Details

Time bar (total: 59.2s)

sample123.0ms

Algorithm
intervals
Results
30.0ms155×body160valid
25.0ms540×pre80true
24.0ms284×body80nan
13.0ms47×body320valid
5.0ms54×body80valid

simplify144.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
144.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.3b

localize26.0ms

Local error

Found 4 expressions with local error:

38.4b
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.3b
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
0.3b
(* (* 3 a) c)
0.1b
(- (* b b) (* (* 3 a) c))

rewrite194.0ms

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
92.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
60.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
26.0ms
(* (* 3 a) c)
14.0ms
(- (* b b) (* (* 3 a) c))

series346.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
156.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
106.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
60.0ms
(- (* b b) (* (* 3 a) c))
23.0ms
(* (* 3 a) c)

simplify5.3s

Counts
50 → 91
Calls
50 calls:
Slowest
513.0ms
(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
497.0ms
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
405.0ms
(- (pow (sqrt (- (* b b) (* (* 3 a) c))) 3) (pow b 3))
402.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
272.0ms
(/ (* (* (- (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)))

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.8b

localize6.0ms

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

prune77.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 4.8b

localize20.0ms

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))

rewrite76.0ms

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))
22.0ms
(* -3/2 (/ (* a c) b))
17.0ms
(/ (* a c) b)

series89.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
32.0ms
(* -3/2 (/ (* a c) b))
30.0ms
(/ (* a c) b)
26.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))

simplify13.1s

Counts
58 → 90
Calls
58 calls:
Slowest
1.8s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.3s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a a) a) (* (* c c) 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)))
1.1s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 3 3) 3) (* (* a a) a)))
815.0ms
(/ (* (* (* -3/2 (/ (* a c) b)) (* -3/2 (/ (* a c) b))) (* -3/2 (/ (* a c) b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))

prune889.0ms

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 4.7b

localize31.0ms

Local error

Found 2 expressions with local error:

0.4b
(* (* -3/2 (/ a 1)) (/ c b))
0.4b
(/ (* (* -3/2 (/ a 1)) (/ c b)) (* 3 a))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
115×add-exp-log
88×add-cbrt-cube
51×prod-exp
42×div-exp
37×cbrt-unprod
29×cbrt-undiv
13×associate-*r*
10×times-frac
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×pow1
6×1-exp associate-*r/
3×pow-prod-down associate-/l/
2×frac-times associate-*l/ insert-posit16 div-inv add-log-exp
1×clear-num associate-/r* frac-2neg associate-*l* *-commutative associate-/l*
Counts
2 → 91
Calls
2 calls:
Slowest
54.0ms
(/ (* (* -3/2 (/ a 1)) (/ c b)) (* 3 a))
20.0ms
(* (* -3/2 (/ a 1)) (/ c b))

series71.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
47.0ms
(* (* -3/2 (/ a 1)) (/ c b))
24.0ms
(/ (* (* -3/2 (/ a 1)) (/ c b)) (* 3 a))

simplify30.4s

Counts
76 → 97
Calls
76 calls:
Slowest
2.0s
(/ (* (* (* (* -3/2 (/ a 1)) (* -3/2 (/ a 1))) (* -3/2 (/ a 1))) (/ (* (* c c) c) (* (* b b) b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.9s
(/ (* (* (* (* -3/2 (/ a 1)) (/ c b)) (* (* -3/2 (/ a 1)) (/ c b))) (* (* -3/2 (/ a 1)) (/ c b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.5s
(/ (* (* (* (* -3/2 (/ a 1)) (* -3/2 (/ a 1))) (* -3/2 (/ a 1))) (* (* (/ c b) (/ c b)) (/ c b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.5s
(/ (* (* (* (* -3/2 -3/2) -3/2) (* (* (/ a 1) (/ a 1)) (/ a 1))) (/ (* (* c c) c) (* (* b b) b))) (* (* (* 3 3) 3) (* (* a a) a)))
1.5s
(/ (* (* (* (* -3/2 (/ a 1)) (* -3/2 (/ a 1))) (* -3/2 (/ a 1))) (/ (* (* c c) c) (* (* b b) b))) (* (* (* 3 3) 3) (* (* a a) a)))

prune801.0ms

Pruning

34 alts after pruning (33 fresh and 1 done)

Merged error: 4.7b

regimes887.0ms

Accuracy

13.8% (5.9b remaining)

Error of 10.9b against oracle of 5.0b and baseline of 11.9b

bsearch7.0ms

end0.0ms

sample5.5s

Algorithm
intervals
Results
1.6s4798×body160valid
1.4s16151×pre80true
1.1s8151×body80nan
571.0ms1382×body320valid
225.0ms1820×body80valid