Details

Time bar (total: 21.1s)

sample71.0ms

Algorithm
intervals
Results
31.0ms275×body80valid
9.0ms90×body80nan

simplify249.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
02038
13938
27937
314337
417937
518937
619337
done19337

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.0b

localize163.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (* b b) (* (* 4.0 a) c))
22.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 66
Calls
4 calls:
16.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series428.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(- (* b b) (* (* 4.0 a) c))
129.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
133.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify991.0ms

Counts
78 → 78
Iterations

Useful iterations: 2 (133.0ms)

IterNodesCost
0711146
11851058
2843952
done5000952

prune499.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.1b

localize115.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
3.1b
(/ (* 2.0 c) (- (- (* 2.0 (/ (* a c) b)) b) b))
5.5b
(/ (* a c) b)
22.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-sqr-sqrt add-cbrt-cube
13×*-un-lft-identity
9×add-cube-cbrt
8×times-frac associate-/r*
6×add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×flip3-- sqrt-prod flip--
2×frac-2neg sqrt-div prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l* distribute-lft-out-- difference-of-squares
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 85
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
158.0ms
(/ (* 2.0 c) (- (- (* 2.0 (/ (* a c) b)) b) b))
16.0ms
(/ (* a c) b)
37.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series330.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(- (* b b) (* (* 4.0 a) c))
106.0ms
(/ (* 2.0 c) (- (- (* 2.0 (/ (* a c) b)) b) b))
44.0ms
(/ (* a c) b)
118.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
97 → 97
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01721401
14491329
224821176
done50001170

prune609.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.4b

localize162.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
2.8b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.1b
(/ (* 2.0 c) (- (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b) b))
22.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
33×times-frac
30×add-exp-log
26×*-un-lft-identity
23×add-cbrt-cube
22×add-cube-cbrt associate-*r*
11×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
7×pow1 associate-*l*
6×add-log-exp unswap-sqr
5×associate-/r*
4×expm1-log1p-u log1p-expm1-u
3×flip3-- sqrt-prod flip-- div-inv
2×sqrt-div associate-/r/ distribute-lft-out-- difference-of-squares
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 123
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
57.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
960.0ms
(/ (* 2.0 c) (- (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b) b))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series441.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(- (* b b) (* (* 4.0 a) c))
86.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
159.0ms
(/ (* 2.0 c) (- (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b) b))
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts
135 → 135
Iterations

Useful iterations: 2 (861.0ms)

IterNodesCost
02552527
17502434
243441921
done50001921

prune871.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.9b

localize151.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
1.7b
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
3.1b
(/ (* 2.0 c) (- (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b))))) b) b))
22.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite6.3s

Algorithm
rewrite-expression-head
Rules
78×add-exp-log
44×add-cbrt-cube
33×prod-exp cbrt-unprod
24×cbrt-undiv div-exp
21×add-sqr-sqrt
14×*-un-lft-identity
13×times-frac
10×add-cube-cbrt
7×pow1 associate-*l*
6×add-log-exp
5×associate-*r* associate-/r*
4×expm1-log1p-u log1p-expm1-u unswap-sqr
3×flip3-- sqrt-prod flip-- div-inv
2×sqrt-div associate-/r/ distribute-lft-out-- difference-of-squares
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 122
Calls
4 calls:
11.0ms
(- (* b b) (* (* 4.0 a) c))
93.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
6.2s
(/ (* 2.0 c) (- (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b))))) b) b))
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series525.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (* b b) (* (* 4.0 a) c))
265.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
81.0ms
(/ (* 2.0 c) (- (- (* 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b))))) b) b))
105.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify473.0ms

Counts
134 → 134
Iterations

Useful iterations: done (467.0ms)

IterNodesCost
02733987
18463857
done50003095

prune890.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.9b

regimes371.0ms

Accuracy

85% (2.2b remaining)

Error of 9.0b against oracle of 6.8b and baseline of 21.5b

bsearch350.0ms

Steps
ItersRangePoint
11
8.182113676652236e-12
2116652649.122401
2098867031.9345784
5
-2.851981511485346e+134
-8.519391106473126e+133
-1.3965834663888141e+134

simplify12.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
058172
169172
done69172

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.2s8755×body80valid
315.0ms2934×body80nan