Details

Time bar (total: 19.3s)

sample81.0ms

Algorithm
intervals
Results
17.0ms37×body2560valid
14.0ms185×body80valid
12.0ms33×body1280valid
6.0ms81×body80nan
6.0ms20×body640valid
1.0ms5×body320valid
0.0ms2×body160valid

simplify178.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01417
12917
26417
312017
414517
515217
615617
done15617

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* a c))
0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite254.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
61×*-un-lft-identity
60×prod-diff
49×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
14×add-exp-log add-cbrt-cube
10×pow1 fma-neg
8×add-log-exp
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u
3×flip3-- associate-*l* pow-prod-down flip--
2×cbrt-undiv sqrt-div diff-log div-exp associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub associate-*r* neg-log clear-num associate-/r* *-commutative div-inv
Counts
4 → 161
Calls
4 calls:
20.0ms
(* 4.0 (* a c))
137.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
55.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
35.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series395.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* 4.0 (* a c))
155.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
120.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
85.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.8s

Counts
173 → 173
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02556590
16234603
218343668
done50013021

prune633.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.1b
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
9.8b
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite433.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
78×times-frac
72×*-un-lft-identity
50×add-cube-cbrt
27×associate-/l*
26×sqrt-prod
22×difference-of-squares
18×add-exp-log prod-diff add-cbrt-cube
11×distribute-lft-out--
7×cbrt-undiv div-exp associate-/r*
6×fma-neg associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 173
Calls
4 calls:
89.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
203.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
116.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
18.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series793.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
251.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
284.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
113.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.8s

Counts
185 → 185
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02885475
17064743
226154289
done50004221

prune803.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.3b

localize42.0ms

Local error

Found 4 expressions with local error:

9.9b
(/ (+ 0 (* (* a c) 4.0)) (+ (fma (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c))))) (- b)) (+ (- b) b)))
17.1b
(fma (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c))))) (- b))
25.1b
(cbrt (- (* b b) (* 4.0 (* a c))))
25.1b
(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
49×*-un-lft-identity
20×distribute-lft-out
18×times-frac
17×add-sqr-sqrt add-cube-cbrt
6×add-exp-log cbrt-prod associate-/r* add-cbrt-cube
4×pow1 expm1-log1p-u cbrt-div distribute-rgt-neg-in log1p-expm1-u add-log-exp
3×associate-/l*
2×flip3-- flip3-+ pow1/3 associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv
Counts
4 → 85
Calls
4 calls:
152.0ms
(/ (+ 0 (* (* a c) 4.0)) (+ (fma (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c))))) (- b)) (+ (- b) b)))
0.0ms
(fma (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c))))) (- b))
6.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))
6.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))

series1.4s

Counts
4 → 12
Calls
4 calls:
922.0ms
(/ (+ 0 (* (* a c) 4.0)) (+ (fma (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c))))) (- b)) (+ (- b) b)))
138.0ms
(fma (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c))))) (- b))
195.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))
171.0ms
(cbrt (- (* b b) (* 4.0 (* a c))))

simplify2.5s

Counts
97 → 97
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02373687
16193396
222593128
done50002989

prune711.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.3b

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt prod-diff
59×*-un-lft-identity
47×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
10×fma-neg
8×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/l* add-log-exp
6×distribute-lft-out-- difference-of-squares
4×pow1
3×expm1-log1p-u flip3-- flip-- log1p-expm1-u
2×cbrt-undiv sqrt-div diff-log div-exp associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
3 → 141
Calls
3 calls:
95.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
37.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series335.0ms

Counts
3 → 9
Calls
3 calls:
126.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
116.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
93.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts
150 → 150
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02286424
15604450
216483535
done50002888

prune362.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.3b

regimes453.0ms

Accuracy

85.1% (4.0b remaining)

Error of 9.6b against oracle of 5.6b and baseline of 32.3b

bsearch405.0ms

Steps
ItersRangePoint
8
1.538525478595148e+72
6.402915924844171e+74
2.9725940607578363e+74
9
-7.826064039423189e-132
-1.1138670077130767e-140
-6.373481960958038e-132
6
-3.4377365604695865e-95
-7.852755480555329e-96
-9.940959811381676e-96
9
-5.194408462768213e+38
-1.5993742599293638e+29
-3.438870219673744e+36

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
04794
15692
done5692

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.2s5850×body80valid
767.0ms1054×body2560valid
497.0ms110×body5120valid
362.0ms924×body1280valid
226.0ms2933×body80nan
153.0ms502×body640valid
103.0ms207×body320valid
16.0ms108×body160valid