Details

Time bar (total: 29.8s)

sample130.0ms

Algorithm
intervals
Results
41.0ms34×body2560valid
24.0ms179×body80valid
19.0ms31×body1280valid
10.0ms82×body80nan
9.0ms17×body640valid
5.0ms5×body5120valid
3.0ms7×body320valid
1.0ms4×body160valid

simplify137.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
137.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.1b

localize33.0ms

Local error

Found 4 expressions with local error:

21.5b
(sqrt (- (* b b) (* (* 3 a) c)))
1.2b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.4b
(- (* b b) (* (* 3 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×fma-def add-cube-cbrt add-log-exp
9×add-cbrt-cube add-exp-log
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×neg-sub0 cbrt-undiv sum-log flip3-+ flip3-- sqrt-div div-exp associate-+l- flip-+ flip-- associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-/r* neg-mul-1 sub-neg frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 94
Calls
4 calls:
Slowest
66.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
18.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
15.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
8.0ms
(- (* b b) (* (* 3 a) c))

series426.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
161.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
113.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
96.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
56.0ms
(- (* b b) (* (* 3 a) c))

simplify5.4s

Counts
52 → 106
Calls
52 calls:
Slowest
546.0ms
(- (* (- b) (- b)) (* (sqrt (- (* b b) (* (* 3 a) c))) (sqrt (- (* b b) (* (* 3 a) c)))))
421.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
363.0ms
(/ (* (* (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
297.0ms
(/ (* (* (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))) (* (* (* 3 3) 3) (* (* a a) a)))
254.0ms
(/ (exp (* b b)) (exp (* (* 3 a) c)))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize25.0ms

Local error

Found 4 expressions with local error:

21.5b
(sqrt (- (* b b) (* (* 3 a) c)))
1.2b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.4b
(- (* b b) (* (* 3 a) c))
0.2b
(* (* 3 a) c)

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
10×add-sqr-sqrt pow1 fma-def add-log-exp
9×add-cbrt-cube add-exp-log add-cube-cbrt
4×expm1-log1p-u distribute-rgt-neg-in insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in associate-*r* pow-prod-down prod-exp sqrt-prod 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 fma-neg diff-log associate-*l* prod-diff neg-log *-commutative associate-+l- flip-+
Counts
4 → 84
Calls
4 calls:
Slowest
16.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
15.0ms
(* (* 3 a) c)
15.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
12.0ms
(- (* b b) (* (* 3 a) c))

series269.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
99.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
81.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
66.0ms
(- (* b b) (* (* 3 a) c))
23.0ms
(* (* 3 a) c)

simplify3.4s

Counts
41 → 96
Calls
41 calls:
Slowest
422.0ms
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
415.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
408.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
243.0ms
(/ (exp (* b b)) (exp (* (* 3 a) c)))
242.0ms
(- b (* 3/2 (/ (* a c) b)))

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.1b

localize43.0ms

Local error

Found 4 expressions with local error:

21.5b
(sqrt (fma -3 (* c a) (* b b)))
1.2b
(- (sqrt (fma -3 (* c a) (* b b))) b)
0.5b
(fma -3 (* c a) (* b b))
0.3b
(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt
38×*-un-lft-identity
30×add-cube-cbrt
22×associate-*r*
19×times-frac sqrt-prod
18×prod-diff
9×add-cbrt-cube add-exp-log
8×difference-of-squares
7×pow1
6×fma-neg add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u distribute-lft-out--
3×associate-*l*
2×prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log div-exp pow-prod-down associate-*r/ *-commutative fma-udef div-inv flip--
Counts
4 → 113
Calls
4 calls:
Slowest
34.0ms
(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))
16.0ms
(- (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))

series378.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
117.0ms
(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))
102.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
94.0ms
(sqrt (fma -3 (* c a) (* b b)))
65.0ms
(fma -3 (* c a) (* b b))

simplify4.1s

Counts
97 → 125
Calls
97 calls:
Slowest
226.0ms
(* (* (* 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)))
163.0ms
(* (* (* 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)))
124.0ms
(+ (log 1/3) (log (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a)))
113.0ms
(* 1/3 (/ (- (sqrt (fma -3 (* c a) (* b b))) b) a))
107.0ms
(- (pow b 2) (* 3 (* a c)))

prune1.6s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.1b

localize33.0ms

Local error

Found 4 expressions with local error:

21.5b
(sqrt (- (* b b) (* (* 3 a) c)))
1.2b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.4b
(- (* b b) (* (* 3 a) c))
0.3b
(/ 1 (* 3 a))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
15×add-exp-log
14×*-un-lft-identity
11×add-sqr-sqrt
10×fma-def add-cube-cbrt add-log-exp
9×add-cbrt-cube
8×pow1
4×expm1-log1p-u distribute-rgt-neg-in div-exp insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in times-frac prod-exp sqrt-prod associate-/l*
2×cbrt-undiv rec-exp sum-log flip3-- sqrt-div 1-exp pow-flip flip-- distribute-lft-out
1×neg-sub0 +-commutative rem-sqrt-square clear-num associate-/r* neg-mul-1 sub-neg frac-2neg sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff pow-prod-down neg-log associate-+l- cbrt-unprod flip-+ div-inv inv-pow
Counts
4 → 94
Calls
4 calls:
Slowest
36.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
18.0ms
(/ 1 (* 3 a))
16.0ms
(- (* b b) (* (* 3 a) c))
11.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

series306.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
118.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
102.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
58.0ms
(- (* b b) (* (* 3 a) c))
27.0ms
(/ 1 (* 3 a))

simplify4.2s

Counts
49 → 106
Calls
49 calls:
Slowest
730.0ms
(/ (* (* 1 1) 1) (* (* (* 3 a) (* 3 a)) (* 3 a)))
655.0ms
(/ (exp (* b b)) (exp (* (* 3 a) c)))
431.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
315.0ms
(/ (* (* 1 1) 1) (* (* (* 3 3) 3) (* (* a a) a)))
211.0ms
(- b (* 3/2 (/ (* a c) b)))

prune1.3s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.1b

regimes849.0ms

Accuracy

83.9% (4.5b remaining)

Error of 10.3b against oracle of 5.8b and baseline of 33.6b

bsearch397.0ms

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.2s5836×body80valid
886.0ms1052×body2560valid
744.0ms871×body1280valid
392.0ms2786×body80nan
237.0ms469×body640valid
111.0ms124×body5120valid
81.0ms237×body320valid
24.0ms108×body160valid