Details

Time bar (total: 18.3s)

sample89.0ms

Algorithm
intervals
Results
16.0ms36×body2560valid
16.0ms188×body80valid
10.0ms24×body1280valid
9.0ms108×body80nan
5.0ms17×body640valid
3.0ms5×body5120valid
1.0ms6×body320valid
1.0ms5×body160valid

simplify116.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
01217
12117
24116
37616
49616
510416
done10416

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b
(- (* b b) (* (* 3.0 a) c))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
103.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms
(- (* b b) (* (* 3.0 a) c))
36.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series452.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
97.0ms
(- (* b b) (* (* 3.0 a) c))
111.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
92.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.1s

Counts
82 → 82
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01541565
14141463
218791247
done50011241

prune320.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.1b

localize36.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.0b
(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
8.0b
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite319.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 154
Calls
4 calls:
35.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
164.0ms
(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
85.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
19.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series753.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
219.0ms
(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
291.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
139.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.3s

Counts
166 → 166
Iterations

Useful iterations: 2 (686.0ms)

IterNodesCost
02535113
16574543
237264211
done50004211

prune635.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.0b

localize48.0ms

Local error

Found 4 expressions with local error:

6.7b
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))
8.6b
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))))
23.5b
(cbrt (- (* b b) (* (* 3.0 a) c)))
23.5b
(cbrt (- (* b b) (* (* 3.0 a) c)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
8×add-log-exp
6×add-exp-log cbrt-prod add-cbrt-cube
4×pow1 cbrt-div flip3-- flip--
3×associate-/r* associate-/l*
2×pow1/3 diff-log associate-/r/ associate-/l/
1×cbrt-undiv associate--l- neg-sub0 sub-neg frac-2neg flip3-+ div-exp neg-log clear-num flip-+ div-inv
Counts
4 → 71
Calls
4 calls:
17.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))
45.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))))
10.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))
10.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))

series1.7s

Counts
4 → 12
Calls
4 calls:
128.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))
818.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))))
134.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))
579.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))

simplify2.1s

Counts
83 → 83
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02383166
16452980
234622694
done50002684

prune654.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.0b

localize30.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.0b
(* (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (/ 1 (* 3.0 a)))
8.0b
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite299.0ms

Algorithm
rewrite-expression-head
Rules
68×add-sqr-sqrt
62×*-un-lft-identity
51×add-exp-log
46×times-frac
30×add-cube-cbrt
27×associate-*l* add-cbrt-cube
20×prod-exp
16×div-exp distribute-lft-out-- difference-of-squares
11×sqrt-prod
8×cbrt-undiv distribute-rgt-neg-in cbrt-unprod add-log-exp
7×pow1 associate-*r* associate-/r*
4×rec-exp flip3-- 1-exp associate-/r/ flip--
3×div-inv associate-/l*
2×sqrt-div diff-log associate-/l/ unswap-sqr
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 149
Calls
4 calls:
32.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
173.0ms
(* (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (/ 1 (* 3.0 a)))
71.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
17.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series674.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
216.0ms
(* (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (/ 1 (* 3.0 a)))
259.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
93.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.7s

Counts
161 → 161
Iterations

Useful iterations: 2 (860.0ms)

IterNodesCost
02584703
17564099
246763645
done50013645

prune400.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.0b

regimes326.0ms

Accuracy

86.3% (3.6b remaining)

Error of 8.9b against oracle of 5.3b and baseline of 31.9b

bsearch152.0ms

Steps
ItersRangePoint
8
2.2795539252788044e+111
1.0533334563517102e+114
1.6705206762421073e+112
5
-1.7140185252229956e-250
-6.426569281983545e-251
-6.5022252901143814e-251
4
-2.602501271628617e+37
-1.4953728705056508e+37
-2.5481725115075804e+37

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03769
14467
24567
done4567

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.0s1074×body2560valid
494.0ms5853×body80valid
352.0ms902×body1280valid
281.0ms2902×body80nan
156.0ms452×body640valid
48.0ms111×body5120valid
46.0ms224×body320valid
14.0ms111×body160valid