Details

Time bar (total: 4.4m)

sample172.0ms

Algorithm
intervals
Results
61.0ms147×body160valid
33.0ms261×body80nan
32.0ms517×pre80true
18.0ms48×body320valid
7.0ms61×body80valid

simplify169.0ms

Calls
1 calls:
Slowest
169.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.2b

localize26.0ms

Local error

Found 4 expressions with local error:

37.0b
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
0.4b
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
0.2b
(* (* 3 a) c)
0.1b
(- (* b b) (* (* 3 a) c))

rewrite996.0ms

Algorithm
rewrite-expression-head
Rules
164×add-sqr-sqrt
82×*-un-lft-identity
72×times-frac
45×associate-*l*
43×difference-of-squares
42×add-cube-cbrt
29×unswap-sqr
27×associate-*r*
20×distribute-lft-out--
14×add-cbrt-cube add-exp-log sqrt-prod
12×associate-/r* *-commutative
9×pow1
8×add-log-exp
6×associate-/l*
4×prod-exp cbrt-unprod insert-posit16
3×flip3-- swap-sqr pow-prod-down flip--
2×cbrt-undiv sub-neg diff-log div-exp associate-/l/
1×clear-num frac-2neg div-sub div-inv
Calls
4 calls:
Slowest
573.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
330.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
63.0ms
(- (* b b) (* (* 3 a) c))
23.0ms
(* (* 3 a) c)

series373.0ms

Calls
4 calls:
Slowest
165.0ms
(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
90.0ms
(- (sqrt (- (* b b) (* (* 3 a) c))) b)
77.0ms
(- (* b b) (* (* 3 a) c))
41.0ms
(* (* 3 a) c)

simplify18.5s

Calls
239 calls:
Slowest
571.0ms
(- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* b b))
474.0ms
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
397.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
360.0ms
(- (pow (sqrt (- (* b b) (* (* 3 a) c))) 3) (pow b 3))
353.0ms
(/ (exp (* b b)) (exp (* (* 3 a) c)))

prune2.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.3b

localize5.0ms

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

prune69.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 5.3b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
1180×times-frac
860×associate-*r*
853×add-sqr-sqrt
531×*-un-lft-identity
527×add-cube-cbrt
344×associate-*l*
156×unswap-sqr
114×*-commutative
91×associate-/l*
49×add-cbrt-cube add-exp-log
36×associate-*r/
21×associate-/r* associate-/l/
17×prod-exp cbrt-unprod
16×cbrt-undiv div-exp div-inv
6×clear-num un-div-inv
5×pow1
4×frac-2neg
3×insert-posit16 add-log-exp
1×pow-prod-down
Calls
3 calls:
Slowest
70.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
48.0ms
(* -3/2 (/ (* a c) b))
24.0ms
(/ (* a c) b)

series104.0ms

Calls
3 calls:
Slowest
43.0ms
(/ (* -3/2 (/ (* a c) b)) (* 3 a))
36.0ms
(* -3/2 (/ (* a c) b))
25.0ms
(/ (* a c) b)

simplify3.6m

Calls
1484 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)))
1.2s
(/ (* (* (* -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 3) 3) (* (* a a) a)))
1.2s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 3 3) 3) (* (* a a) a)))
913.0ms
(/ (* -3/2 (/ (* a c) b)) 3)

prune9.4s

Pruning

38 alts after pruning (37 fresh and 1 done)

Merged error: 5.3b

localize7.0ms

Local error

Found 1 expressions with local error:

0.3b
(* (/ c -2) (/ 1 b))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-times
72×add-sqr-sqrt
61×associate-/l*
60×associate-/r*
58×*-un-lft-identity
55×add-cube-cbrt
25×times-frac
23×add-exp-log
21×clear-num
20×frac-2neg
13×add-cbrt-cube associate-*r* associate-*l*
9×associate-*l/ associate-*r/
8×div-exp prod-exp
6×unswap-sqr
4×cbrt-undiv cbrt-unprod
3×pow1 un-div-inv
2×rec-exp 1-exp div-inv
1×pow-prod-down *-commutative insert-posit16 add-log-exp
Calls
1 calls:
Slowest
16.0ms
(* (/ c -2) (/ 1 b))

series41.0ms

Calls
1 calls:
Slowest
41.0ms
(* (/ c -2) (/ 1 b))

simplify8.3s

Calls
232 calls:
Slowest
688.0ms
(* (/ (* (* c c) c) (* (* -2 -2) -2)) (* (* (/ 1 b) (/ 1 b)) (/ 1 b)))
363.0ms
(* (* (* (/ c -2) (/ c -2)) (/ c -2)) (* (* (/ 1 b) (/ 1 b)) (/ 1 b)))
274.0ms
(* (/ c (* (cbrt -2) (cbrt -2))) (/ 1 (* (cbrt b) (cbrt b))))
208.0ms
(* (/ c (sqrt -2)) (/ 1 (* (cbrt b) (cbrt b))))
206.0ms
(* (/ c (* (cbrt -2) (cbrt -2))) (/ 1 b))

prune1.1s

Pruning

38 alts after pruning (36 fresh and 2 done)

Merged error: 5.3b

regimes1.0s

Accuracy

14.1% (6.2b remaining)

Error of 11.3b against oracle of 5.1b and baseline of 12.3b

bsearch13.0ms

end0.0ms

sample5.4s

Algorithm
intervals
Results
1.9s4787×body160valid
1.2s8215×body80nan
1.1s16215×pre80true
557.0ms1336×body320valid
221.0ms1877×body80valid