Details

Time bar (total: 4.8s)

sample35.0ms

Algorithm
intervals
Results
14.0ms275×body80valid
4.0ms91×body80nan

simplify14.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03818
17918
213618
316118
417318
517718
617718
done17718

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize86.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.6b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite68.0ms

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-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 63
Calls
4 calls:
21.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series310.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify112.0ms

Counts
75 → 75
Iterations

Useful iterations: 3 (106.0ms)

IterNodesCost
0246646
1890606
23700588
35001584
done5001584

prune292.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.6b

localize87.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
4.7b
(/ (* a c) b)
22.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
14×add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt times-frac
8×add-log-exp
7×associate-/l*
5×pow1
4×cbrt-undiv div-exp associate-/r* distribute-lft-out--
3×distribute-rgt-neg-in sqrt-prod
2×flip3-- frac-2neg sqrt-div prod-exp clear-num sum-log flip-- cbrt-unprod div-inv associate-/l/ distribute-lft-out difference-of-squares
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 div-sub neg-log flip-+
Counts
4 → 81
Calls
4 calls:
21.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
51.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
10.0ms
(/ (* a c) b)
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series242.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
64.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
21.0ms
(/ (* a c) b)
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify58.0ms

Counts
93 → 93
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0489748
12180661
25002653
done5002653

prune355.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

localize85.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.6b
(- (* b b) (* (* 4.0 a) c))
0.7b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/r*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv flip3-- flip3-+ sqrt-div div-exp sum-log associate-/r/ flip-- flip-+
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log neg-log prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 69
Calls
4 calls:
47.0ms
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
21.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series414.0ms

Counts
4 → 12
Calls
4 calls:
207.0ms
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
52.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify43.0ms

Counts
81 → 81
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0368755
11530656
25001644
done5001644

prune303.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize91.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 c)))
0.6b
(- (* b b) (* (* 4.0 a) c))
0.7b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.3b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
47×times-frac
43×*-un-lft-identity
25×add-exp-log
24×add-sqr-sqrt
23×add-cube-cbrt
13×add-cbrt-cube
12×div-exp
10×distribute-lft-out add-log-exp
9×associate-/r*
6×pow1
5×cbrt-undiv distribute-rgt-neg-in div-inv
3×rec-exp 1-exp prod-exp sqrt-prod associate-/l*
2×flip3-- sqrt-div sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square pow-flip frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log neg-log clear-num associate-/r/ cbrt-unprod flip-+ inv-pow
Counts
4 → 106
Calls
4 calls:
50.0ms
(/ 1 (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 c)))
8.0ms
(- (* b b) (* (* 4.0 a) c))
25.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series323.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ 1 (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 c)))
51.0ms
(- (* b b) (* (* 4.0 a) c))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify59.0ms

Counts
118 → 118
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05291373
123721225
250011167
done50011167

prune307.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

regimes198.0ms

Accuracy

92.7% (1.1b remaining)

Error of 7.2b against oracle of 6.1b and baseline of 21.4b

bsearch171.0ms

Steps
ItersRangePoint
8
1.2146045965263502e+46
6.67231609761305e+48
2.9068079006396814e+48
10
-1.2433634659052315e+163
-1.0287718737452788e+153
-9.50165850365896e+153

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05253
15253
done5253

end0.0ms

sample903.0ms

Algorithm
intervals
Results
429.0ms8681×body80valid
128.0ms2842×body80nan