Details

Time bar (total: 26.5s)

sample114.0ms

Algorithm
intervals
Results
26.0ms29×body2560valid
25.0ms191×body80valid
16.0ms26×body1280valid
14.0ms80×body80nan
9.0ms18×body640valid
4.0ms8×body320valid
2.0ms3×body5120valid
1.0ms2×body160valid

simplify273.0ms

Counts
1 → 1

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.0b

localize32.0ms

Local error

Found 4 expressions with local error:

20.9b
(sqrt (- (* b b) (* 4 (* a c))))
1.0b
(- (* b b) (* 4 (* a c)))
0.3b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-cbrt-cube add-exp-log
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u flip--
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp cbrt-unprod div-inv
Counts
4 → 161
Calls
4 calls:
Slowest
78.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
26.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
19.0ms
(sqrt (- (* b b) (* 4 (* a c))))
17.0ms
(- (* b b) (* 4 (* a c)))

series412.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
129.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
112.0ms
(sqrt (- (* b b) (* 4 (* a c))))
108.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
64.0ms
(- (* b b) (* 4 (* a c)))

simplify857.0ms

Counts
173 → 173

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

localize46.0ms

Local error

Found 4 expressions with local error:

20.9b
(sqrt (- (* b b) (* 4 (* a c))))
1.0b
(- (* b b) (* 4 (* a c)))
0.3b
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
0.2b
(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
68×add-sqr-sqrt
62×*-un-lft-identity
61×prod-diff
54×add-cube-cbrt
35×sqrt-prod
23×distribute-rgt-neg-in
21×distribute-lft-neg-in
13×associate-*r*
11×fma-neg
10×times-frac add-log-exp
9×add-cbrt-cube add-exp-log
7×pow1 neg-mul-1 associate-*l*
5×flip3-- flip--
4×expm1-log1p-u insert-posit16 log1p-expm1-u distribute-lft-out-- difference-of-squares
3×diff-log
2×frac-times sub-neg sqrt-div associate-*l/ prod-exp cbrt-unprod unswap-sqr
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp pow-prod-down neg-log associate-*r/ *-commutative div-inv
Counts
4 → 169
Calls
4 calls:
Slowest
88.0ms
(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
23.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
19.0ms
(sqrt (- (* b b) (* 4 (* a c))))
17.0ms
(- (* b b) (* 4 (* a c)))

series423.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
127.0ms
(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
115.0ms
(sqrt (- (* b b) (* 4 (* a c))))
99.0ms
(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
82.0ms
(- (* b b) (* 4 (* a c)))

simplify828.0ms

Counts
181 → 181

prune2.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.6b

localize32.0ms

Local error

Found 4 expressions with local error:

20.9b
(sqrt (fma b b (* (* -4 a) c)))
1.3b
(fma b b (* (* -4 a) c))
0.3b
(- (- b) (sqrt (fma b b (* (* -4 a) c))))
0.2b
(/ 1 (/ (* a 2) (- (- b) (sqrt (fma b b (* (* -4 a) c))))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
88×*-un-lft-identity
68×add-cube-cbrt
67×times-frac
60×prod-diff
38×sqrt-prod
26×distribute-rgt-neg-in
25×add-exp-log
21×distribute-lft-neg-in
13×associate-/r* add-cbrt-cube
12×div-exp
10×fma-neg distribute-lft-out-- difference-of-squares
9×associate-/r/
8×add-log-exp
7×neg-mul-1
6×pow1
5×cbrt-undiv flip3-- div-inv flip--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×rec-exp 1-exp prod-exp associate-/l*
2×diff-log
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 neg-log cbrt-unprod fma-udef pow-flip inv-pow
Counts
4 → 201
Calls
4 calls:
Slowest
18.0ms
(/ 1 (/ (* a 2) (- (- b) (sqrt (fma b b (* (* -4 a) c))))))
10.0ms
(- (- b) (sqrt (fma b b (* (* -4 a) c))))
1.0ms
(sqrt (fma b b (* (* -4 a) c)))
0.0ms
(fma b b (* (* -4 a) c))

series476.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
185.0ms
(/ 1 (/ (* a 2) (- (- b) (sqrt (fma b b (* (* -4 a) c))))))
113.0ms
(sqrt (fma b b (* (* -4 a) c)))
100.0ms
(- (- b) (sqrt (fma b b (* (* -4 a) c))))
78.0ms
(fma b b (* (* -4 a) c))

simplify913.0ms

Counts
213 → 213

prune2.8s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.6b

localize51.0ms

Local error

Found 4 expressions with local error:

20.9b
(sqrt (fma b b (* (* -4 a) c)))
1.3b
(fma b b (* (* -4 a) c))
0.3b
(- (- b) (sqrt (fma b b (* (* -4 a) c))))
0.3b
(/ (/ 1 a) (/ 2 (- (- b) (sqrt (fma b b (* (* -4 a) c))))))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
897×times-frac
569×add-sqr-sqrt
568×*-un-lft-identity
396×add-cube-cbrt
86×distribute-lft-out-- difference-of-squares
76×sqrt-prod
64×distribute-rgt-neg-in
60×prod-diff
43×div-inv
29×associate-/r/
27×associate-/r*
26×add-exp-log
21×distribute-lft-neg-in
16×add-cbrt-cube div-exp
15×flip3-- flip--
13×associate-/l*
10×fma-neg
8×cbrt-undiv add-log-exp
7×neg-mul-1
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
2×rec-exp diff-log 1-exp
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 neg-log fma-udef associate-/l/
Counts
4 → 536
Calls
4 calls:
Slowest
29.0ms
(/ (/ 1 a) (/ 2 (- (- b) (sqrt (fma b b (* (* -4 a) c))))))
21.0ms
(- (- b) (sqrt (fma b b (* (* -4 a) c))))
3.0ms
(sqrt (fma b b (* (* -4 a) c)))
0.0ms
(fma b b (* (* -4 a) c))

series487.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(/ (/ 1 a) (/ 2 (- (- b) (sqrt (fma b b (* (* -4 a) c))))))
143.0ms
(sqrt (fma b b (* (* -4 a) c)))
112.0ms
(- (- b) (sqrt (fma b b (* (* -4 a) c))))
69.0ms
(fma b b (* (* -4 a) c))

simplify1.3s

Counts
548 → 548

prune7.7s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 4.6b

regimes389.0ms

Accuracy

84% (4.4b remaining)

Error of 9.7b against oracle of 5.3b and baseline of 32.6b

bsearch206.0ms

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.2s1075×body2560valid
809.0ms5877×body80valid
551.0ms846×body1280valid
487.0ms113×body5120valid
434.0ms2806×body80nan
234.0ms462×body640valid
75.0ms221×body320valid
23.0ms102×body160valid