Details

Time bar (total: 20.5s)

sample114.0ms

Algorithm
intervals
Results
65.0ms272×body80valid
20.0ms85×body80nan

simplify180.0ms

Counts
1 → 1
Iterations
IterNodes
done168
7168
6166
5160
4151
3125
275
138
020

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize117.0ms

Local error

Found 4 expressions with local error:

0.9b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.2b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-sqr-sqrt add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-cbrt-cube sqrt-div add-exp-log insert-posit16
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sum-log distribute-rgt-neg-in sqrt-pow1 pow1/2 diff-log neg-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×associate--l- +-commutative sub-neg flip3-+ associate-+l- flip-+
Counts
4 → 67
Calls
4 calls:
26.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
29.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
19.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series430.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
97.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
102.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
119.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.1s

Counts
79 → 79
Iterations
IterNodes
done2000
32000
2773
1250
0102

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.8b

localize193.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
3.7b
(/ (* 2 c) (+ (- b) (- (/ (* 2 a) (/ b c)) b)))
5.5b
(/ (* 2 a) (/ b c))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
45×*-un-lft-identity
38×times-frac
26×add-sqr-sqrt
21×add-cbrt-cube add-exp-log add-cube-cbrt
20×associate-/r*
8×cbrt-undiv div-exp distribute-lft-out add-log-exp
6×distribute-lft-out--
5×pow1 distribute-rgt-neg-in
4×sqrt-prod insert-posit16 div-inv
3×prod-exp associate-/r/ cbrt-unprod
2×clear-num frac-2neg flip3-- sqrt-div diff-log flip-- associate-/l* difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square sub-neg sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 114
Calls
4 calls:
30.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
105.0ms
(/ (* 2 c) (+ (- b) (- (/ (* 2 a) (/ b c)) b)))
11.0ms
(/ (* 2 a) (/ b c))
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series496.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
252.0ms
(/ (* 2 c) (+ (- b) (- (/ (* 2 a) (/ b c)) b)))
43.0ms
(/ (* 2 a) (/ b c))
97.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.1s

Counts
126 → 126
Iterations
IterNodes
done2000
22000
1646
0244

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize186.0ms

Local error

Found 4 expressions with local error:

5.5b
(/ (* 2 a) (/ b c))
5.5b
(/ (* 2 a) (/ b c))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))
25.6b
(cbrt (* (* (/ (* 2 a) (/ b c)) (/ (* 2 a) (/ b c))) (/ (* 2 a) (/ b c))))

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
62×times-frac
34×add-sqr-sqrt
33×*-un-lft-identity add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×associate-/r*
12×cbrt-undiv div-exp
7×cbrt-div
6×div-inv
5×frac-times pow1 associate-*l/
4×prod-exp cbrt-unprod insert-posit16 add-log-exp
3×associate-*r/ sqrt-prod
2×clear-num frac-2neg sqrt-div associate-/r/ associate-/l*
1×cbrt-prod rem-sqrt-square sqrt-pow1 flip3-- pow1/2 pow1/3 pow3 rem-cbrt-cube flip--
Counts
4 → 128
Calls
4 calls:
11.0ms
(/ (* 2 a) (/ b c))
18.0ms
(/ (* 2 a) (/ b c))
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
128.0ms
(cbrt (* (* (/ (* 2 a) (/ b c)) (/ (* 2 a) (/ b c))) (/ (* 2 a) (/ b c))))

series246.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ (* 2 a) (/ b c))
42.0ms
(/ (* 2 a) (/ b c))
101.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
63.0ms
(cbrt (* (* (/ (* 2 a) (/ b c)) (/ (* 2 a) (/ b c))) (/ (* 2 a) (/ b c))))

simplify1.4s

Counts
140 → 140
Iterations
IterNodes
done2011
32011
21815
1513
0197

prune2.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.8b

localize165.0ms

Local error

Found 4 expressions with local error:

3.7b
(/ (* 2 c) (+ (- b) (- (/ (* 2 a) (/ b c)) b)))
4.6b
(/ (- (- b) (- b (/ (* 2 a) (/ b c)))) (* 2 a))
5.5b
(/ (* 2 a) (/ b c))
5.5b
(/ (* 2 a) (/ b c))

rewrite606.0ms

Algorithm
rewrite-expression-head
Rules
77×times-frac
76×*-un-lft-identity
40×add-sqr-sqrt
38×add-cbrt-cube add-exp-log
36×add-cube-cbrt
34×associate-/r*
16×cbrt-undiv div-exp distribute-lft-out--
11×associate-/l*
8×distribute-rgt-neg-in div-inv distribute-lft-out
6×prod-exp cbrt-unprod
4×pow1 clear-num frac-2neg associate-/r/ insert-posit16 add-log-exp
2×difference-of-squares associate-/l/
1×flip3-+ flip3-- div-sub flip-+ flip--
Counts
4 → 161
Calls
4 calls:
88.0ms
(/ (* 2 c) (+ (- b) (- (/ (* 2 a) (/ b c)) b)))
493.0ms
(/ (- (- b) (- b (/ (* 2 a) (/ b c)))) (* 2 a))
10.0ms
(/ (* 2 a) (/ b c))
10.0ms
(/ (* 2 a) (/ b c))

series415.0ms

Counts
4 → 12
Calls
4 calls:
251.0ms
(/ (* 2 c) (+ (- b) (- (/ (* 2 a) (/ b c)) b)))
77.0ms
(/ (- (- b) (- b (/ (* 2 a) (/ b c)))) (* 2 a))
44.0ms
(/ (* 2 a) (/ b c))
43.0ms
(/ (* 2 a) (/ b c))

simplify1.2s

Counts
173 → 173
Iterations
IterNodes
done2005
22005
1616
0221

prune2.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.7b

regimes372.0ms

Accuracy

93.6% (1.0b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 21.8b

bsearch490.0ms

Steps
ItersRangePoint
8
2.231296991249122e+66
2.5939819947174796e+69
1.559394358097289e+69
9
-9.434568284397946e-302
-1.1161865709419737e-308
-1.165097522778907e-308
9
-2.2464591800446616e+91
-3.153507839293123e+86
-2.723731815549707e+89

simplify67.0ms

Iterations
IterNodes
done77
377
274
170
057

end0.0ms

sample3.1s

Algorithm
intervals
Results
2.2s8671×body80valid
600.0ms2938×body80nan