Details

Time bar (total: 9.0s)

sample85.0ms

Algorithm
intervals
Results
15.0ms33×body2560valid
13.0ms35×body1280valid
13.0ms168×body80valid
7.0ms92×body80nan
5.0ms15×body640valid
3.0ms6×body5120valid
2.0ms9×body320valid
1.0ms8×body160valid

simplify7.0ms

Counts
1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize65.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.2b
(- (* b b) (* (* 4.0 a) c))
2.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
112.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
16.0ms
(- (* b b) (* (* 4.0 a) c))
42.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series476.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
69.0ms
(- (* b b) (* (* 4.0 a) c))
130.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
99.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify56.0ms

Counts
82 → 82

prune316.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.3b

localize21.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
3.8b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.6b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 148
Calls
4 calls:
14.0ms
(- (* b b) (* (* 4.0 a) c))
145.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
63.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series697.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(- (* b b) (* (* 4.0 a) c))
213.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
293.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
130.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify90.0ms

Counts
160 → 160

prune668.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
16.5b
(/ (* 2.0 a) (* 4.0 (* a c)))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt add-log-exp
9×*-un-lft-identity prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 70
Calls
4 calls:
42.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
21.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series306.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms
(- (* b b) (* (* 4.0 a) c))
19.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
105.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify80.0ms

Counts
82 → 82

prune341.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ 1 1) (* (/ (/ 1.0 2.0) c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
98×add-exp-log
65×div-exp
36×add-cbrt-cube
31×times-frac
24×add-sqr-sqrt
23×*-un-lft-identity
21×prod-exp
20×1-exp
19×add-cube-cbrt
18×cbrt-undiv
13×associate-/l*
10×add-log-exp
8×rec-exp
6×cbrt-unprod
5×pow1 flip3-- associate-/r/ flip--
4×sqrt-prod
3×diff-log div-inv
2×frac-times sub-neg sqrt-div associate-*r/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 neg-log associate-*l/ clear-num associate-/r* associate-/l/
Counts
4 → 124
Calls
4 calls:
47.0ms
(/ (/ 1 1) (* (/ (/ 1.0 2.0) c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
46.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms
(- (* b b) (* (* 4.0 a) c))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series430.0ms

Counts
4 → 12
Calls
4 calls:
218.0ms
(/ (/ 1 1) (* (/ (/ 1.0 2.0) c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
86.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
52.0ms
(- (* b b) (* (* 4.0 a) c))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify108.0ms

Counts
136 → 136

prune447.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.2b

regimes385.0ms

Accuracy

95.4% (1.1b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 29.6b

bsearch301.0ms

Steps
ItersRangePoint
5
3.1594096090812424e+104
8.241903478382293e+104
6.2080577970805e+104
8
-4.3193946104502796e-226
-4.381317687258745e-230
-7.892835993842436e-230
10
-3.742210988141449e+103
-1.1204690717208776e+87
-8.301687926884189e+98

simplify94.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.1s1051×body2560valid
878.0ms5870×body80valid
319.0ms893×body1280valid
216.0ms2845×body80nan
122.0ms480×body640valid
87.0ms98×body5120valid
42.0ms218×body320valid
14.0ms108×body160valid