Details

Time bar (total: 25.0s)

sample68.0ms

Algorithm
intervals
Results
32.0ms275×body80valid
7.0ms90×body80nan

simplify195.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
02038
13838
27837
313637
416337
517537
617937
done17937

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.0b

localize131.0ms

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)))

rewrite58.0ms

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 flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 54
Calls
4 calls:
23.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(- (* b b) (* (* 4.0 a) c))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series354.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (* b b) (* (* 4.0 a) c))
57.0ms
(- (* b b) (* (* 4.0 a) c))
113.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.9s

Counts
66 → 66
Iterations

Useful iterations: 2 (109.0ms)

IterNodesCost
0621010
1165930
2739834
34972834
done5001834

prune440.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.1b

localize151.0ms

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)))

rewrite234.0ms

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 div-exp
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 diff-log
Counts
4 → 75
Calls
4 calls:
11.0ms
(- (* b b) (* (* 4.0 a) c))
177.0ms
(/ (* 2.0 c) (- (- (* 2.0 (/ (* a c) b)) b) b))
26.0ms
(/ (* a c) b)
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series275.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(- (* b b) (* (* 4.0 a) c))
96.0ms
(/ (* 2.0 c) (- (- (* 2.0 (/ (* a c) b)) b) b))
29.0ms
(/ (* a c) b)
87.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
87 → 87
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01591289
14211219
223051075
done50011069

prune500.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.4b

localize170.0ms

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)))

rewrite970.0ms

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*
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 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 113
Calls
4 calls:
9.0ms
(- (* b b) (* (* 4.0 a) c))
57.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
881.0ms
(/ (* 2.0 c) (- (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b) b))
18.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series362.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (* b b) (* (* 4.0 a) c))
76.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
126.0ms
(/ (* 2.0 c) (- (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b) b))
84.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts
125 → 125
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02422387
17202298
241291806
done50001606

prune687.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.9b

localize166.0ms

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)))

rewrite6.4s

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×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 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 112
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
69.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
6.3s
(/ (* 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))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series494.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(- (* b b) (* (* 4.0 a) c))
260.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
89.0ms
(/ (* 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))
91.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts
124 → 124
Iterations

Useful iterations: 2 (681.0ms)

IterNodesCost
02603797
18213671
249012912
done50012912

prune778.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.9b

regimes374.0ms

Accuracy

85.4% (2.1b remaining)

Error of 8.9b against oracle of 6.8b and baseline of 21.4b

bsearch264.0ms

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

simplify19.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
058182
169182
done69182

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.3s8755×body80valid
259.0ms2934×body80nan