Details

Time bar (total: 1.3m)

sample169.0ms

Algorithm
intervals
Results
50.0ms152×body160valid
32.0ms276×body80nan
32.0ms532×pre80true
17.0ms43×body320valid
8.0ms61×body80valid

simplify160.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
160.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.6b

localize41.0ms

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))

rewrite170.0ms

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
95.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
44.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
22.0ms
(* (* 3 a) c)
7.0ms
(- (* b b) (* (* 3 a) c))

series339.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
148.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
100.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
60.0ms
(- (* b b) (* (* 3 a) c))
31.0ms
(* (* 3 a) c)

simplify11.7s

Counts
104 → 91
Calls
104 calls:
Slowest
571.0ms
(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
560.0ms
(* (* (* (* 3 a) c) (* (* 3 a) c)) (* (* 3 a) c))
434.0ms
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
393.0ms
(- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c)))
385.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.1b

localize12.0ms

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

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.1b

localize28.0ms

Local error

Found 3 expressions with local error:

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

rewrite82.0ms

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
32.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
25.0ms
(* -3/2 (/ (* a c) b))
22.0ms
(/ (* a c) b)

series81.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
30.0ms
(/ (* a c) b)
29.0ms
(* -3/2 (/ (* a c) b))
22.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))

simplify18.3s

Counts
96 → 90
Calls
96 calls:
Slowest
1.7s
(/ (* (* (* -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 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)))
905.0ms
(/ (* (* (* -3/2 (/ (* a c) b)) (* -3/2 (/ (* a c) b))) (* -3/2 (/ (* a c) b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))

prune782.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 5.1b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
207×times-frac
109×sqrt-prod
99×add-sqr-sqrt
91×*-un-lft-identity add-cube-cbrt
77×add-cbrt-cube add-exp-log
64×associate-*r*
32×cbrt-undiv div-exp
22×prod-exp cbrt-unprod
17×div-inv
13×associate-/r*
12×associate-/l*
6×pow1
4×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*l* unswap-sqr
2×associate-*r/ associate-/l/
1×pow-prod-down *-commutative
Counts
4 → 246
Calls
4 calls:
Slowest
47.0ms
(/ (* -3/2 (/ (/ (* a c) (sqrt b)) (sqrt b))) (* 3 a))
32.0ms
(* -3/2 (/ (/ (* a c) (sqrt b)) (sqrt b)))
17.0ms
(/ (/ (* a c) (sqrt b)) (sqrt b))
10.0ms
(/ (* a c) (sqrt b))

series284.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
90.0ms
(* -3/2 (/ (/ (* a c) (sqrt b)) (sqrt b)))
69.0ms
(/ (/ (* a c) (sqrt b)) (sqrt b))
69.0ms
(/ (* a c) (sqrt b))
56.0ms
(/ (* -3/2 (/ (/ (* a c) (sqrt b)) (sqrt b))) (* 3 a))

simplify37.9s

Counts
330 → 258
Calls
330 calls:
Slowest
1.7s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (/ (* (* (* a a) a) (* (* c c) c)) (* (* (sqrt b) (sqrt b)) (sqrt b))) (* (* (sqrt b) (sqrt b)) (sqrt b)))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.4s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (/ (* (* (* a c) (* a c)) (* a c)) (* (* (sqrt b) (sqrt b)) (sqrt b))) (* (* (sqrt b) (sqrt b)) (sqrt b)))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.3s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (/ (* (* (* a a) a) (* (* c c) c)) (* (* (sqrt b) (sqrt b)) (sqrt b))) (* (* (sqrt b) (sqrt b)) (sqrt b)))) (* (* (* 3 3) 3) (* (* a a) a)))
1.1s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (/ (* (* (* a c) (* a c)) (* a c)) (* (* (sqrt b) (sqrt b)) (sqrt b))) (* (* (sqrt b) (sqrt b)) (sqrt b)))) (* (* (* 3 3) 3) (* (* a a) a)))
953.0ms
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (/ (* a c) (sqrt b)) (/ (* a c) (sqrt b))) (/ (* a c) (sqrt b))) (* (* (sqrt b) (sqrt b)) (sqrt b)))) (* (* (* 3 3) 3) (* (* a a) a)))

prune2.4s

Pruning

31 alts after pruning (30 fresh and 1 done)

Merged error: 5.1b

regimes762.0ms

Accuracy

12.5% (5.9b remaining)

Error of 11.0b against oracle of 5.1b and baseline of 11.8b

bsearch17.0ms

end0.0ms

sample5.6s

Algorithm
intervals
Results
1.5s16087×pre80true
1.4s4874×body160valid
1.0s8087×body80nan
583.0ms1759×body80valid
539.0ms1367×body320valid