Details

Time bar (total: 18.2s)

sample90.0ms

Algorithm
intervals
Results
50.0ms266×body80valid
9.0ms79×body80nan

simplify159.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
02038
13538
26637
311637
413937
515137
615337
done15337

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize156.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 distribute-rgt-neg-in neg-log
Counts
4 → 60
Calls
4 calls:
14.0ms
(- (* b b) (* (* 4.0 a) c))
26.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series434.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(- (* b b) (* (* 4.0 a) c))
124.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
116.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.9s

Counts
72 → 72
Iterations

Useful iterations: done (2.9s)

IterNodesCost
0971211
12261091
27561009
32904998
done5001996

prune390.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.1b

localize146.0ms

Local error

Found 4 expressions with local error:

9.7b
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div add-log-exp
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg diff-log difference-of-squares
Counts
4 → 58
Calls
4 calls:
64.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
17.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series472.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(- (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))) b)
100.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
110.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
132.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts
70 → 70
Iterations

Useful iterations: done (2.6s)

IterNodesCost
0841388
1204992
2612942
32017936
done5001930

prune651.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.1b

localize125.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
3.4b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
6.0b
(/ (* a c) b)
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
14×add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt times-frac associate-/r*
6×add-log-exp
5×pow1
4×cbrt-undiv div-exp distribute-lft-out--
3×flip3-- sqrt-prod flip--
2×distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l* difference-of-squares
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 77
Calls
4 calls:
17.0ms
(- (* b b) (* (* 4.0 a) c))
57.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
10.0ms
(/ (* a c) b)
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series488.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(- (* b b) (* (* 4.0 a) c))
294.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
24.0ms
(/ (* a c) b)
108.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
89 → 89
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01611349
13921285
215271111
done50001083

prune597.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.9b

localize149.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
0.7b
(* (/ a (sqrt b)) (/ c (sqrt b)))
1.0b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))))))
20.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
68×add-sqr-sqrt
54×times-frac
41×*-un-lft-identity
33×add-cube-cbrt
27×sqrt-prod
22×associate-*r* associate-*l*
21×add-exp-log add-cbrt-cube
9×unswap-sqr
7×pow1
6×cbrt-undiv div-exp associate-/r* add-log-exp
5×prod-exp cbrt-unprod
4×distribute-lft-out--
3×flip3-- flip-- div-inv
2×distribute-rgt-neg-in sqrt-div associate-/r/ difference-of-squares
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 129
Calls
4 calls:
13.0ms
(- (* b b) (* (* 4.0 a) c))
50.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))
73.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))))))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series582.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (* b b) (* (* 4.0 a) c))
52.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))
354.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))))))
105.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts
141 → 141
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02662383
17252248
226831818
done50011814

prune919.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.9b

regimes323.0ms

Accuracy

93.5% (0.9b remaining)

Error of 7.5b against oracle of 6.6b and baseline of 21.1b

bsearch482.0ms

Steps
ItersRangePoint
4
9.936283634246925e+77
1.8488019868481542e+78
1.2875942964765074e+78
10
-3.579862835853504e-259
-1.0472779812871276e-269
-4.452231346955638e-267
9
-4.4874797001979404e+160
-1.588602326591779e+153
-1.3506760573432116e+154

simplify18.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
062204
172203
280203
388203
done88203

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.3s8712×body80valid
427.0ms2994×body80nan