Details

Time bar (total: 16.9s)

sample52.0ms

Algorithm
intervals
Results
10.0ms36×body2560valid
9.0ms188×body80valid
5.0ms24×body1280valid
5.0ms108×body80nan
3.0ms17×body640valid
2.0ms5×body5120valid
1.0ms6×body320valid
0.0ms5×body160valid

simplify115.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
01217
12217
24216
38316
411216
512016
done12016

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize23.0ms

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)))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-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 neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
97.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
20.0ms
(- (* b b) (* (* 3.0 a) c))
37.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
19.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series407.0ms

Counts
4 → 12
Calls
4 calls:
170.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
62.0ms
(- (* b b) (* (* 3.0 a) c))
89.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
86.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.2s

Counts
102 → 102
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01671697
14451590
220861363
done50001354

prune494.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.1b

localize28.0ms

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)))

rewrite284.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
124×*-un-lft-identity
90×times-frac
80×add-cube-cbrt
60×prod-diff
44×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
10×fma-neg
8×associate-/r* add-log-exp
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u 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 → 232
Calls
4 calls:
31.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
138.0ms
(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
82.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
20.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series682.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
215.0ms
(/ (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
259.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
86.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.1s

Counts
244 → 244
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
033410067
18487629
247426518
done50006518

prune770.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.0b

localize35.0ms

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)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
10×fma-neg prod-diff
9×times-frac
8×add-log-exp
6×add-exp-log cbrt-prod distribute-lft-neg-in distribute-rgt-neg-in add-cbrt-cube
4×pow1 expm1-log1p-u cbrt-div flip3-- flip-- log1p-expm1-u
3×associate-/r* associate-/l*
2×neg-mul-1 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 → 99
Calls
4 calls:
22.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))
53.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))))
9.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))
9.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))

series1.1s

Counts
4 → 12
Calls
4 calls:
126.0ms
(- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))
727.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))))
151.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))
137.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))

simplify2.2s

Counts
111 → 111
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02674347
17194144
241343731
done50003729

prune662.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.0b

localize25.0ms

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)))

rewrite328.0ms

Algorithm
rewrite-expression-head
Rules
109×add-sqr-sqrt
103×*-un-lft-identity
71×add-cube-cbrt
60×prod-diff
51×add-exp-log
46×times-frac
41×sqrt-prod
29×distribute-rgt-neg-in
27×associate-*l* add-cbrt-cube
21×distribute-lft-neg-in
20×prod-exp
16×div-exp distribute-lft-out-- difference-of-squares
10×fma-neg
8×cbrt-undiv cbrt-unprod add-log-exp
7×pow1 neg-mul-1 associate-*r* associate-/r*
4×expm1-log1p-u rec-exp flip3-- 1-exp associate-/r/ flip-- log1p-expm1-u
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 → 227
Calls
4 calls:
48.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
165.0ms
(* (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (/ 1 (* 3.0 a)))
84.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
17.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series632.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
189.0ms
(* (/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (/ 1 (* 3.0 a)))
242.0ms
(/ (+ 0 (* (* 3.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
89.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify540.0ms

Counts
239 → 239
Iterations

Useful iterations: done (522.0ms)

IterNodesCost
03399661
19477185
done50016075

prune658.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.0b

regimes372.0ms

Accuracy

86.7% (3.5b remaining)

Error of 8.8b against oracle of 5.3b and baseline of 31.9b

bsearch209.0ms

Steps
ItersRangePoint
8
2.2795539252788044e+111
1.0533334563517102e+114
4.2658835753170375e+111
9
2.2663179710940456e-250
3.3396535119009455e-244
3.2462184449910304e-248
10
-2.8734245235493903e+48
-2.602501271628617e+37
-2.8472042802820317e+48

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03771
14369
done4369

end0.0ms

sample2.7s

Algorithm
intervals
Results
560.0ms2902×body80nan
527.0ms5853×body80valid
399.0ms902×body1280valid
398.0ms1074×body2560valid
131.0ms452×body640valid
80.0ms224×body320valid
67.0ms111×body5120valid
12.0ms111×body160valid