Details

Time bar (total: 18.7s)

sample91.0ms

Algorithm
intervals
Results
16.0ms184×body80valid
16.0ms32×body2560valid
16.0ms31×body1280valid
7.0ms84×body80nan
6.0ms17×body640valid
2.0ms3×body5120valid
1.0ms6×body320valid
0.0ms1×body160valid

simplify113.0ms

Counts
1 → 1
Iterations
IterNodes
done94
794
693
591
483
368
239
121
012

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
0.2b
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
1.4b
(- (* b b) (* (* 3.0 a) c))
24.6b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×add-cube-cbrt
6×times-frac sqrt-prod associate-/l* difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
1×rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp cbrt-unprod div-inv
Counts
4 → 72
Calls
4 calls:
44.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
91.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
7.0ms
(- (* b b) (* (* 3.0 a) c))
8.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series431.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
164.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
77.0ms
(- (* b b) (* (* 3.0 a) c))
83.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.6s

Counts
84 → 84
Iterations
IterNodes
done5002
21253
1393
0154

prune548.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.2b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
1.4b
(- (* b b) (* (* 3.0 a) c))
24.6b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×add-cbrt-cube add-exp-log
8×*-un-lft-identity add-log-exp
6×add-cube-cbrt
4×sqrt-prod
3×flip3-- associate-*r* pow-prod-down prod-exp cbrt-unprod flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* *-commutative distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
13.0ms
(* (* 3.0 a) c)
64.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
11.0ms
(- (* b b) (* (* 3.0 a) c))
13.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series327.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (* 3.0 a) c)
127.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
70.0ms
(- (* b b) (* (* 3.0 a) c))
99.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.0s

Counts
72 → 72
Iterations
IterNodes
done5000
33541
2911
1293
0120

prune392.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
0.3b
(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a))
1.4b
(- (* b b) (* (* 3.0 a) c))
24.6b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt
34×times-frac
32×*-un-lft-identity
26×add-exp-log
22×associate-*r* add-cube-cbrt
16×add-cbrt-cube
13×associate-*l*
8×div-exp prod-exp add-log-exp difference-of-squares
7×pow1 sqrt-prod
6×unswap-sqr
4×cbrt-undiv cbrt-unprod distribute-lft-out--
3×flip3-- flip--
2×rec-exp sub-neg sqrt-div diff-log 1-exp div-inv
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 107
Calls
4 calls:
67.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
95.0ms
(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a))
6.0ms
(- (* b b) (* (* 3.0 a) c))
11.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series449.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
172.0ms
(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) a))
72.0ms
(- (* b b) (* (* 3.0 a) c))
94.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.1s

Counts
119 → 119
Iterations
IterNodes
done5001
21998
1604
0220

prune679.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
0.2b
(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (cbrt 3.0))
1.4b
(- (* b b) (* 3.0 (* a c)))
24.6b
(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
42×*-un-lft-identity
36×times-frac
26×add-cube-cbrt
21×cbrt-prod
16×difference-of-squares
11×sqrt-prod
8×distribute-lft-out-- add-log-exp
6×associate-/r* add-exp-log associate-/l*
5×pow1 add-cbrt-cube
4×flip3-- flip--
2×sub-neg sqrt-div diff-log associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-sub div-exp div-inv
Counts
4 → 105
Calls
4 calls:
42.0ms
(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
94.0ms
(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (cbrt 3.0))
7.0ms
(- (* b b) (* 3.0 (* a c)))
7.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

series550.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
243.0ms
(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (cbrt 3.0))
82.0ms
(- (* b b) (* 3.0 (* a c)))
96.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

simplify3.0s

Counts
117 → 117
Iterations
IterNodes
done5004
34899
21211
1429
0180

prune721.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.8b

regimes714.0ms

Accuracy

83.7% (4.6b remaining)

Error of 10.7b against oracle of 6.1b and baseline of 34.5b

bsearch191.0ms

Steps
ItersRangePoint
8
2.8373581988670566e-35
2.2677514638291856e-31
3.264293321664548e-35
9
-2.18251428070208e+135
-2.7037994126971227e+126
-2.2866170111505574e+129

simplify10.0ms

Iterations
IterNodes
done32
132
027

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.1s5834×body80valid
573.0ms1040×body2560valid
418.0ms910×body1280valid
223.0ms2881×body80nan
125.0ms453×body640valid
104.0ms101×body5120valid
45.0ms232×body320valid
16.0ms116×body160valid