Details

Time bar (total: 1.7m)

sample143.0ms

Algorithm
intervals
Results
34.0ms195×body80valid
32.0ms32×body2560valid
23.0ms28×body1280valid
17.0ms108×body80nan
6.0ms12×body320valid
5.0ms8×body640valid
4.0ms3×body5120valid
0.0ms1×body160valid

simplify180.0ms

Calls
1 calls:
Slowest
180.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize24.0ms

Local error

Found 4 expressions with local error:

23.7b
(sqrt (- (* b b) (* (* c a) 4)))
0.8b
(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.4b
(- (* b b) (* (* c a) 4))
0.1b
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
200×add-sqr-sqrt
91×*-un-lft-identity
72×times-frac
58×difference-of-squares
43×unswap-sqr
39×associate-*l* add-cube-cbrt
38×sqrt-prod
26×distribute-lft-out--
21×associate-*r*
13×*-commutative
12×associate-/r*
9×add-cbrt-cube add-exp-log
8×add-log-exp
6×swap-sqr associate-/l*
5×pow1
4×flip3-- insert-posit16 flip--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp cbrt-unprod div-inv
Calls
4 calls:
Slowest
559.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
382.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
67.0ms
(- (* b b) (* (* c a) 4))
55.0ms
(sqrt (- (* b b) (* (* c a) 4)))

series460.0ms

Calls
4 calls:
Slowest
142.0ms
(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
135.0ms
(- (sqrt (- (* b b) (* (* c a) 4))) b)
104.0ms
(sqrt (- (* b b) (* (* c a) 4)))
78.0ms
(- (* b b) (* (* c a) 4))

simplify17.5s

Calls
247 calls:
Slowest
478.0ms
(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
357.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
291.0ms
(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
279.0ms
(/ (exp (* b b)) (exp (* (* c a) 4)))
255.0ms
(/ (* (* (- (sqrt (- (* b b) (* (* c a) 4))) b) (- (sqrt (- (* b b) (* (* c a) 4))) b)) (- (sqrt (- (* b b) (* (* c a) 4))) b)) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune2.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.5b

localize14.0ms

Local error

Found 4 expressions with local error:

23.7b
(sqrt (+ (* b b) (* (* c -4) a)))
0.8b
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
0.4b
(+ (* b b) (* (* c -4) a))
0.1b
(/ (- (sqrt (+ (* b b) (* (* c -4) a))) b) (* 2 a))

rewrite850.0ms

Algorithm
rewrite-expression-head
Rules
110×add-sqr-sqrt
91×*-un-lft-identity
72×times-frac
39×associate-*l* add-cube-cbrt
28×difference-of-squares
23×sqrt-prod
21×associate-*r*
14×distribute-lft-out--
12×associate-/r* distribute-lft-out
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×*-commutative unswap-sqr
6×associate-/l*
5×pow1
4×insert-posit16
2×cbrt-undiv flip3-+ flip3-- sqrt-div div-exp flip-+ flip-- associate-/l/
1×+-commutative rem-sqrt-square clear-num sum-log sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub prod-exp cbrt-unprod div-inv
Calls
4 calls:
Slowest
472.0ms
(/ (- (sqrt (+ (* b b) (* (* c -4) a))) b) (* 2 a))
278.0ms
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
67.0ms
(sqrt (+ (* b b) (* (* c -4) a)))
30.0ms
(+ (* b b) (* (* c -4) a))

series393.0ms

Calls
4 calls:
Slowest
119.0ms
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
114.0ms
(/ (- (sqrt (+ (* b b) (* (* c -4) a))) b) (* 2 a))
88.0ms
(sqrt (+ (* b b) (* (* c -4) a)))
71.0ms
(+ (* b b) (* (* c -4) a))

simplify9.5s

Calls
202 calls:
Slowest
558.0ms
(- (* (sqrt (+ (* b b) (* (* c -4) a))) (sqrt (+ (* b b) (* (* c -4) a)))) (* b b))
294.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c -4) a) (* (* c -4) a))))
249.0ms
(/ (* (* (- (sqrt (+ (* b b) (* (* c -4) a))) b) (- (sqrt (+ (* b b) (* (* c -4) a))) b)) (- (sqrt (+ (* b b) (* (* c -4) a))) b)) (* (* (* 2 a) (* 2 a)) (* 2 a)))
219.0ms
(- (pow (sqrt (+ (* b b) (* (* c -4) a))) 3) (pow b 3))
215.0ms
(* (exp (* b b)) (exp (* (* c -4) a)))

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.5b

localize6.0ms

Local error

Found 4 expressions with local error:

23.7b
(sqrt (+ (* b b) (* (* c -4) a)))
0.8b
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
0.4b
(+ (* b b) (* (* c -4) a))
0.2b
(/ 1 (/ (* 2 a) (- (sqrt (+ (* b b) (* (* c -4) a))) b)))

rewrite667.0ms

Algorithm
rewrite-expression-head
Rules
522×times-frac
463×add-sqr-sqrt
338×*-un-lft-identity
212×add-cube-cbrt
100×difference-of-squares
94×associate-*l*
84×associate-/r*
75×associate-*r*
59×sqrt-prod
50×distribute-lft-out--
29×associate-/r/
25×add-exp-log *-commutative unswap-sqr
17×associate-/l*
13×add-cbrt-cube
12×div-exp distribute-lft-out
8×add-log-exp
6×pow1
5×cbrt-undiv flip3-- div-inv flip--
4×insert-posit16
3×rec-exp clear-num 1-exp prod-exp remove-double-div
2×frac-2neg flip3-+ sqrt-div flip-+
1×+-commutative rem-sqrt-square sum-log sub-neg sqrt-pow1 pow1/2 diff-log cbrt-unprod pow-flip inv-pow
Calls
4 calls:
Slowest
363.0ms
(/ 1 (/ (* 2 a) (- (sqrt (+ (* b b) (* (* c -4) a))) b)))
217.0ms
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
46.0ms
(sqrt (+ (* b b) (* (* c -4) a)))
29.0ms
(+ (* b b) (* (* c -4) a))

series363.0ms

Calls
4 calls:
Slowest
150.0ms
(/ 1 (/ (* 2 a) (- (sqrt (+ (* b b) (* (* c -4) a))) b)))
89.0ms
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
73.0ms
(sqrt (+ (* b b) (* (* c -4) a)))
50.0ms
(+ (* b b) (* (* c -4) a))

simplify1.0m

Calls
620 calls:
Slowest
586.0ms
(/ (sqrt 1) (/ (* 2 a) (- (sqrt (+ (* b b) (* (* c -4) a))) b)))
384.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (sqrt 2) (sqrt a)) 1))
311.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* 2 (* (cbrt a) (cbrt a))) (sqrt (- (sqrt (+ (* b b) (* (* c -4) a))) b))))
300.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* 2 a) (- (* (sqrt (+ (* b b) (* (* c -4) a))) (sqrt (+ (* b b) (* (* c -4) a)))) (* b b))))
299.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* 2 a) (- (pow (sqrt (+ (* b b) (* (* c -4) a))) 3) (pow b 3))))

prune3.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.5b

localize10.0ms

Local error

Found 4 expressions with local error:

23.7b
(sqrt (+ (* b b) (* (* c -4) a)))
0.8b
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
0.4b
(* (sqrt 2) a)
0.4b
(+ (* b b) (* (* c -4) a))

rewrite292.0ms

Algorithm
rewrite-expression-head
Rules
34×*-un-lft-identity
24×associate-*l*
17×add-sqr-sqrt
14×sqrt-prod
12×distribute-lft-out
8×add-cube-cbrt add-log-exp
7×pow1
6×add-cbrt-cube add-exp-log
4×insert-posit16
3×associate-*r*
2×flip3-+ sqrt-div flip-+ difference-of-squares unswap-sqr
1×+-commutative rem-sqrt-square sum-log sub-neg sqrt-pow1 flip3-- pow1/2 diff-log pow-prod-down prod-exp *-commutative cbrt-unprod flip-- distribute-lft-out--
Calls
4 calls:
Slowest
210.0ms
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
45.0ms
(sqrt (+ (* b b) (* (* c -4) a)))
29.0ms
(+ (* b b) (* (* c -4) a))
7.0ms
(* (sqrt 2) a)

series247.0ms

Calls
4 calls:
Slowest
84.0ms
(- (sqrt (+ (* b b) (* (* c -4) a))) b)
72.0ms
(sqrt (+ (* b b) (* (* c -4) a)))
45.0ms
(* (sqrt 2) a)
45.0ms
(+ (* b b) (* (* c -4) a))

simplify1.5s

Calls
52 calls:
Slowest
249.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* c -4) a) (* (* c -4) a))))
160.0ms
(* (exp (* b b)) (exp (* (* c -4) a)))
154.0ms
(- b (* 2 (/ (* a c) b)))
104.0ms
(* (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* a a) a))
80.0ms
(sqrt (+ (pow (* b b) 3) (pow (* (* c -4) a) 3)))

prune720.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.5b

regimes238.0ms

Accuracy

80.9% (5.3b remaining)

Error of 10.9b against oracle of 5.6b and baseline of 33.4b

bsearch138.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
785.0ms1038×body2560valid
627.0ms5823×body80valid
549.0ms486×body640valid
451.0ms889×body1280valid
327.0ms2837×body80nan
89.0ms258×body320valid
70.0ms108×body5120valid
22.0ms129×body160valid