Details

Time bar (total: 12.5s)

sample87.0ms

Algorithm
intervals
Results
57.0ms277×body80valid
12.0ms84×body80nan

simplify199.0ms

Counts
1 → 1
Iterations
IterNodes
done152
7152
6151
5144
4132
3101
262
135
020

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.8b

localize145.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.7b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
23.7b
(sqrt (- (* b b) (* (* 4 a) c)))
23.7b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite46.0ms

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:
14.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
15.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
8.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
9.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series460.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
119.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
108.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
127.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify638.0ms

Counts
79 → 79
Iterations
IterNodes
done2000
2773
1250
0102

prune621.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.1b

localize190.0ms

Local error

Found 4 expressions with local error:

9.0b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
23.7b
(sqrt (- (* b b) (* (* 4 a) c)))
23.7b
(sqrt (- (* b b) (* (* 4 a) c)))
23.7b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×add-log-exp
7×pow1 *-un-lft-identity add-cube-cbrt
6×sqrt-div
4×flip3-- add-cbrt-cube add-exp-log insert-posit16 flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 64
Calls
4 calls:
17.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series431.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
107.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
114.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
118.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify493.0ms

Counts
76 → 76
Iterations
IterNodes
done2000
2669
1226
091

prune637.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.1b

localize165.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
2.6b
(/ (* 2 (- (/ a (/ b c)) b)) (* 2 a))
5.7b
(/ a (/ b c))
23.7b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
52×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
21×add-cbrt-cube add-exp-log
14×associate-/r*
8×add-log-exp
7×cbrt-undiv div-exp
6×div-inv
5×pow1
4×prod-exp sqrt-prod cbrt-unprod insert-posit16 associate-/l*
3×flip3-- flip--
2×clear-num frac-2neg sqrt-div diff-log associate-*r/ distribute-lft-out-- difference-of-squares associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square sub-neg distribute-rgt-neg-in sqrt-pow1 pow1/2 neg-log associate-/r/
Counts
4 → 130
Calls
4 calls:
25.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
82.0ms
(/ (* 2 (- (/ a (/ b c)) b)) (* 2 a))
12.0ms
(/ a (/ b c))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
58.0ms
(/ (* 2 (- (/ a (/ b c)) b)) (* 2 a))
26.0ms
(/ a (/ b c))
86.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify549.0ms

Counts
142 → 142
Iterations
IterNodes
done2000
1760
0285

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.0b

localize144.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))))
1.0b
(- (* b b) (* (* 4 a) c))
1.7b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
23.7b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-cbrt-cube add-exp-log
7×associate-/r* times-frac add-cube-cbrt
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- insert-posit16 flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 80
Calls
4 calls:
57.0ms
(/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))))
7.0ms
(- (* b b) (* (* 4 a) c))
15.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
8.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series573.0ms

Counts
4 → 12
Calls
4 calls:
254.0ms
(/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))))
79.0ms
(- (* b b) (* (* 4 a) c))
119.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
120.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.2s

Counts
92 → 92
Iterations
IterNodes
done2007
21283
1387
0152

prune507.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.0b

regimes403.0ms

Accuracy

86.8% (2.1b remaining)

Error of 7.2b against oracle of 5.2b and baseline of 20.9b

bsearch434.0ms

Steps
ItersRangePoint
7
1.9723660647371773e+81
3.4101289177416236e+83
3.060834910674178e+83
6
-6.8156570572547095e-267
-1.1055728218964216e-267
-1.1253904323982412e-267
9
-7.806260788625035e+148
-1.2289413495061505e+143
-1.6844644503075447e+144

simplify18.0ms

Iterations
IterNodes
done57
157
048

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.0s8767×body80valid
578.0ms2981×body80nan