Details

Time bar (total: 19.0s)

sample63.0ms

Algorithm
intervals
Results
35.0ms283×body80valid
7.0ms106×body80nan

simplify258.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
02038
13638
26637
312237
415437
516637
616837
done16837

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.8b

localize121.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
78×prod-diff
71×add-sqr-sqrt
67×*-un-lft-identity
61×add-cube-cbrt
50×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
16×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
3×diff-log distribute-lft-out--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2
1×associate--l- neg-sub0 neg-log
Counts
4 → 165
Calls
4 calls:
51.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
28.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series545.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
151.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
112.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
138.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts
177 → 177
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02086992
14584570
212263570
done50002949

prune706.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.2b

localize180.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.8b
(/ (* 2.0 c) (fma 2.0 (/ (* a c) b) (* -2 b)))
4.8b
(/ (* a c) b)
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
25×*-un-lft-identity
23×add-cube-cbrt
18×prod-diff
16×sqrt-prod
14×add-exp-log add-cbrt-cube
6×times-frac fma-neg associate-/r* add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
2×flip3-- frac-2neg sqrt-div prod-exp clear-num flip-- cbrt-unprod div-inv associate-/l* difference-of-squares
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out--
Counts
4 → 104
Calls
4 calls:
104.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
29.0ms
(/ (* 2.0 c) (fma 2.0 (/ (* a c) b) (* -2 b)))
20.0ms
(/ (* a c) b)
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series370.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
103.0ms
(/ (* 2.0 c) (fma 2.0 (/ (* a c) b) (* -2 b)))
32.0ms
(/ (* a c) b)
109.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
116 → 116
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01992109
14651818
214941527
done50001458

prune663.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.3b

localize162.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
2.7b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.8b
(/ (* 2.0 c) (fma 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))) (* -2 b)))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
38×*-un-lft-identity
36×add-cube-cbrt
31×times-frac
30×add-exp-log
23×add-cbrt-cube
22×associate-*r*
18×prod-diff
16×sqrt-prod
11×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
7×pow1 associate-*l*
6×fma-neg add-log-exp unswap-sqr
4×expm1-log1p-u log1p-expm1-u
3×associate-/r* div-inv
2×flip3-- sqrt-div flip-- 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* distribute-lft-out--
Counts
4 → 142
Calls
4 calls:
78.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
91.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
10.0ms
(/ (* 2.0 c) (fma 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))) (* -2 b)))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
67.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
178.0ms
(/ (* 2.0 c) (fma 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))) (* -2 b)))
90.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts
154 → 154
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02813186
17342842
225792088
done50002001

prune999.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.3b

localize203.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.8b
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
3.8b
(/ (* 2.0 c) (fma 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b)))) (* -2 b)))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
78×add-exp-log
44×add-cbrt-cube
35×add-sqr-sqrt
33×prod-exp cbrt-unprod
26×*-un-lft-identity
24×cbrt-undiv add-cube-cbrt div-exp
18×prod-diff
16×sqrt-prod
11×times-frac
7×pow1 associate-*l*
6×fma-neg add-log-exp
5×associate-*r*
4×expm1-log1p-u log1p-expm1-u unswap-sqr
3×associate-/r* div-inv
2×flip3-- sqrt-div flip-- 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* distribute-lft-out--
Counts
4 → 141
Calls
4 calls:
72.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
89.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
10.0ms
(/ (* 2.0 c) (fma 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b)))) (* -2 b)))
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series681.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
326.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b)))))
113.0ms
(/ (* 2.0 c) (fma 2.0 (* (* (/ a (* (cbrt b) (cbrt b))) (/ (* (cbrt c) (cbrt c)) (* (cbrt (cbrt b)) (cbrt (cbrt b))))) (/ (cbrt c) (cbrt (cbrt b)))) (* -2 b)))
127.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts
153 → 153
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02994534
18044139
230413267
done50002630

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.3b

regimes370.0ms

Accuracy

91% (1.3b remaining)

Error of 8.3b against oracle of 7.0b and baseline of 21.5b

bsearch334.0ms

Steps
ItersRangePoint
9
1.7084993271036838e+35
8.915315724770326e+40
1.7754385347718217e+40
8
-4.810799056667626e+157
-8.81647488783933e+153
-1.367002129773412e+154

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
052146
159146
done59146

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.2s8744×body80valid
333.0ms3010×body80nan