Details

Time bar (total: 19.2s)

sample58.0ms

Algorithm
intervals
Results
30.0ms274×body80valid
7.0ms92×body80nan

simplify179.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
02038
13538
26637
311637
413937
515137
615337
done15337

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.2b

localize177.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
2.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×*-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--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log difference-of-squares
1×distribute-lft-out--
Counts
4 → 57
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series500.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(- (* b b) (* (* 4.0 a) c))
148.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
119.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
147.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts
69 → 69
Iterations

Useful iterations: done (2.6s)

IterNodesCost
0911129
12071001
2651935
32361930
done5000924

prune434.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 10.1b

localize145.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.9b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
5.4b
(/ (* a c) b)
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
18×add-sqr-sqrt
14×add-exp-log add-cbrt-cube
9×add-cube-cbrt times-frac associate-/r*
6×add-log-exp
5×pow1 distribute-lft-out--
4×cbrt-undiv div-exp sqrt-prod difference-of-squares
3×flip3-- flip--
2×distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l*
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 80
Calls
4 calls:
60.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
45.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
11.0ms
(/ (* a c) b)
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series554.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
276.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
36.0ms
(/ (* a c) b)
115.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
92 → 92
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01781468
14331368
216081212
done50001182

prune534.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.6b

localize154.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.4b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.9b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
34×times-frac
32×*-un-lft-identity
30×add-exp-log
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×associate-/r* add-log-exp unswap-sqr
5×distribute-lft-out--
4×sqrt-prod difference-of-squares
3×flip3-- flip-- div-inv
2×distribute-rgt-neg-in sqrt-div associate-/r/
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 → 118
Calls
4 calls:
62.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
74.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
78.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series595.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
94.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
275.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
93.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts
130 → 130
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02622573
17102440
227771940
done50021753

prune903.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.5b

localize156.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.0b
(* (/ (/ (/ a (cbrt b)) (cbrt b)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))
3.9b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ (/ (/ a (cbrt b)) (cbrt b)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite857.0ms

Algorithm
rewrite-expression-head
Rules
501×times-frac
287×add-sqr-sqrt
191×cbrt-prod
160×*-un-lft-identity
150×add-cube-cbrt
140×associate-*l*
74×add-exp-log
43×add-cbrt-cube
33×cbrt-undiv div-exp
32×unswap-sqr
31×associate-*r*
21×prod-exp cbrt-unprod
10×div-inv
7×pow1
6×associate-/r* add-log-exp
5×distribute-lft-out--
4×sqrt-prod difference-of-squares
3×flip3-- flip--
2×distribute-rgt-neg-in sqrt-div associate-/r/
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 → 302
Calls
4 calls:
59.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
709.0ms
(* (/ (/ (/ a (cbrt b)) (cbrt b)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))
50.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ (/ (/ a (cbrt b)) (cbrt b)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series601.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
70.0ms
(* (/ (/ (/ a (cbrt b)) (cbrt b)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))
313.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ (/ (/ a (cbrt b)) (cbrt b)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))) (/ c (cbrt (cbrt b))))))))
103.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
314 → 314
Iterations

Useful iterations: done (1.3s)

IterNodesCost
05487979
116497792
done50007106

prune2.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.5b

regimes431.0ms

Accuracy

91.3% (1.3b remaining)

Error of 7.9b against oracle of 6.7b and baseline of 21.4b

bsearch267.0ms

Steps
ItersRangePoint
5
1.2073698495971617e+61
2.9312978430050554e+61
2.269665110513951e+61
10
-1.437929939467773e+163
-1.7004475472942417e+152
-1.3404533579516929e+154

simplify11.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
064151
176151
done76151

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.2s8718×body80valid
290.0ms2845×body80nan