Details

Time bar (total: 15.4s)

sample57.0ms

Algorithm
intervals
Results
12.0ms206×body80valid
9.0ms29×body2560valid
8.0ms28×body1280valid
5.0ms96×body80nan
3.0ms12×body640valid
1.0ms4×body320valid
0.0ms1×body5120valid
0.0ms3×body160valid

simplify210.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01417
12917
26417
312017
414517
515217
615617
done15617

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize33.0ms

Local error

Found 4 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)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite195.0ms

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:
106.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
33.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0ms
(- (* b b) (* 4.0 (* a c)))
26.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series395.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
122.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
65.0ms
(- (* b b) (* 4.0 (* a c)))
84.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.9s

Counts
169 → 169
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02436690
15874705
217513760
done50003113

prune622.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
88×*-un-lft-identity
68×add-cube-cbrt
67×times-frac
61×prod-diff
38×sqrt-prod
26×distribute-rgt-neg-in
25×add-exp-log
21×distribute-lft-neg-in
13×associate-/r* add-cbrt-cube
12×div-exp
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
7×neg-mul-1 flip3-- flip--
6×pow1
5×cbrt-undiv div-inv
4×expm1-log1p-u log1p-expm1-u
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 205
Calls
4 calls:
80.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
61.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series495.0ms

Counts
4 → 12
Calls
4 calls:
207.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
117.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(- (* b b) (* 4.0 (* a c)))
100.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts
217 → 217
Iterations

Useful iterations: done (1.5s)

IterNodesCost
03118365
17016123
219285076
done50014340

prune579.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
1.2b
(- (* b b) (* 4.0 (* a c)))
5.1b
(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite203.0ms

Algorithm
rewrite-expression-head
Rules
204×times-frac
141×prod-diff
101×*-un-lft-identity
98×add-sqr-sqrt
95×add-cube-cbrt
51×sqrt-prod
34×distribute-rgt-neg-in
33×distribute-lft-neg-in
28×div-inv
15×fma-neg
11×neg-mul-1
9×add-exp-log add-cbrt-cube
8×add-log-exp
6×associate-/l*
5×pow1
4×expm1-log1p-u flip3-- sqrt-div flip-- log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv sub-neg diff-log div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-out-- frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* frac-sub cbrt-unprod sub-div difference-of-squares
Counts
4 → 240
Calls
4 calls:
23.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
10.0ms
(- (* b b) (* 4.0 (* a c)))
120.0ms
(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
22.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series538.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
60.0ms
(- (* b b) (* 4.0 (* a c)))
181.0ms
(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
129.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts
252 → 252
Iterations

Useful iterations: done (1.7s)

IterNodesCost
035615508
184412760
2220910138
done50006606

prune702.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.6b

localize24.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
2.0b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.1b
(/ (+ 0 (* (* a c) 4.0)) (* 2.0 a))
24.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u distribute-rgt-neg-in log1p-expm1-u
3×distribute-lft-neg-in times-frac sqrt-prod associate-/l*
2×cbrt-undiv flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/ distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 85
Calls
4 calls:
18.0ms
(- (* b b) (* 4.0 (* a c)))
43.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
35.0ms
(/ (+ 0 (* (* a c) 4.0)) (* 2.0 a))
19.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series269.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(- (* b b) (* 4.0 (* a c)))
97.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms
(/ (+ 0 (* (* a c) 4.0)) (* 2.0 a))
100.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.1s

Counts
97 → 97
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01581361
14051174
217941053
done50001052

prune427.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.6b

regimes302.0ms

Accuracy

94.7% (1.3b remaining)

Error of 6.8b against oracle of 5.5b and baseline of 29.4b

bsearch370.0ms

Steps
ItersRangePoint
9
1.2073698495971617e+61
8.75865749938149e+67
5.099089738165329e+67
10
1.610059141238142e-239
1.618698210595833e-224
2.094358742794728e-239
10
-3.742210988141449e+103
-1.0235731023437291e+92
-3.359953003549157e+103

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03464
14364
done4364

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.1s1047×body2560valid
595.0ms897×body1280valid
557.0ms5837×body80valid
331.0ms2844×body80nan
143.0ms466×body640valid
60.0ms112×body5120valid
54.0ms241×body320valid
18.0ms106×body160valid