Details

Time bar (total: 21.8s)

sample135.0ms

Algorithm
intervals
Results
45.0ms31×body2560valid
18.0ms203×body80valid
9.0ms21×body1280valid
7.0ms95×body80nan
7.0ms21×body640valid
1.0ms4×body320valid
1.0ms1×body5120valid
0.0ms2×body160valid

simplify84.0ms

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

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize35.0ms

Local error

Found 4 expressions with local error:

24.0b
(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)

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
7×fma-neg
6×sqrt-prod add-log-exp
4×expm1-log1p-u pow1 flip3-- add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u flip--
3×associate-/l*
2×sub-neg sqrt-div associate-/l/
1×rem-sqrt-square clear-num frac-2neg pow1/2 diff-log div-sub prod-diff div-inv
Calls
4 calls:
Slowest
50.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
30.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms
(sqrt (- (* b_2 b_2) (* a c)))
5.0ms
(- (* b_2 b_2) (* a c))

series400.0ms

Calls
4 calls:
Slowest
142.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
112.0ms
(sqrt (- (* b_2 b_2) (* a c)))
100.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
46.0ms
(- (* b_2 b_2) (* a c))

simplify2.4s

Calls
31 calls:
Slowest
522.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
340.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
261.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
208.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
170.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))

prune878.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize1.0ms

Local error

Found 4 expressions with local error:

24.0b
(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)

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
7×fma-neg
6×sqrt-prod add-log-exp
4×expm1-log1p-u pow1 flip3-- add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u flip--
3×associate-/l*
2×sub-neg sqrt-div associate-/l/
1×rem-sqrt-square clear-num frac-2neg pow1/2 diff-log div-sub prod-diff div-inv
Calls
4 calls:
Slowest
60.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
17.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.0ms
(- (* b_2 b_2) (* a c))
3.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series370.0ms

Calls
4 calls:
Slowest
138.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
105.0ms
(sqrt (- (* b_2 b_2) (* a c)))
83.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
44.0ms
(- (* b_2 b_2) (* a c))

simplify2.3s

Calls
31 calls:
Slowest
489.0ms
(- (* (sqrt (- (* b_2 b_2) (* a c))) (sqrt (- (* b_2 b_2) (* a c)))) (* b_2 b_2))
381.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
227.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
205.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
154.0ms
(- (pow (sqrt (- (* b_2 b_2) (* a c))) 3) (pow b_2 3))

prune906.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.5b

localize6.0ms

Local error

Found 4 expressions with local error:

24.0b
(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))
0.2b
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
7×fma-neg
6×associate-/r* sqrt-prod add-log-exp
5×pow1 add-exp-log
4×expm1-log1p-u flip3-- add-cbrt-cube insert-posit16 log1p-expm1-u flip--
3×associate-/r/
2×sub-neg sqrt-div div-inv
1×rem-sqrt-square rec-exp clear-num frac-2neg pow1/2 diff-log prod-diff pow-flip inv-pow
Calls
4 calls:
Slowest
16.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
3.0ms
(sqrt (- (* b_2 b_2) (* a c)))
3.0ms
(- (* b_2 b_2) (* a c))

series404.0ms

Calls
4 calls:
Slowest
192.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
87.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
71.0ms
(sqrt (- (* b_2 b_2) (* a c)))
53.0ms
(- (* b_2 b_2) (* a c))

simplify1.9s

Calls
34 calls:
Slowest
390.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
310.0ms
(+ (* (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)))
205.0ms
(- b_2 (* 1/2 (/ (* a c) b_2)))
195.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
108.0ms
(- (* 1/2 (/ (* a c) b_2)) (* 2 b_2))

prune1.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.5b

localize12.0ms

Local error

Found 4 expressions with local error:

24.0b
(sqrt (- (* b_2 b_2) (* a c)))
17.4b
(/ (- (* a c)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.7b
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b
(- (* b_2 b_2) (* a c))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
6×fma-def times-frac add-cbrt-cube add-exp-log sqrt-prod associate-/l* add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
2×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in flip3-+ flip3-- sqrt-div associate-*r/ associate-/r/ flip-+ flip--
1×neg-sub0 cbrt-undiv +-commutative rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg pow1/2 fma-neg diff-log div-sub div-exp prod-diff distribute-frac-neg div-inv
Calls
4 calls:
Slowest
15.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0ms
(/ (- (* a c)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))
3.0ms
(- (* b_2 b_2) (* a c))

series401.0ms

Calls
4 calls:
Slowest
184.0ms
(/ (- (* a c)) (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)))
89.0ms
(sqrt (- (* b_2 b_2) (* a c)))
88.0ms
(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
40.0ms
(- (* b_2 b_2) (* a c))

simplify5.1s

Calls
48 calls:
Slowest
1.5s
(/ (* (* (- (* 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))))
537.0ms
(sqrt (- (* (* b_2 b_2) (* b_2 b_2)) (* (* a c) (* a c))))
515.0ms
(+ (* (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)))
408.0ms
(sqrt (- (pow (* b_2 b_2) 3) (pow (* a c) 3)))
332.0ms
(- (log (- (* a c))) (log (* a (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))))

prune907.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.5b

regimes384.0ms

Accuracy

95.6% (1.1b remaining)

Error of 6.3b against oracle of 5.3b and baseline of 29.8b

bsearch339.0ms

end18.0ms

sample3.5s

Algorithm
intervals
Results
1.1s1037×body2560valid
867.0ms5885×body80valid
539.0ms887×body1280valid
312.0ms2915×body80nan
288.0ms460×body640valid
74.0ms242×body320valid
67.0ms95×body5120valid
23.0ms109×body160valid