Details

Time bar (total: 15.9s)

sample88.0ms

Algorithm
intervals
Results
22.0ms167×body160valid
16.0ms269×body80nan
14.0ms525×pre80true
6.0ms33×body320valid
3.0ms56×body80valid

simplify115.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
014365
125365
246325
386325
4119325
5128325
done128325

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
42.2b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
19×prod-diff
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×fma-neg
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv associate-/r* flip3-- div-exp flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-/l/
Counts
4 → 183
Calls
4 calls:
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(- (* b b) (* (* 4.0 a) c))
73.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
41.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series391.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
58.0ms
(- (* b b) (* (* 4.0 a) c))
133.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
90.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify2.6s

Counts
195 → 195
Iterations

Useful iterations: done (2.5s)

IterNodesCost
0321102660
181795887
2389991777
done500091727

prune1.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 5.7b

localize12.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune160.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 5.7b

localize23.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
0.3b
(/ (* a c) b)

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
27×add-cbrt-cube add-exp-log
20×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×cbrt-undiv div-exp
8×associate-/l*
6×associate-/r* div-inv
5×prod-exp cbrt-unprod
2×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
1×associate-/l/
Counts
2 → 77
Calls
2 calls:
34.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
16.0ms
(/ (* a c) b)

series71.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
31.0ms
(/ (* a c) b)

simplify2.2s

Counts
83 → 83
Iterations

Useful iterations: done (2.2s)

IterNodesCost
017124170
146822409
2299521888
done500121648

prune601.0ms

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 5.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) 2.0) a)
0.3b
(/ c (sqrt b))
0.3b
(/ a (sqrt b))
0.4b
(* (/ a (sqrt b)) (/ c (sqrt b)))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
117×times-frac
106×add-sqr-sqrt
76×*-un-lft-identity add-cube-cbrt
53×add-cbrt-cube add-exp-log
48×sqrt-prod
23×cbrt-undiv div-exp
22×associate-*r* associate-*l*
15×associate-/r*
13×prod-exp cbrt-unprod associate-/l*
9×div-inv unswap-sqr
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l/
Counts
4 → 215
Calls
4 calls:
64.0ms
(/ (/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) 2.0) a)
9.0ms
(/ c (sqrt b))
5.0ms
(/ a (sqrt b))
40.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

series268.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(/ (/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) 2.0) a)
61.0ms
(/ c (sqrt b))
82.0ms
(/ a (sqrt b))
65.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

simplify1.3s

Counts
227 → 227
Iterations

Useful iterations: done (1.3s)

IterNodesCost
036573764
1107266185
done500165420

prune1.4s

Pruning

37 alts after pruning (36 fresh and 1 done)

Merged error: 5.6b

regimes1.1s

Accuracy

0% (6.8b remaining)

Error of 12.0b against oracle of 5.1b and baseline of 12.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0583
1683
done683

end0.0ms

sample4.0s

Algorithm
intervals
Results
989.0ms16183×pre80true
913.0ms4824×body160valid
719.0ms8183×body80nan
496.0ms1803×body80valid
332.0ms1373×body320valid