Details

Time bar (total: 5.1m)

sample118.0ms

Algorithm
intervals
Results
27.0ms187×body80valid
24.0ms29×body2560valid
22.0ms32×body1280valid
12.0ms94×body80nan
9.0ms16×body640valid
3.0ms7×body320valid
2.0ms2×body5120valid

simplify181.0ms

Calls
1 calls:
Slowest
181.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.1b

localize27.0ms

Local error

Found 4 expressions with local error:

22.6b
(sqrt (- (* b b) (* (* 3 a) c)))
0.8b
(- (* b b) (* (* 3 a) c))
0.5b
(* (* 3 a) c)
0.4b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

rewrite519.0ms

Algorithm
rewrite-expression-head
Rules
491×add-sqr-sqrt
345×associate-*l*
330×prod-diff
306×*-un-lft-identity
230×add-cube-cbrt
183×associate-*r*
129×unswap-sqr
75×swap-sqr
67×*-commutative
60×times-frac
30×difference-of-squares
26×distribute-lft-out
24×sqrt-prod
15×fma-neg
14×add-cbrt-cube add-exp-log
13×distribute-rgt-neg-in
12×associate-/r* distribute-lft-out--
10×pow1
6×add-log-exp
5×associate-/l*
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×pow-prod-down
2×cbrt-undiv flip3-- sqrt-div div-exp flip-- associate-/l/
1×neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log div-sub associate-+l- flip-+ div-inv
Calls
4 calls:
Slowest
347.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
87.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
56.0ms
(- (* b b) (* (* 3 a) c))
18.0ms
(* (* 3 a) c)

series326.0ms

Calls
4 calls:
Slowest
155.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
87.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
54.0ms
(- (* b b) (* (* 3 a) c))
29.0ms
(* (* 3 a) c)

simplify2.4m

Calls
906 calls:
Slowest
659.0ms
(- (* (- b) (- b)) (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))))
622.0ms
(fma (- (* (* (sqrt 3) (sqrt a)) c)) (* (sqrt 3) (sqrt a)) (* (* (* (sqrt 3) (sqrt a)) c) (* (sqrt 3) (sqrt a))))
577.0ms
(fma (* b 1) b (- (* c (* (* 3 a) 1))))
563.0ms
(fma (- (cbrt c)) (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt c) (* (* 3 a) (* (cbrt c) (cbrt c)))))
529.0ms
(fma b b (- (* c (* (* 3 a) 1))))

prune7.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.6b

localize24.0ms

Local error

Found 4 expressions with local error:

22.6b
(sqrt (fma -3 (* c a) (* b b)))
0.9b
(fma -3 (* c a) (* b b))
0.3b
(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))
0.2b
(- (sqrt (fma -3 (* c a) (* b b))) b)

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
45×*-un-lft-identity
32×add-cube-cbrt
22×associate-*r*
20×sqrt-prod
19×times-frac
18×prod-diff
14×associate-*r/
10×difference-of-squares
9×add-cbrt-cube add-exp-log
8×associate-/l*
7×pow1
6×fma-neg distribute-lft-out-- add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* associate-*l* un-div-inv
2×clear-num flip3-- prod-exp cbrt-unprod flip-- unswap-sqr associate-/l/
1×cbrt-undiv rem-sqrt-square sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-exp pow-prod-down *-commutative fma-udef div-inv
Calls
4 calls:
Slowest
70.0ms
(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))
15.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
2.0ms
(sqrt (fma -3 (* c a) (* b b)))
0.0ms
(fma -3 (* c a) (* b b))

series386.0ms

Calls
4 calls:
Slowest
109.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
107.0ms
(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))
106.0ms
(sqrt (fma -3 (* c a) (* b b)))
63.0ms
(fma -3 (* c a) (* b b))

simplify4.8s

Calls
112 calls:
Slowest
238.0ms
(* (* (* 1/3 1/3) 1/3) (/ (* (* (- (sqrt (fma -3 (* c a) (* b b))) b) (- (sqrt (fma -3 (* c a) (* b b))) b)) (- (sqrt (fma -3 (* c a) (* b b))) b)) (* (* a a) a)))
197.0ms
(* a (+ (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (+ (* b b) (* (sqrt (fma -3 (* c a) (* b b))) b))))
172.0ms
(* (* (* 1/3 1/3) 1/3) (* (* (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a) (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a)) (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a)))
155.0ms
(+ (log 1/3) (log (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a)))
134.0ms
(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))

prune1.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.6b

localize28.0ms

Local error

Found 4 expressions with local error:

22.6b
(sqrt (fma -3 (* c a) (* b b)))
0.9b
(fma -3 (* c a) (* b b))
0.2b
(* 1/3 (- (sqrt (fma -3 (* c a) (* b b))) b))
0.2b
(- (sqrt (fma -3 (* c a) (* b b))) b)

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt
54×prod-diff
49×*-un-lft-identity
45×add-cube-cbrt
35×sqrt-prod
20×distribute-rgt-in distribute-lft-in
7×pow1
6×add-cbrt-cube fma-neg associate-*r* add-exp-log add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u difference-of-squares
3×sub-neg associate-*l*
2×flip3-- associate-*r/ flip-- distribute-lft-out--
1×rem-sqrt-square sqrt-pow1 pow1/2 diff-log pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
Calls
4 calls:
Slowest
37.0ms
(* 1/3 (- (sqrt (fma -3 (* c a) (* b b))) b))
7.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
3.0ms
(sqrt (fma -3 (* c a) (* b b)))
0.0ms
(fma -3 (* c a) (* b b))

series414.0ms

Calls
4 calls:
Slowest
134.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
114.0ms
(* 1/3 (- (sqrt (fma -3 (* c a) (* b b))) b))
90.0ms
(sqrt (fma -3 (* c a) (* b b)))
76.0ms
(fma -3 (* c a) (* b b))

simplify5.6s

Calls
119 calls:
Slowest
475.0ms
(* (* (* 1/3 1/3) 1/3) (* (* (- (sqrt (fma -3 (* c a) (* b b))) b) (- (sqrt (fma -3 (* c a) (* b b))) b)) (- (sqrt (fma -3 (* c a) (* b b))) b)))
133.0ms
(+ (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (+ (* b b) (* (sqrt (fma -3 (* c a) (* b b))) b)))
122.0ms
(* 1/3 (fma (- (cbrt b)) (* (cbrt b) (cbrt b)) (* (cbrt b) (* (cbrt b) (cbrt b)))))
118.0ms
(* (fma (- (cbrt b)) (* (cbrt b) (cbrt b)) (* (cbrt b) (* (cbrt b) (cbrt b)))) 1/3)
100.0ms
(/ (exp (sqrt (fma -3 (* c a) (* b b)))) (exp b))

prune2.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.6b

localize54.0ms

Local error

Found 4 expressions with local error:

22.6b
(sqrt (- (* b b) (* (* 3 a) c)))
0.8b
(- (* b b) (* (* 3 a) c))
0.5b
(* (* 3 a) c)
0.2b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))

rewrite415.0ms

Algorithm
rewrite-expression-head
Rules
451×add-sqr-sqrt
330×prod-diff
327×associate-*l*
230×*-un-lft-identity
202×add-cube-cbrt
165×associate-*r*
123×unswap-sqr
75×swap-sqr
61×*-commutative
30×difference-of-squares
24×sqrt-prod
15×fma-neg
12×distribute-lft-out--
10×pow1 fma-def add-log-exp
9×add-cbrt-cube add-exp-log
4×expm1-log1p-u distribute-rgt-neg-in insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in pow-prod-down prod-exp cbrt-unprod
2×sum-log flip3-- sqrt-div flip-- distribute-lft-out
1×neg-sub0 +-commutative rem-sqrt-square neg-mul-1 sub-neg sqrt-pow1 flip3-+ pow1/2 diff-log neg-log associate-+l- flip-+
Calls
4 calls:
Slowest
147.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
125.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
83.0ms
(- (* b b) (* (* 3 a) c))
38.0ms
(* (* 3 a) c)

series302.0ms

Calls
4 calls:
Slowest
115.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
103.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
52.0ms
(- (* b b) (* (* 3 a) c))
32.0ms
(* (* 3 a) c)

simplify2.2m

Calls
779 calls:
Slowest
893.0ms
(fma (* (cbrt b) (cbrt b)) (* (cbrt b) b) (- (* (* (* (sqrt 3) (sqrt a)) c) (* (sqrt 3) (sqrt a)))))
808.0ms
(fma (* (sqrt b) (sqrt b)) (* (sqrt b) (sqrt b)) (- (* (* (cbrt a) c) (* 3 (* (cbrt a) (cbrt a))))))
772.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
542.0ms
(fma (- (* (* (sqrt 3) a) c)) (sqrt 3) (* (* (* (sqrt 3) a) c) (sqrt 3)))
521.0ms
(fma (- (* (* (sqrt 3) (sqrt a)) (sqrt c))) (* (* (sqrt 3) (sqrt a)) (sqrt c)) (* (* (* (sqrt 3) (sqrt a)) (sqrt c)) (* (* (sqrt 3) (sqrt a)) (sqrt c))))

prune6.4s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.6b

regimes1.0s

Accuracy

85.3% (4.1b remaining)

Error of 10.0b against oracle of 5.9b and baseline of 33.9b

bsearch124.0ms

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.4s1070×body2560valid
923.0ms5833×body80valid
747.0ms906×body1280valid
410.0ms2889×body80nan
271.0ms476×body640valid
138.0ms110×body5120valid
126.0ms226×body320valid
44.0ms89×body160valid