Details

Time bar (total: 8.6s)

sample34.0ms

Algorithm
intervals
Results
14.0ms277×body80valid
4.0ms94×body80nan

simplify114.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
02038
13938
27937
314337
416937
517837
618137
done18137

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.5b

localize117.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
2.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
26.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
26.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
37×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×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
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 neg-log
Counts
4 → 140
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series263.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify738.0ms

Counts
152 → 152
Iterations

Useful iterations: done (732.0ms)

IterNodesCost
01816137
14064178
211913279
done50013272

prune399.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.6b

localize114.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
4.0b
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
4.8b
(/ (* a c) b)
26.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
14×add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt times-frac
7×associate-/l*
6×add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp associate-/r* log1p-expm1-u distribute-lft-out--
3×flip3-- sqrt-prod flip--
2×distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num cbrt-unprod div-inv associate-/l/ difference-of-squares
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff
Counts
4 → 88
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
29.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
3.0ms
(/ (* a c) b)
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series194.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* (* 4.0 a) c))
60.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
19.0ms
(/ (* a c) b)
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify789.0ms

Counts
100 → 100
Iterations

Useful iterations: 2 (168.0ms)

IterNodesCost
01791531
14511455
217501277
done50011277

prune373.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.5b

localize116.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
0.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.8b
(- (* b b) (* (* 4.0 a) c))
26.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
18×sqrt-prod
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
6×times-frac associate-/r* difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/r/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 105
Calls
4 calls:
20.0ms
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
21.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series393.0ms

Counts
4 → 12
Calls
4 calls:
196.0ms
(/ (* 2.0 c) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
77.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
48.0ms
(- (* b b) (* (* 4.0 a) c))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify819.0ms

Counts
117 → 117
Iterations

Useful iterations: done (816.0ms)

IterNodesCost
01862435
14422125
213821819
done50011798

prune382.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize121.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* 2.0 c) (/ 1 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.6b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.8b
(- (* b b) (* (* 4.0 a) c))
26.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
37×*-un-lft-identity
29×add-cube-cbrt
26×add-exp-log
24×associate-*r*
19×prod-diff sqrt-prod
18×times-frac
16×add-cbrt-cube
12×prod-exp
10×pow1
8×add-log-exp difference-of-squares
7×fma-neg
6×cbrt-unprod
4×expm1-log1p-u flip3-- div-exp flip-- log1p-expm1-u distribute-lft-out--
3×pow-prod-down
2×cbrt-undiv sub-neg rec-exp sqrt-div diff-log 1-exp associate-/r/
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ associate-*l* un-div-inv *-commutative div-inv
Counts
4 → 125
Calls
4 calls:
40.0ms
(* (* 2.0 c) (/ 1 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
21.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.0ms
(- (* b b) (* (* 4.0 a) c))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series391.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(* (* 2.0 c) (/ 1 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
82.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
48.0ms
(- (* b b) (* (* 4.0 a) c))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
137 → 137
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02242856
15872441
219082017
done50001999

prune382.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.3b

regimes244.0ms

Accuracy

89.3% (1.5b remaining)

Error of 7.9b against oracle of 6.3b and baseline of 20.7b

bsearch168.0ms

Steps
ItersRangePoint
9
2.944023772201993e+37
9.447687191993962e+42
9.148614558474486e+42
8
-6.10058349091927e+155
-9.408528429616011e+151
-1.3696490745623736e+154

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
046124
155124
done55124

end0.0ms

sample839.0ms

Algorithm
intervals
Results
450.0ms8731×body80valid
135.0ms2868×body80nan