Details

Time bar (total: 7.0m)

sample586.0ms

Algorithm
intervals
Results
424.0ms88×body160valid
79.0ms125×body320valid
25.0ms539×pre80true
24.0ms283×body80nan
5.0ms14×body640valid
3.0ms29×body80valid

simplify115.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
114.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.6b

localize35.0ms

Local error

Found 4 expressions with local error:

24.4b
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.3b
(* (* 3 a) c)
0.2b
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
0.1b
(- (* b b) (* (* 3 a) c))

rewrite237.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
14×add-cbrt-cube add-exp-log
13×*-un-lft-identity
9×pow1
8×add-log-exp
7×add-cube-cbrt
6×times-frac associate-/l* difference-of-squares
4×prod-exp cbrt-unprod insert-posit16
3×flip3-- associate-*r* pow-prod-down sqrt-prod flip-- distribute-lft-out--
2×cbrt-undiv sub-neg diff-log div-exp associate-/l/
1×clear-num associate-/r* frac-2neg div-sub associate-*l* *-commutative div-inv
Counts
4 → 79
Calls
4 calls:
Slowest
122.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
71.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
28.0ms
(* (* 3 a) c)
15.0ms
(- (* b b) (* (* 3 a) c))

series362.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
148.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
120.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
60.0ms
(- (* b b) (* (* 3 a) c))
34.0ms
(* (* 3 a) c)

simplify5.4s

Counts
50 → 91
Calls
50 calls:
Slowest
521.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
507.0ms
(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
468.0ms
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
415.0ms
(- (pow (sqrt (- (* b b) (* (* 3 a) c))) 3) (pow b 3))
265.0ms
(/ (exp (* b b)) (exp (* (* 3 a) c)))

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.5b

localize13.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0
Calls
0 calls:
Slowest

series0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

simplify0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

prune82.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.5b

localize32.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
0.3b
(* -3/2 (/ (* a c) b))
0.2b
(/ (* a c) b)

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
49×add-cbrt-cube add-exp-log
17×prod-exp cbrt-unprod
16×cbrt-undiv div-exp
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
7×times-frac associate-*r*
5×pow1
4×associate-/r*
3×associate-*l* insert-posit16 div-inv add-log-exp
2×clear-num frac-2neg associate-*r/ associate-/l*
1×pow-prod-down *-commutative unswap-sqr associate-/l/
Counts
3 → 81
Calls
3 calls:
Slowest
36.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
26.0ms
(* -3/2 (/ (* a c) b))
19.0ms
(/ (* a c) b)

series96.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
43.0ms
(* -3/2 (/ (* a c) b))
31.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
22.0ms
(/ (* a c) b)

simplify12.5s

Counts
58 → 90
Calls
58 calls:
Slowest
1.3s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.3s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.1s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 3 3) 3) (* (* a a) a)))
1.0s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 3 3) 3) (* (* a a) a)))
959.0ms
(/ (* (* (* -3/2 (/ (* a c) b)) (* -3/2 (/ (* a c) b))) (* -3/2 (/ (* a c) b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))

prune944.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 2.4b

localize58.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (/ -27/8 (* (* (* (/ (* a 3) c) (/ b a)) (* (/ (* a 3) c) (/ b a))) (* (/ (* a 3) c) (/ b a)))))
0.5b
(* (* (/ (* a 3) c) (/ b a)) (* (/ (* a 3) c) (/ b a)))
0.4b
(* (* (* (/ (* a 3) c) (/ b a)) (* (/ (* a 3) c) (/ b a))) (* (/ (* a 3) c) (/ b a)))
0.4b
(* (/ (* a 3) c) (/ b a))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
3596×add-cbrt-cube add-exp-log
2046×prod-exp cbrt-unprod
1141×cbrt-undiv div-exp
276×frac-times
200×pow1
162×associate-*l/
138×associate-*r/
87×pow-prod-down
70×cbrt-prod
63×associate-/r/
38×pow-prod-up
20×add-sqr-sqrt
19×pow-plus
16×times-frac pow-sqr
15×*-un-lft-identity associate-*r* add-cube-cbrt
9×associate-*l*
4×pow2 insert-posit16 add-log-exp
3×*-commutative div-inv
2×unswap-sqr
1×cbrt-div pow1/3 swap-sqr pow3
Counts
4 → 1085
Calls
4 calls:
Slowest
558.0ms
(* (* (* (/ (* a 3) c) (/ b a)) (* (/ (* a 3) c) (/ b a))) (* (/ (* a 3) c) (/ b a)))
466.0ms
(cbrt (/ -27/8 (* (* (* (/ (* a 3) c) (/ b a)) (* (/ (* a 3) c) (/ b a))) (* (/ (* a 3) c) (/ b a)))))
100.0ms
(* (* (/ (* a 3) c) (/ b a)) (* (/ (* a 3) c) (/ b a)))
22.0ms
(* (/ (* a 3) c) (/ b a))

series383.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
143.0ms
(cbrt (/ -27/8 (* (* (* (/ (* a 3) c) (/ b a)) (* (/ (* a 3) c) (/ b a))) (* (/ (* a 3) c) (/ b a)))))
120.0ms
(* (* (* (/ (* a 3) c) (/ b a)) (* (/ (* a 3) c) (/ b a))) (* (/ (* a 3) c) (/ b a)))
83.0ms
(* (* (/ (* a 3) c) (/ b a)) (* (/ (* a 3) c) (/ b a)))
36.0ms
(* (/ (* a 3) c) (/ b a))

simplify6.3m

Counts
1142 → 1097
Calls
1142 calls:
Slowest
2.3s
(* (* (* (/ (* (* (* a 3) (* a 3)) (* a 3)) (* (* c c) c)) (/ (* (* b b) b) (* (* a a) a))) (* (* (* (/ (* a 3) c) (/ (* a 3) c)) (/ (* a 3) c)) (/ (* (* b b) b) (* (* a a) a)))) (* (/ (* (* (* a 3) (* a 3)) (* a 3)) (* (* c c) c)) (/ (* (* b b) b) (* (* a a) a))))
2.2s
(* (* (* (/ (* (* (* a a) a) (* (* 3 3) 3)) (* (* c c) c)) (/ (* (* b b) b) (* (* a a) a))) (* (/ (* (* (* a a) a) (* (* 3 3) 3)) (* (* c c) c)) (/ (* (* b b) b) (* (* a a) a)))) (* (/ (* (* (* a a) a) (* (* 3 3) 3)) (* (* c c) c)) (/ (* (* b b) b) (* (* a a) a))))
2.2s
(* (* (* (/ (* (* (* a 3) (* a 3)) (* a 3)) (* (* c c) c)) (* (* (/ b a) (/ b a)) (/ b a))) (* (/ (* (* (* a 3) (* a 3)) (* a 3)) (* (* c c) c)) (/ (* (* b b) b) (* (* a a) a)))) (* (/ (* (* (* a 3) (* a 3)) (* a 3)) (* (* c c) c)) (/ (* (* b b) b) (* (* a a) a))))
2.2s
(* (* (* (/ (* (* (* a 3) (* a 3)) (* a 3)) (* (* c c) c)) (/ (* (* b b) b) (* (* a a) a))) (* (/ (* (* (* a 3) (* a 3)) (* a 3)) (* (* c c) c)) (* (* (/ b a) (/ b a)) (/ b a)))) (* (/ (* (* (* a 3) (* a 3)) (* a 3)) (* (* c c) c)) (* (* (/ b a) (/ b a)) (/ b a))))
2.1s
(* (* (* (/ (* (* (* a 3) (* a 3)) (* a 3)) (* (* c c) c)) (/ (* (* b b) b) (* (* a a) a))) (* (/ (* (* (* a 3) (* a 3)) (* a 3)) (* (* c c) c)) (/ (* (* b b) b) (* (* a a) a)))) (* (/ (* (* (* a 3) (* a 3)) (* a 3)) (* (* c c) c)) (/ (* (* b b) b) (* (* a a) a))))

prune15.7s

Pruning

25 alts after pruning (23 fresh and 2 done)

Merged error: 2.4b

regimes893.0ms

Accuracy

0% (3.6b remaining)

Error of 6.2b against oracle of 2.6b and baseline of 6.2b

bsearch1.0ms

end0.0ms

sample6.6s

Algorithm
intervals
Results
1.6s3732×body320valid
1.5s15991×pre80true
1.1s7991×body80nan
892.0ms2845×body160valid
701.0ms491×body640valid
112.0ms932×body80valid