Details

Time bar (total: 9.4s)

sample36.0ms

Algorithm
intervals
Results
15.0ms277×body80valid
4.0ms84×body80nan

simplify95.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
02038
13938
27937
314337
417037
517937
618237
done18237

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.8b

localize116.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.3b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
78×prod-diff
71×add-sqr-sqrt
67×*-un-lft-identity
61×add-cube-cbrt
50×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
16×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u difference-of-squares
3×diff-log distribute-lft-out--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2
1×associate--l- neg-sub0 neg-log
Counts
4 → 165
Calls
4 calls:
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
78.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify909.0ms

Counts
177 → 177
Iterations

Useful iterations: 2 (157.0ms)

IterNodesCost
02086992
14784627
216653552
done50013552

prune425.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.2b

localize118.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.2b
(/ (* 2.0 c) (- (- (* 2.0 (/ (* a c) b)) b) b))
4.5b
(/ (* a c) b)
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
59×add-sqr-sqrt
58×*-un-lft-identity
50×add-cube-cbrt
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
14×add-exp-log add-cbrt-cube
10×fma-neg
8×times-frac associate-/r* add-log-exp
7×neg-mul-1
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u distribute-lft-out-- difference-of-squares
3×flip3-- flip--
2×frac-2neg sqrt-div diff-log prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l*
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 159
Calls
4 calls:
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(/ (* 2.0 c) (- (- (* 2.0 (/ (* a c) b)) b) b))
3.0ms
(/ (* a c) b)
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series237.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms
(/ (* 2.0 c) (- (- (* 2.0 (/ (* a c) b)) b) b))
19.0ms
(/ (* a c) b)
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify787.0ms

Counts
171 → 171
Iterations

Useful iterations: 2 (196.0ms)

IterNodesCost
02616392
16354465
223963464
done50003464

prune502.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.4b

localize120.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0b
(/ a (/ b c))
3.2b
(/ (* 2.0 c) (- (- (* 2.0 (/ a (/ b c))) b) b))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt
98×*-un-lft-identity
90×add-cube-cbrt
80×times-frac
60×prod-diff
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
18×associate-/r*
14×add-exp-log add-cbrt-cube
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×div-inv
5×pow1 cbrt-undiv div-exp
4×expm1-log1p-u log1p-expm1-u associate-/l* distribute-lft-out-- difference-of-squares
3×flip3-- associate-/r/ flip--
2×frac-2neg sqrt-div diff-log clear-num
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log prod-exp cbrt-unprod
Counts
4 → 208
Calls
4 calls:
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms
(/ a (/ b c))
60.0ms
(/ (* 2.0 c) (- (- (* 2.0 (/ a (/ b c))) b) b))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms
(/ a (/ b c))
71.0ms
(/ (* 2.0 c) (- (- (* 2.0 (/ a (/ b c))) b) b))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts
220 → 220
Iterations

Useful iterations: 2 (283.0ms)

IterNodesCost
03667086
18565101
233424088
done50014088

prune750.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.4b

localize123.0ms

Local error

Found 4 expressions with local error:

12.0b
(cbrt (/ b c))
12.0b
(cbrt (/ b c))
12.0b
(cbrt (/ b c))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×add-sqr-sqrt times-frac
26×add-cube-cbrt *-un-lft-identity
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 89
Calls
4 calls:
1.0ms
(cbrt (/ b c))
2.0ms
(cbrt (/ b c))
2.0ms
(cbrt (/ b c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series263.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(cbrt (/ b c))
59.0ms
(cbrt (/ b c))
65.0ms
(cbrt (/ b c))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts
101 → 101
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01291048
1246981
2755932
32909914
done5000913

prune534.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.4b

regimes233.0ms

Accuracy

90.1% (1.5b remaining)

Error of 7.8b against oracle of 6.4b and baseline of 21.2b

bsearch170.0ms

Steps
ItersRangePoint
9
1.790439840991813e+53
4.6520850645607246e+61
4.581932003920303e+61
7
-2.4291110075415274e+53
-8.95268880325176e+51
-2.3219741201870814e+53

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
048138
155138
done55138

end0.0ms

sample877.0ms

Algorithm
intervals
Results
461.0ms8710×body80valid
144.0ms2882×body80nan