Details

Time bar (total: 43.2s)

sample241.0ms

Algorithm
intervals
Results
29.0ms189×body80valid
25.0ms30×body2560valid
22.0ms32×body1280valid
13.0ms99×body80nan
8.0ms15×body640valid
2.0ms4×body320valid
2.0ms5×body160valid
1.0ms1×body5120valid

simplify83.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
83.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize20.0ms

Local error

Found 4 expressions with local error:

20.7b
(sqrt (- (* b_2 b_2) (* a c)))
1.3b
(- (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)

rewrite207.0ms

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
94.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
78.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))
15.0ms
(- (* b_2 b_2) (* a c))

series368.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
129.0ms
(sqrt (- (* b_2 b_2) (* a c)))
109.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
93.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
37.0ms
(- (* b_2 b_2) (* a c))

simplify4.5s

Counts
73 → 100
Calls
73 calls:
Slowest
521.0ms
(- (* 1/2 (/ (* a c) b_2)) (* 2 b_2))
373.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
337.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
324.0ms
(/ (* (* (- (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))
302.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize35.0ms

Local error

Found 4 expressions with local error:

20.7b
(sqrt (- (* b_2 b_2) (* a c)))
5.7b
(- (/ (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)

rewrite85.0ms

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
47.0ms
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
15.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))
8.0ms
(- (* b_2 b_2) (* a c))

series461.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
167.0ms
(/ (sqrt (- (* b_2 b_2) (* a c))) a)
132.0ms
(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
106.0ms
(sqrt (- (* b_2 b_2) (* a c)))
56.0ms
(- (* b_2 b_2) (* a c))

simplify4.1s

Counts
92 → 109
Calls
92 calls:
Slowest
316.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
313.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
285.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
205.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
180.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.1b

localize34.0ms

Local error

Found 4 expressions with local error:

20.7b
(sqrt (- (* b_2 b_2) (* a c)))
9.3b
(- (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
0.6b
(- (* b_2 b_2) (* a c))
0.2b
(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))

rewrite159.0ms

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
124.0ms
(- (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
17.0ms
(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))
8.0ms
(- (* b_2 b_2) (* a c))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series406.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
138.0ms
(- (/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c))))) (/ b_2 a))
130.0ms
(/ 1 (/ a (sqrt (- (* b_2 b_2) (* a c)))))
77.0ms
(sqrt (- (* b_2 b_2) (* a c)))
61.0ms
(- (* b_2 b_2) (* a c))

simplify17.5s

Counts
233 → 193
Calls
233 calls:
Slowest
525.0ms
(/ (* (* 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))))))
366.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (* (cbrt (sqrt (- (* b_2 b_2) (* a c)))) (cbrt (sqrt (- (* b_2 b_2) (* a c)))))))
357.0ms
(/ (sqrt 1) (/ (* (cbrt a) (cbrt a)) (* (cbrt (sqrt (- (* b_2 b_2) (* a c)))) (cbrt (sqrt (- (* b_2 b_2) (* a c)))))))
344.0ms
(/ (* (* 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))))))
326.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ a (sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))))

prune2.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.1b

localize27.0ms

Local error

Found 4 expressions with local error:

20.7b
(sqrt (- (* b_2 b_2) (* a c)))
20.7b
(sqrt (- (* b_2 b_2) (* a c)))
14.4b
(- (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) a)) (/ b_2 a))
0.6b
(- (* b_2 b_2) (* a c))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
12×sqrt-div
8×add-sqr-sqrt add-log-exp
6×pow1 *-un-lft-identity flip3-- add-cube-cbrt sqrt-prod flip--
5×frac-sub
4×add-cbrt-cube add-exp-log insert-posit16
2×frac-times rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log associate-*l/ associate-*r/
1×sub-div
Counts
4 → 64
Calls
4 calls:
Slowest
52.0ms
(- (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) a)) (/ b_2 a))
16.0ms
(sqrt (- (* b_2 b_2) (* a c)))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))
8.0ms
(- (* b_2 b_2) (* a c))

series363.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(- (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) a)) (/ b_2 a))
110.0ms
(sqrt (- (* b_2 b_2) (* a c)))
68.0ms
(sqrt (- (* b_2 b_2) (* a c)))
44.0ms
(- (* b_2 b_2) (* a c))

simplify4.1s

Counts
39 → 76
Calls
39 calls:
Slowest
344.0ms
(/ (exp (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) a))) (exp (/ b_2 a)))
312.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
274.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
257.0ms
(- (* (* (sqrt (sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))) a) (* (* (sqrt (sqrt (+ (* (* b_2 b_2) (* b_2 b_2)) (+ (* (* a c) (* a c)) (* (* b_2 b_2) (* a c)))))) a) b_2))
250.0ms
(- (* (* (sqrt (sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))) (/ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) a)) a) (* (sqrt (sqrt (+ (* (* b_2 b_2) (* b_2 b_2)) (+ (* (* a c) (* a c)) (* (* b_2 b_2) (* a c)))))) b_2))

prune924.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.1b

regimes385.0ms

Accuracy

83.4% (4.7b remaining)

Error of 9.8b against oracle of 5.1b and baseline of 33.5b

bsearch194.0ms

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.3s1123×body2560valid
1.0s876×body1280valid
732.0ms5825×body80valid
361.0ms2896×body80nan
281.0ms461×body640valid
124.0ms109×body5120valid
102.0ms209×body320valid
28.0ms124×body160valid