Details

Time bar (total: 23.8s)

sample81.0ms

Algorithm
intervals
Results
18.0ms45×body1280valid
15.0ms184×body80valid
12.0ms25×body2560valid
6.0ms69×body80nan
6.0ms17×body640valid
2.0ms8×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify125.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
01217
12217
24216
38216
410416
511216
done11216

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b
(- (* b b) (* (* 3.0 a) c))
22.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
10×pow1 add-sqr-sqrt fma-def add-log-exp
9×add-exp-log add-cube-cbrt add-cbrt-cube
4×expm1-log1p-u distribute-rgt-neg-in log1p-expm1-u
3×distribute-lft-neg-in associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×flip3-- sqrt-div sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log associate-*l* prod-diff neg-log *-commutative flip-+
Counts
4 → 80
Calls
4 calls:
18.0ms
(* (* 3.0 a) c)
36.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms
(- (* b b) (* (* 3.0 a) c))
17.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series340.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (* 3.0 a) c)
126.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
83.0ms
(- (* b b) (* (* 3.0 a) c))
99.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify4.7s

Counts
92 → 92
Iterations

Useful iterations: 3 (2.5s)

IterNodesCost
01351109
13321006
21193900
34662889
done5000889

prune483.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.0b

localize31.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 3.0 a) c))
3.5b
(/ (/ (+ (* 3.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
10.2b
(/ (+ (* 3.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite309.0ms

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×expm1-log1p-u log1p-expm1-u 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 fma-neg diff-log prod-diff flip-+
Counts
4 → 158
Calls
4 calls:
17.0ms
(- (* b b) (* (* 3.0 a) c))
161.0ms
(/ (/ (+ (* 3.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
97.0ms
(/ (+ (* 3.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
27.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series647.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(- (* b b) (* (* 3.0 a) c))
231.0ms
(/ (/ (+ (* 3.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
258.0ms
(/ (+ (* 3.0 (* a c)) 0) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
94.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.1s

Counts
170 → 170
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02625076
16534509
228324180
done50004178

prune700.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.9b

localize25.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 3.0 a) c))
3.5b
(/ (/ (/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
10.2b
(/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
376×times-frac
188×add-sqr-sqrt
187×*-un-lft-identity
131×add-cube-cbrt
44×associate-/l*
33×add-exp-log add-cbrt-cube
28×distribute-lft-out-- difference-of-squares
26×associate-/r/
18×div-inv
17×sqrt-prod
15×cbrt-undiv flip3-- div-exp flip--
14×distribute-rgt-neg-in
10×associate-/r*
6×prod-exp cbrt-unprod add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff associate-/l/
Counts
4 → 266
Calls
4 calls:
18.0ms
(- (* b b) (* (* 3.0 a) c))
118.0ms
(/ (/ (/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
96.0ms
(/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
18.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series681.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(- (* b b) (* (* 3.0 a) c))
238.0ms
(/ (/ (/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
270.0ms
(/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
107.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.0s

Counts
278 → 278
Iterations

Useful iterations: done (3.0s)

IterNodesCost
05079705
112679064
248128567
done50008566

prune1.4s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 11.9b

localize24.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 3.0 a) c))
3.5b
(/ (/ (/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
10.2b
(/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.9b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite315.0ms

Algorithm
rewrite-expression-head
Rules
376×times-frac
188×add-sqr-sqrt
187×*-un-lft-identity
131×add-cube-cbrt
44×associate-/l*
28×distribute-lft-out-- difference-of-squares
26×associate-/r/
23×add-exp-log add-cbrt-cube
18×div-inv
17×sqrt-prod
15×flip3-- flip--
14×distribute-rgt-neg-in
11×cbrt-undiv div-exp
10×associate-/r*
6×add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff associate-/l/
Counts
4 → 262
Calls
4 calls:
18.0ms
(- (* b b) (* (* 3.0 a) c))
165.0ms
(/ (/ (/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
78.0ms
(/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series675.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(- (* b b) (* (* 3.0 a) c))
235.0ms
(/ (/ (/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) 3.0) a)
260.0ms
(/ (* a c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
85.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.6s

Counts
274 → 274
Iterations

Useful iterations: done (2.6s)

IterNodesCost
04948983
112098368
239637971
done50027968

prune1.3s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.9b

regimes517.0ms

Accuracy

89.6% (2.4b remaining)

Error of 11.6b against oracle of 9.3b and baseline of 32.0b

bsearch294.0ms

Steps
ItersRangePoint
7
1.8931325595256007e+133
5.341589198600723e+134
9.53632028454962e+133
9
9.448397398655464e-278
1.4829972419072586e-270
1.6982775252499256e-273
9
-8.712513212907472e+114
-1.0414090820182828e+108
-2.8954145393623046e+111

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
046109
154109
done54109

end0.0ms

sample3.1s

Algorithm
intervals
Results
602.0ms1055×body2560valid
511.0ms5850×body80valid
487.0ms113×body5120valid
483.0ms923×body1280valid
269.0ms2941×body80nan
228.0ms480×body640valid
44.0ms206×body320valid
15.0ms108×body160valid