Details

Time bar (total: 49.6s)

sample124.0ms

Algorithm
intervals
Results
29.0ms148×body160valid
26.0ms508×pre80true
24.0ms252×body80nan
21.0ms50×body320valid
6.0ms58×body80valid

simplify168.0ms

Calls
1 calls:
Slowest
168.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.8b

localize29.0ms

Local error

Found 4 expressions with local error:

37.9b
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.3b
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
0.2b
(* (* 3 a) c)
0.1b
(- (* b b) (* (* 3 a) c))

rewrite176.0ms

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
Calls
4 calls:
Slowest
85.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
53.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
28.0ms
(* (* 3 a) c)
9.0ms
(- (* b b) (* (* 3 a) c))

series344.0ms

Calls
4 calls:
Slowest
139.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
94.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
79.0ms
(- (* b b) (* (* 3 a) c))
32.0ms
(* (* 3 a) c)

simplify5.5s

Calls
50 calls:
Slowest
541.0ms
(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
425.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
406.0ms
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
366.0ms
(- (pow (sqrt (- (* b b) (* (* 3 a) c))) 3) (pow b 3))
310.0ms
(/ (* (* (- (sqrt (- (* b b) (* (* 3 a) c))) b) (- (sqrt (- (* b b) (* (* 3 a) c))) b)) (- (sqrt (- (* b b) (* (* 3 a) c))) b)) (* (* (* 3 a) (* 3 a)) (* 3 a)))

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.2b

localize6.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

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

series0.0ms

Calls
0 calls:
Slowest

simplify0.0ms

Calls
0 calls:
Slowest

prune64.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.2b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite85.0ms

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/
Calls
3 calls:
Slowest
40.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
25.0ms
(* -3/2 (/ (* a c) b))
18.0ms
(/ (* a c) b)

series103.0ms

Calls
3 calls:
Slowest
38.0ms
(/ (* a c) b)
35.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
31.0ms
(* -3/2 (/ (* a c) b))

simplify12.7s

Calls
58 calls:
Slowest
1.3s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 3 3) 3) (* (* a a) a)))
1.2s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.2s
(/ (* (* (* -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 c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 3 3) 3) (* (* a a) a)))
910.0ms
(/ (* (* (* -3/2 (/ (* a c) b)) (* -3/2 (/ (* a c) b))) (* -3/2 (/ (* a c) b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))

prune927.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 5.1b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
52×add-cbrt-cube add-exp-log
42×times-frac
29×add-sqr-sqrt
27×*-un-lft-identity add-cube-cbrt
21×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
9×associate-/r* associate-/l*
8×div-inv
7×associate-*r*
6×pow1
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*l*
2×associate-*r/ associate-/l/
1×pow-prod-down *-commutative unswap-sqr
Calls
4 calls:
Slowest
28.0ms
(/ (/ (* -3/2 (/ (* a c) b)) 3) a)
21.0ms
(* -3/2 (/ (* a c) b))
19.0ms
(/ (* a c) b)
16.0ms
(/ (* -3/2 (/ (* a c) b)) 3)

series130.0ms

Calls
4 calls:
Slowest
39.0ms
(/ (* -3/2 (/ (* a c) b)) 3)
37.0ms
(/ (* a c) b)
31.0ms
(* -3/2 (/ (* a c) b))
22.0ms
(/ (/ (* -3/2 (/ (* a c) b)) 3) a)

simplify20.6s

Calls
120 calls:
Slowest
839.0ms
(/ (/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* 3 3) 3)) (* (* a a) a))
653.0ms
(/ (/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* 3 3) 3)) (* (* a a) a))
579.0ms
(- (- (+ (log -3/2) (- (+ (log a) (log c)) (log b))) (log 3)) (log a))
548.0ms
(/ (/ (/ (* a c) b) 3) a)
537.0ms
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* 3 3) 3))

prune1.2s

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 5.1b

regimes755.0ms

Accuracy

-6% (7.4b remaining)

Error of 12.3b against oracle of 4.9b and baseline of 11.9b

bsearch63.0ms

end0.0ms

sample5.5s

Algorithm
intervals
Results
1.8s4830×body160valid
1.0s8251×body80nan
998.0ms16251×pre80true
645.0ms1777×body80valid
560.0ms1393×body320valid