Details

Time bar (total: 17.7s)

sample56.0ms

Algorithm
intervals
Results
12.0ms40×body2560valid
9.0ms181×body80valid
6.0ms26×body1280valid
4.0ms92×body80nan
3.0ms14×body640valid
2.0ms7×body5120valid
1.0ms5×body320valid
0.0ms3×body160valid

simplify222.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01417
12917
26417
312017
414517
515217
615617
done15617

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b
(- (* b b) (* 4.0 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 157
Calls
4 calls:
98.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
18.0ms
(- (* b b) (* 4.0 (* a c)))
52.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series416.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
63.0ms
(- (* b b) (* 4.0 (* a c)))
114.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
114.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts
169 → 169
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02436690
15874705
217533760
done50003113

prune521.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.3b

localize38.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
2.8b
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (* 2.0 a))
8.4b
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
23.4b
(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite137.0ms

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
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 171
Calls
4 calls:
11.0ms
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
75.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (* 2.0 a))
40.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
2.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

series895.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
275.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (* 2.0 a))
350.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
135.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify1.4s

Counts
183 → 183
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02755401
16554711
222914237
done50014169

prune848.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize37.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
2.9b
(* (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (/ 1 (* 2.0 a)))
8.4b
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
23.4b
(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite209.0ms

Algorithm
rewrite-expression-head
Rules
80×add-sqr-sqrt
58×*-un-lft-identity
51×add-exp-log
42×add-cube-cbrt
40×times-frac
27×add-cbrt-cube
24×associate-*l*
23×sqrt-prod
20×prod-exp
18×prod-diff
16×div-exp difference-of-squares
8×cbrt-undiv cbrt-unprod distribute-lft-out--
7×pow1 associate-*r*
6×fma-neg associate-/r* add-log-exp
4×expm1-log1p-u rec-exp 1-exp associate-/r/ log1p-expm1-u
3×flip3-- flip-- div-inv associate-/l*
2×associate-/l/ unswap-sqr
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 169
Calls
4 calls:
22.0ms
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
100.0ms
(* (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (/ 1 (* 2.0 a)))
76.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
3.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

series793.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
249.0ms
(* (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (/ 1 (* 2.0 a)))
305.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
105.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify1.7s

Counts
181 → 181
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02805119
17144377
225023764
done50003696

prune685.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.3b

localize17.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
2.7b
(/ (* 2.0 a) (/ (* (* a c) 4.0) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)))
8.4b
(/ (* (* a c) 4.0) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
23.4b
(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
45×add-exp-log add-cbrt-cube
35×*-un-lft-identity
30×times-frac
25×add-cube-cbrt
20×sqrt-prod
18×prod-diff associate-/r*
17×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
10×difference-of-squares
7×associate-/r/
6×fma-neg add-log-exp
5×pow1 distribute-lft-out--
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u div-inv
2×frac-2neg clear-num associate-/l*
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 143
Calls
4 calls:
15.0ms
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
50.0ms
(/ (* 2.0 a) (/ (* (* a c) 4.0) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)))
61.0ms
(/ (* (* a c) 4.0) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
2.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

series812.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
151.0ms
(/ (* 2.0 a) (/ (* (* a c) 4.0) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)))
354.0ms
(/ (* (* a c) 4.0) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
141.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify1.8s

Counts
155 → 155
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02484126
16433761
227573043
done50002976

prune553.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.3b

regimes388.0ms

Accuracy

87.7% (3.4b remaining)

Error of 8.7b against oracle of 5.3b and baseline of 32.7b

bsearch780.0ms

Steps
ItersRangePoint
10
4.61796087672408e+142
1.3206820209921783e+153
1.974261024048121e+145
10
-7.804748171248596e-210
-1.2742380330863746e-228
-3.1153949179978696e-213
10
-7.296408209838224e+27
-1014094955833491.1
-1.1509557557359616e+21

simplify13.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
04169
15267
26367
done6367

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.1s956×body1280valid
664.0ms1095×body2560valid
528.0ms5729×body80valid
289.0ms2914×body80nan
131.0ms457×body640valid
88.0ms241×body320valid
74.0ms119×body5120valid
16.0ms115×body160valid