Details

Time bar (total: 16.6s)

sample120.0ms

Algorithm
intervals
Results
20.0ms41×body2560valid
15.0ms186×body80valid
11.0ms28×body1280valid
8.0ms108×body80nan
5.0ms17×body640valid
2.0ms5×body5120valid
1.0ms6×body320valid
1.0ms4×body160valid

simplify234.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01417
12917
26417
312017
414517
515217
615617
done15617

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite244.0ms

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:
123.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
20.0ms
(- (* b b) (* 4.0 (* a c)))
61.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series483.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
58.0ms
(- (* b b) (* 4.0 (* a c)))
129.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
141.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts
169 → 169
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02436690
15874705
217533760
done50003113

prune666.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize39.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
5.1b
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (* 2.0 a))
10.3b
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
24.0b
(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite169.0ms

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:
13.0ms
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
87.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (* 2.0 a))
58.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
3.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

series803.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
251.0ms
(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (* 2.0 a))
308.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
118.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify1.5s

Counts
183 → 183
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02755401
16554711
222914237
done50014169

prune769.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize33.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
5.2b
(* (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (/ 1 (* 2.0 a)))
10.3b
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
24.0b
(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite223.0ms

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:
26.0ms
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
130.0ms
(* (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (/ 1 (* 2.0 a)))
55.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
4.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

series774.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
236.0ms
(* (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (/ 1 (* 2.0 a)))
298.0ms
(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
120.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify1.9s

Counts
181 → 181
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02805119
17144377
225023764
done50003696

prune729.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.1b

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b
(fma b b (- (* 4.0 (* a c))))
1.4b
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
14.5b
(/ (* (* a c) 4.0) (* 2.0 a))
24.0b
(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
24×add-sqr-sqrt
21×*-un-lft-identity
19×add-cube-cbrt
18×prod-diff
16×sqrt-prod
9×prod-exp cbrt-unprod
6×cbrt-undiv fma-neg div-exp add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×difference-of-squares
1×sub-neg rem-sqrt-square flip3-- frac-2neg sqrt-pow1 times-frac pow1/2 diff-log clear-num associate-/r* flip-- fma-udef div-inv associate-/l* distribute-lft-out--
Counts
4 → 93
Calls
4 calls:
0.0ms
(fma b b (- (* 4.0 (* a c))))
13.0ms
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
34.0ms
(/ (* (* a c) 4.0) (* 2.0 a))
2.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

series392.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(fma b b (- (* 4.0 (* a c))))
165.0ms
(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
21.0ms
(/ (* (* a c) 4.0) (* 2.0 a))
126.0ms
(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify1.2s

Counts
105 → 105
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01681926
14131650
218051333
done50001266

prune358.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.1b

regimes294.0ms

Accuracy

77.2% (5.5b remaining)

Error of 11.3b against oracle of 5.8b and baseline of 30.0b

bsearch166.0ms

Steps
ItersRangePoint
6
1.6855676195581707e-170
7.565529323099765e-170
7.455592343308264e-170
5
-2.3823986784004295e+101
-6.644598008915225e+100
-1.8696623466311214e+101

simplify14.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02638
13538
24338
done4338

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.0s1050×body2560valid
727.0ms5893×body80valid
622.0ms831×body1280valid
284.0ms2996×body80nan
179.0ms449×body640valid
82.0ms225×body320valid
80.0ms135×body5120valid
19.0ms123×body160valid