Details

Time bar (total: 22.7s)

sample98.0ms

Algorithm
intervals
Results
24.0ms120×body80nan
20.0ms34×body2560valid
19.0ms205×body80valid
13.0ms26×body1280valid
4.0ms12×body640valid
2.0ms3×body5120valid
1.0ms3×body320valid
0.0ms2×body160valid

simplify118.0ms

Calls
1 calls:
Slowest
118.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.1b

localize22.0ms

Local error

Found 4 expressions with local error:

22.1b
(sqrt (- (* b b) (* (* 3 a) c)))
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
0.2b
(- (* b b) (* (* 3 a) c))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
9×add-sqr-sqrt
8×add-cube-cbrt add-log-exp
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u pow1 fma-def times-frac insert-posit16 log1p-expm1-u associate-/l*
3×sqrt-prod distribute-lft-out
2×neg-sub0 flip3-+ flip3-- sqrt-div associate-+l- flip-+ flip-- associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square clear-num associate-/r* neg-mul-1 sum-log sub-neg frac-2neg pow1/2 fma-neg diff-log div-sub div-exp prod-diff div-inv
Calls
4 calls:
Slowest
21.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
7.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
7.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
3.0ms
(- (* b b) (* (* 3 a) c))

series219.0ms

Calls
4 calls:
Slowest
86.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
62.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
40.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
31.0ms
(- (* b b) (* (* 3 a) c))

simplify4.4s

Calls
40 calls:
Slowest
608.0ms
(sqrt (- (pow (* b b) 3) (pow (* (* 3 a) c) 3)))
572.0ms
(- (* (- b) (- b)) (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))))
297.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
253.0ms
(- b (* 3/2 (/ (* a c) b)))
249.0ms
(+ (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 3 a) c))) 3))

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.1b

localize6.0ms

Local error

Found 4 expressions with local error:

22.1b
(sqrt (- (* b b) (* (* 3 a) c)))
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.3b
(/ 1 (* 3 a))
0.2b
(- (* b b) (* (* 3 a) c))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity add-log-exp
7×add-sqr-sqrt
6×add-cube-cbrt
5×pow1 add-exp-log
4×expm1-log1p-u fma-def add-cbrt-cube insert-posit16 log1p-expm1-u
3×sqrt-prod
2×flip3-- sqrt-div flip--
1×neg-sub0 +-commutative rem-sqrt-square rec-exp clear-num associate-/r* neg-mul-1 sum-log sub-neg frac-2neg flip3-+ pow1/2 fma-neg diff-log prod-diff associate-+l- flip-+ div-inv pow-flip distribute-lft-out inv-pow
Calls
4 calls:
Slowest
7.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
3.0ms
(- (* b b) (* (* 3 a) c))
1.0ms
(/ 1 (* 3 a))

series173.0ms

Calls
4 calls:
Slowest
65.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
55.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
42.0ms
(- (* b b) (* (* 3 a) c))
11.0ms
(/ 1 (* 3 a))

simplify2.3s

Calls
26 calls:
Slowest
482.0ms
(sqrt (- (pow (* b b) 3) (pow (* (* 3 a) c) 3)))
260.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
240.0ms
(- b (* 3/2 (/ (* a c) b)))
148.0ms
(/ (exp (* b b)) (exp (* (* 3 a) c)))
144.0ms
(* (exp (- b)) (exp (sqrt (- (* b b) (* (* 3 a) c)))))

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.1b

localize11.0ms

Local error

Found 4 expressions with local error:

22.1b
(sqrt (- (* b b) (* (* 3 a) c)))
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.3b
(/ (* 3 a) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))))
0.2b
(- (* b b) (* (* 3 a) c))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
9×add-sqr-sqrt
8×add-cube-cbrt add-log-exp
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u pow1 associate-/r* fma-def times-frac insert-posit16 log1p-expm1-u
3×sqrt-prod distribute-lft-out
2×flip3-+ flip3-- sqrt-div associate-/r/ flip-+ flip--
1×neg-sub0 cbrt-undiv +-commutative rem-sqrt-square clear-num neg-mul-1 sum-log sub-neg frac-2neg pow1/2 fma-neg diff-log div-exp prod-diff associate-+l- div-inv associate-/l*
Calls
4 calls:
Slowest
12.0ms
(/ (* 3 a) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))))
7.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
3.0ms
(- (* b b) (* (* 3 a) c))

series341.0ms

Calls
4 calls:
Slowest
178.0ms
(/ (* 3 a) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))))
69.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
53.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
42.0ms
(- (* b b) (* (* 3 a) c))

simplify4.2s

Calls
41 calls:
Slowest
528.0ms
(sqrt (- (pow (* b b) 3) (pow (* (* 3 a) c) 3)))
409.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
280.0ms
(/ (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))))
263.0ms
(+ (* (- b) (- b)) (- (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 3 a) c))))))
257.0ms
(- b (* 3/2 (/ (* a c) b)))

prune1.1s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.1b

localize33.0ms

Local error

Found 4 expressions with local error:

22.1b
(sqrt (fma -3 (* c a) (* b b)))
0.4b
(- (sqrt (fma -3 (* c a) (* b b))) b)
0.3b
(fma -3 (* c a) (* b b))
0.3b
(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×fma-neg sqrt-prod
4×expm1-log1p-u pow1 add-cbrt-cube associate-*r* add-exp-log insert-posit16 log1p-expm1-u add-log-exp
1×rem-sqrt-square sub-neg flip3-- pow1/2 associate-*r/ *-commutative fma-udef div-inv flip--
Calls
4 calls:
Slowest
6.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
6.0ms
(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))
1.0ms
(sqrt (fma -3 (* c a) (* b b)))
0.0ms
(fma -3 (* c a) (* b b))

series237.0ms

Calls
4 calls:
Slowest
81.0ms
(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))
61.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
60.0ms
(sqrt (fma -3 (* c a) (* b b)))
36.0ms
(fma -3 (* c a) (* b b))

simplify602.0ms

Calls
25 calls:
Slowest
91.0ms
(- (pow b 2) (* 3 (* a c)))
60.0ms
(sqrt (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))
59.0ms
(- (pow b 2) (* 3 (* a c)))
56.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) a)
48.0ms
(- (pow b 2) (* 3 (* a c)))

prune851.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 7.1b

regimes692.0ms

Accuracy

83% (4.8b remaining)

Error of 10.3b against oracle of 5.5b and baseline of 33.6b

bsearch264.0ms

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.4s1058×body2560valid
1.1s5816×body80valid
764.0ms935×body1280valid
524.0ms2850×body80nan
298.0ms477×body640valid
97.0ms249×body320valid
87.0ms87×body5120valid
28.0ms106×body160valid