Details

Time bar (total: 20.9s)

sample87.0ms

Algorithm
intervals
Results
22.0ms291×body80nan
15.0ms142×body160valid
14.0ms547×pre80true
6.0ms114×body80valid

simplify123.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
01217
12117
24116
37616
49616
510416
done10416

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* 3.0 a) c)
0.3b
(- (* b b) (* (* 3.0 a) c))
0.4b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
28.6b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
14×add-exp-log add-cbrt-cube
10×add-log-exp
9×pow1
7×add-sqr-sqrt add-cube-cbrt
6×distribute-lft-out
5×times-frac associate-/l*
4×prod-exp cbrt-unprod
3×distribute-rgt-neg-in associate-*r* pow-prod-down
2×cbrt-undiv neg-sub0 associate-+l- flip3-+ div-exp sum-log flip-+ associate-/l/
1×+-commutative sub-neg flip3-- frac-2neg diff-log div-sub associate-*l* neg-log clear-num associate-/r* *-commutative flip-- div-inv
Counts
4 → 73
Calls
4 calls:
33.0ms
(* (* 3.0 a) c)
16.0ms
(- (* b b) (* (* 3.0 a) c))
97.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
54.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series395.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (* 3.0 a) c)
75.0ms
(- (* b b) (* (* 3.0 a) c))
173.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
126.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify1.9s

Counts
85 → 85
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01541437
14381361
225661143
done50001133

prune273.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* 3.0 a) c)
0.3b
(- (* b b) (* (* 3.0 a) c))
0.4b
(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
0.4b
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

rewrite327.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
79×add-sqr-sqrt *-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
23×add-exp-log add-cbrt-cube
20×distribute-lft-out-- difference-of-squares
10×distribute-rgt-neg-in sqrt-prod
9×pow1
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×prod-exp cbrt-unprod
4×flip3-- flip-- div-inv
3×associate-*r* pow-prod-down associate-/l/
2×frac-2neg clear-num
1×sub-neg flip3-+ diff-log associate-*l* *-commutative flip-+
Counts
4 → 151
Calls
4 calls:
28.0ms
(* (* 3.0 a) c)
17.0ms
(- (* b b) (* (* 3.0 a) c))
148.0ms
(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
126.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

series610.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (* 3.0 a) c)
77.0ms
(- (* b b) (* (* 3.0 a) c))
243.0ms
(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
265.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

simplify3.4s

Counts
163 → 163
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
02434784
16684264
246633934
done50013934

prune568.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* 3.0 a) c)
0.3b
(- (* b b) (* (* 3.0 a) c))
0.3b
(/ (+ 0 (* (* 3.0 a) c)) (* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
0.4b
(* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

rewrite292.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log add-cbrt-cube
14×pow1
12×add-sqr-sqrt *-un-lft-identity
10×associate-*r*
9×prod-exp cbrt-unprod
8×add-cube-cbrt
6×pow-prod-down add-log-exp
4×associate-*r/
3×cbrt-undiv sub-neg flip3-- times-frac div-exp flip-- associate-/l*
2×distribute-rgt-in distribute-lft-in associate-*l* associate-/r/ *-commutative associate-/l/ distribute-lft-out-- difference-of-squares
1×distribute-rgt-neg-in frac-2neg flip3-+ diff-log clear-num associate-/r* sqrt-prod flip-+ div-inv
Counts
4 → 85
Calls
4 calls:
36.0ms
(* (* 3.0 a) c)
16.0ms
(- (* b b) (* (* 3.0 a) c))
88.0ms
(/ (+ 0 (* (* 3.0 a) c)) (* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
148.0ms
(* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

series576.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (* 3.0 a) c)
81.0ms
(- (* b b) (* (* 3.0 a) c))
287.0ms
(/ (+ 0 (* (* 3.0 a) c)) (* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
186.0ms
(* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

simplify3.2s

Counts
97 → 97
Iterations

Useful iterations: 2 (786.0ms)

IterNodesCost
01681998
15261820
244591510
done50001510

prune363.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (* b b) (* (* 3.0 a) c))
0.3b
(* (* 3.0 a) (- b))
0.3b
(/ (+ 0 (* (* 3.0 a) c)) (+ (* (* 3.0 a) (- b)) (* (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c)))))))
0.4b
(* (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c)))))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
26×associate-*r*
21×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×add-exp-log add-cbrt-cube
14×pow1
12×times-frac
9×distribute-lft-neg-in distribute-rgt-neg-in
6×pow-prod-down prod-exp sqrt-prod cbrt-unprod add-log-exp
4×associate-/r* distribute-lft-out
3×associate-/l*
2×neg-mul-1 flip3-- flip3-+ sqrt-div associate-*r/ associate-*l* associate-/r/ *-commutative distribute-rgt-neg-out flip-- flip-+ associate-/l/ distribute-neg-frac
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num div-inv
Counts
4 → 107
Calls
4 calls:
8.0ms
(- (* b b) (* (* 3.0 a) c))
29.0ms
(* (* 3.0 a) (- b))
73.0ms
(/ (+ 0 (* (* 3.0 a) c)) (+ (* (* 3.0 a) (- b)) (* (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c)))))))
73.0ms
(* (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c)))))

series677.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (* b b) (* (* 3.0 a) c))
26.0ms
(* (* 3.0 a) (- b))
441.0ms
(/ (+ 0 (* (* 3.0 a) c)) (+ (* (* 3.0 a) (- b)) (* (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c)))))))
135.0ms
(* (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c)))))

simplify3.1s

Counts
119 → 119
Iterations

Useful iterations: done (3.1s)

IterNodesCost
02182702
16382251
240792033
done50012031

prune439.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes198.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 2 (3.0ms)

IterNodesCost
01730
12728
23927
34727
done4727

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.2s8685×body80nan
832.0ms4470×body160valid
730.0ms16685×pre80true
315.0ms3530×body80valid