Details

Time bar (total: 57.5s)

sample171.0ms

Algorithm
intervals
Results
15.0ms34×body2560valid
15.0ms195×body80valid
13.0ms36×body1280valid
10.0ms108×body80nan
2.0ms8×body640valid
1.0ms3×body320valid
0.0ms1×body5120valid

simplify75.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
75.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize19.0ms

Local error

Found 4 expressions with local error:

18.8b
(sqrt (- (* b_2 b_2) (* a c)))
0.4b
(- (* b_2 b_2) (* a c))
0.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
19×prod-diff
18×times-frac
10×difference-of-squares
8×add-log-exp
7×fma-neg
6×add-cbrt-cube add-exp-log associate-/l*
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u 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 → 122
Calls
4 calls:
Slowest
115.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
41.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))
8.0ms
(- (* b_2 b_2) (* a c))

series399.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
130.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
119.0ms
(sqrt (- (* b_2 b_2) (* a c)))
86.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
65.0ms
(- (* b_2 b_2) (* a c))

simplify5.8s

Counts
116 → 134
Calls
116 calls:
Slowest
572.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
323.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))
295.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
269.0ms
(/ (* (* (- (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))
251.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize23.0ms

Local error

Found 4 expressions with local error:

18.8b
(sqrt (- (* b_2 b_2) (* a c)))
0.4b
(- (* b_2 b_2) (* a c))
0.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.2b
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
137×add-sqr-sqrt
110×*-un-lft-identity
84×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
24×associate-/r*
19×prod-diff
15×add-exp-log
13×distribute-lft-out--
9×add-cbrt-cube associate-/r/
8×add-log-exp
7×flip3-- fma-neg div-exp flip--
6×pow1
5×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/l*
2×rec-exp sub-neg sqrt-div diff-log 1-exp
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-flip inv-pow
Counts
4 → 200
Calls
4 calls:
Slowest
56.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
40.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms
(- (* b_2 b_2) (* a c))
10.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series398.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
183.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
98.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
75.0ms
(sqrt (- (* b_2 b_2) (* a c)))
42.0ms
(- (* b_2 b_2) (* a c))

simplify23.8s

Counts
247 → 212
Calls
247 calls:
Slowest
566.0ms
(/ (* (* 1 1) 1) (/ (* (* 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))))
469.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (+ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt b_2))))
442.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (+ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt b_2))))
435.0ms
(/ (sqrt 1) (/ (* (cbrt a) (cbrt a)) (+ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt b_2))))
422.0ms
(/ (sqrt 1) (/ (* (cbrt a) (cbrt a)) (+ (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt b_2))))

prune2.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.3b

localize23.0ms

Local error

Found 4 expressions with local error:

18.8b
(sqrt (- (* b_2 b_2) (* a c)))
0.4b
(- (* b_2 b_2) (* a c))
0.4b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.2b
(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))

rewrite237.0ms

Algorithm
rewrite-expression-head
Rules
67×add-sqr-sqrt
56×*-un-lft-identity
55×prod-diff
51×add-cube-cbrt
35×sqrt-prod
20×distribute-rgt-in distribute-lft-in
13×associate-*l* add-exp-log
11×times-frac
9×add-cbrt-cube
8×add-log-exp
7×pow1 fma-neg
6×associate-*r*
5×flip3-- flip--
4×expm1-log1p-u sub-neg prod-exp insert-posit16 log1p-expm1-u difference-of-squares
3×unswap-sqr
2×frac-times sqrt-div diff-log div-exp associate-*r/ cbrt-unprod distribute-lft-out--
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
4 → 162
Calls
4 calls:
Slowest
133.0ms
(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
70.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0ms
(- (* b_2 b_2) (* a c))
15.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series409.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
182.0ms
(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
90.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
81.0ms
(sqrt (- (* b_2 b_2) (* a c)))
56.0ms
(- (* b_2 b_2) (* a c))

simplify11.3s

Counts
146 → 174
Calls
146 calls:
Slowest
392.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
314.0ms
(+ (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (+ (* b_2 b_2) (* (sqrt (- (* b_2 b_2) (* a c))) b_2)))
314.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
272.0ms
(* (/ 1 a) (fma (- (cbrt b_2)) (* (cbrt b_2) (cbrt b_2)) (* (cbrt b_2) (* (cbrt b_2) (cbrt b_2)))))
266.0ms
(* (/ 1 a) (fma (- (cbrt b_2)) (* (cbrt b_2) (cbrt b_2)) (* (cbrt b_2) (* (cbrt b_2) (cbrt b_2)))))

prune2.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.3b

localize26.0ms

Local error

Found 4 expressions with local error:

18.8b
(sqrt (- (* b_2 b_2) (* a c)))
18.8b
(sqrt (- (* b_2 b_2) (* a c)))
0.4b
(- (* b_2 b_2) (* a c))
0.4b
(- (* b_2 b_2) (* a c))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×expm1-log1p-u flip3-- add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u flip--
2×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 70
Calls
4 calls:
Slowest
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))
19.0ms
(sqrt (- (* b_2 b_2) (* a c)))
16.0ms
(- (* b_2 b_2) (* a c))
16.0ms
(- (* b_2 b_2) (* a c))

series274.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
107.0ms
(sqrt (- (* b_2 b_2) (* a c)))
86.0ms
(sqrt (- (* b_2 b_2) (* a c)))
45.0ms
(- (* b_2 b_2) (* a c))
36.0ms
(- (* b_2 b_2) (* a c))

simplify2.9s

Counts
32 → 82
Calls
32 calls:
Slowest
396.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
333.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
322.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
257.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
252.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))

prune1.2s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 3.3b

regimes376.0ms

Accuracy

80.8% (5.4b remaining)

Error of 10.9b against oracle of 5.6b and baseline of 33.5b

bsearch127.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.0s887×body1280valid
864.0ms5843×body80valid
808.0ms1028×body2560valid
363.0ms2884×body80nan
225.0ms471×body640valid
89.0ms107×body5120valid
80.0ms232×body320valid
59.0ms123×body160valid