*-un-lft-identity
246×add-sqr-sqrt
245×add-cube-cbrt
61×associate-/l*
41×distribute-lft-out
26×associate-/r/
18×div-inv
15×add-exp-log add-cbrt-cube
14×flip3-+ flip-+
7×cbrt-undiv div-exp associate-/r*
6×add-log-exp
5×pow1
4×div-sub distribute-frac-neg
3×sqrt-prod associate-/l/
2×flip3-- frac-2neg sub0-neg sqrt-div clear-num flip--
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
4 → 318
Calls
4 calls:
60.0ms
(+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)
158.0ms
(/ (/ (/ (- 0 (* (* 3.0 a) c)) (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)) 3.0) a)
98.0ms
(/ (- 0 (* (* 3.0 a) c)) (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b))
10.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series679.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)
188.0ms
(/ (/ (/ (- 0 (* (* 3.0 a) c)) (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)) 3.0) a)
270.0ms
(/ (- 0 (* (* 3.0 a) c)) (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b))
103.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.2s

Counts
330 → 330
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
060113349
1144412143
2467011831
done500111831

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.1b

localize34.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)
3.2b
(/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))
4.4b
(/ (/ (- (/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))) 3.0) a)
22.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite483.0ms

Algorithm
rewrite-expression-head
Rules
1690×times-frac
738×*-un-lft-identity
581×add-sqr-sqrt
580×add-cube-cbrt
252×distribute-lft-neg-in distribute-rgt-neg-in
143×associate-/l*
79×distribute-lft-out
56×div-inv
25×associate-/r/
21×add-exp-log add-cbrt-cube
19×associate-/r*
12×neg-mul-1
9×cbrt-undiv div-exp
6×add-log-exp
5×pow1
3×sqrt-prod
2×frac-2neg sqrt-div div-sub distribute-frac-neg prod-exp clear-num cbrt-unprod
1×+-commutative neg-sub0 rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 sum-log flip-- flip-+ associate-/l/
Counts
4 → 667
Calls
4 calls:
44.0ms
(+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)
53.0ms
(/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))
270.0ms
(/ (/ (- (/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))) 3.0) a)
16.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series758.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)
289.0ms
(/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))
238.0ms
(/ (/ (- (/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))) 3.0) a)
109.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.5s

Counts
679 → 679
Iterations

Useful iterations: done (2.5s)

IterNodesCost
0129325182
1304824068
done500023668

prune3.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.0b

localize23.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)
3.2b
(/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))
4.7b
(/ (- (/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))) (* 3.0 a))
22.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite357.0ms

Algorithm
rewrite-expression-head
Rules
198×times-frac
97×*-un-lft-identity
60×add-sqr-sqrt
59×add-cube-cbrt
47×associate-/l*
42×distribute-lft-neg-in distribute-rgt-neg-in
21×add-exp-log add-cbrt-cube
19×distribute-lft-out
17×associate-/r*
12×div-inv
8×cbrt-undiv div-exp
6×add-log-exp
5×pow1 associate-/r/
3×prod-exp sqrt-prod cbrt-unprod
2×neg-mul-1 frac-2neg sqrt-div clear-num
1×+-commutative neg-sub0 rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 div-sub distribute-frac-neg sum-log flip-- flip-+ associate-/l/ distribute-neg-frac
Counts
4 → 189
Calls
4 calls:
56.0ms
(+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)
75.0ms
(/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))
195.0ms
(/ (- (/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))) (* 3.0 a))
18.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series895.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(+ (sqrt (- (* b b) (* (* 3.0 a) c))) b)
328.0ms
(/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))
243.0ms
(/ (- (/ (* a 3.0) (/ (+ (sqrt (- (* b b) (* (* 3.0 a) c))) b) c))) (* 3.0 a))
133.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.6s

Counts
201 → 201
Iterations

Useful iterations: 2 (1.4s)

IterNodesCost
03725253
19025065
233394561
done50024561

prune782.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.0b

regimes536.0ms

Accuracy

93.2% (1.5b remaining)

Error of 9.8b against oracle of 8.3b and baseline of 30.4b

bsearch342.0ms

Steps
ItersRangePoint
9
8.313972478035852e+145
1.3206820209921783e+153
1.6379818719225421e+152
9
-1.2742380330863746e-228
-2.000782339938298e-234
-2.214640747245634e-234
9
-6.354265220965125e+156
-1.769171722317776e+149
-1.1399756785205677e+154

simplify19.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
04488
15886
26686
37486
47686
done7686

end0.0ms

sample3.3s

Algorithm
intervals
Results
707.0ms5881×body80valid
615.0ms2915×body80nan
566.0ms1076×body2560valid
483.0ms849×body1280valid
183.0ms467×body640valid
61.0ms106×body5120valid
47.0ms214×body320valid
17.0ms121×body160valid