Details

Time bar (total: 47.9s)

sample243.0ms

Algorithm
intervals
Results
30.0ms191×body80valid
30.0ms35×body2560valid
26.0ms37×body1280valid
14.0ms106×body80nan
8.0ms16×body640valid
2.0ms4×body320valid
1.0ms4×body160valid
1.0ms1×body5120valid

simplify102.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
101.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize38.0ms

Local error

Found 4 expressions with local error:

19.8b
(sqrt (- (* b_2 b_2) (* a c)))
1.0b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b
(- (* b_2 b_2) (* a c))
0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite226.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×*-un-lft-identity
18×times-frac
16×add-cube-cbrt
10×difference-of-squares
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×flip3-- insert-posit16 flip--
3×associate-/r*
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 88
Calls
4 calls:
Slowest
108.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
69.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
31.0ms
(sqrt (- (* b_2 b_2) (* a c)))
15.0ms
(- (* b_2 b_2) (* a c))

series445.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
143.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
129.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
115.0ms
(sqrt (- (* b_2 b_2) (* a c)))
58.0ms
(- (* b_2 b_2) (* a c))

simplify4.5s

Counts
73 → 100
Calls
73 calls:
Slowest
852.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
249.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
249.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
233.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
228.0ms
(/ (* (* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* (* a a) a))

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.9b

localize31.0ms

Local error

Found 4 expressions with local error:

19.8b
(sqrt (- (* b_2 b_2) (* a c)))
7.4b
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
0.6b
(- (* b_2 b_2) (* a c))
0.1b
(/ (sqrt (- (* b_2 b_2) (* a c))) a)

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
31×times-frac
30×*-un-lft-identity
22×add-cube-cbrt
17×sqrt-prod
8×add-log-exp
6×add-cbrt-cube add-exp-log associate-/l* difference-of-squares
5×pow1
4×flip3-- sqrt-div insert-posit16 flip-- distribute-lft-out--
3×associate-/r* div-inv
2×sub-neg diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 distribute-rgt-out-- pow1/2 div-exp frac-sub sub-div
Counts
4 → 97
Calls
4 calls:
Slowest
43.0ms
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
25.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
14.0ms
(- (* b_2 b_2) (* a c))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series448.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
143.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
134.0ms
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
110.0ms
(sqrt (- (* b_2 b_2) (* a c)))
61.0ms
(- (* b_2 b_2) (* a c))

simplify4.5s

Counts
92 → 109
Calls
92 calls:
Slowest
373.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
299.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
266.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
249.0ms
(/ (* (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (- (* b_2 b_2) (* a c)))) (* (* a a) a))
203.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.9b

localize42.0ms

Local error

Found 4 expressions with local error:

19.8b
(sqrt (- (* b_2 b_2) (* a c)))
11.3b
(- (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
0.6b
(- (* b_2 b_2) (* a c))
0.3b
(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
173×times-frac
132×add-sqr-sqrt
95×*-un-lft-identity
82×add-cube-cbrt
43×sqrt-prod
24×associate-/r*
15×add-exp-log
14×difference-of-squares
10×sqrt-div
9×add-cbrt-cube associate-/r/
8×add-log-exp
7×flip3-- div-exp flip--
6×pow1 div-inv
4×insert-posit16
3×cbrt-undiv associate-/l* distribute-lft-out--
2×rec-exp sub-neg diff-log 1-exp
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 frac-sub pow-flip inv-pow
Counts
4 → 181
Calls
4 calls:
Slowest
123.0ms
(- (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
35.0ms
(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))
21.0ms
(- (* b_2 b_2) (* a c))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series411.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
137.0ms
(- (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
132.0ms
(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))
82.0ms
(sqrt (- (* b_2 b_2) (* a c)))
60.0ms
(- (* b_2 b_2) (* a c))

simplify18.6s

Counts
233 → 193
Calls
233 calls:
Slowest
614.0ms
(/ (* (* 1 1) 1) (* (* (/ a (sqrt (- (* b_2 b_2) (* a c)))) (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ a (sqrt (- (* b_2 b_2) (* a c))))))
357.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (* (cbrt (sqrt (- (* b_2 b_2) (* a c)))) (cbrt (sqrt (- (* b_2 b_2) (* a c)))))))
342.0ms
(/ (* (* 1 1) 1) (/ (* (* a a) a) (* (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (- (* b_2 b_2) (* a c))))))
341.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ a (sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))))
334.0ms
(/ (sqrt 1) (/ (* (cbrt a) (cbrt a)) (* (cbrt (sqrt (- (* b_2 b_2) (* a c)))) (cbrt (sqrt (- (* b_2 b_2) (* a c)))))))

prune2.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.9b

localize25.0ms

Local error

Found 4 expressions with local error:

19.8b
(sqrt (- (* b_2 b_2) (* a c)))
17.1b
(/ (- (* a c)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.9b
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b
(- (* b_2 b_2) (* a c))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity add-cbrt-cube add-exp-log
8×add-sqr-sqrt add-log-exp
7×add-cube-cbrt
6×times-frac associate-/l*
5×pow1
4×insert-posit16
3×sqrt-prod
2×distribute-lft-neg-in cbrt-undiv neg-mul-1 distribute-rgt-neg-in flip3-+ flip3-- sqrt-div div-exp associate-*r/ associate-/r/ flip-+ flip--
1×neg-sub0 +-commutative rem-sqrt-square clear-num associate-/r* sum-log sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub prod-exp distribute-frac-neg cbrt-unprod div-inv distribute-lft-out
Counts
4 → 74
Calls
4 calls:
Slowest
48.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
46.0ms
(/ (- (* a c)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))
7.0ms
(- (* b_2 b_2) (* a c))

series435.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
216.0ms
(/ (- (* a c)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
100.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
76.0ms
(sqrt (- (* b_2 b_2) (* a c)))
42.0ms
(- (* b_2 b_2) (* a c))

simplify7.1s

Counts
46 → 86
Calls
46 calls:
Slowest
2.1s
(/ (* (* (- (* a c)) (- (* a c))) (- (* a c))) (* (* (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))))
1.5s
(/ (* (* (- (* a c)) (- (* a c))) (- (* a c))) (* (* (* a a) a) (* (* (+ (sqrt (- (* b_2 b_2) (* a c))) b_2) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))))
426.0ms
(- (log (- (* a c))) (+ (log a) (log (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))))
385.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
373.0ms
(- (log (- (* a c))) (log (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))))

prune937.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.9b

regimes295.0ms

Accuracy

95.4% (1.1b remaining)

Error of 6.9b against oracle of 5.9b and baseline of 29.1b

bsearch220.0ms

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.1s940×body1280valid
872.0ms1071×body2560valid
815.0ms5819×body80valid
546.0ms93×body5120valid
386.0ms2833×body80nan
203.0ms422×body640valid
113.0ms234×body320valid
28.0ms130×body160valid