Details

Time bar (total: 1.3m)

sample120.0ms

Algorithm
intervals
Results
75.0ms284×body80valid
20.0ms91×body80nan

simplify166.0ms

Counts
1 → 1
Iterations
IterNodes
8168
7168
6166
5160
4151
3125
275
138
020

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.0b

localize199.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
1.7b
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite74.0ms

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:
18.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
25.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series445.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
130.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
107.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
88.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify885.0ms

Counts
79 → 79
Iterations
IterNodes
32437
2760
1248
0102

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize172.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
3.8b
(/ (* 2 c) (* (- (* (/ a b) c) b) 2))
3.9b
(* (/ a b) c)
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cbrt-cube add-exp-log
17×*-un-lft-identity
13×associate-*l* add-cube-cbrt
11×times-frac
8×add-log-exp
7×pow1
6×prod-exp cbrt-unprod
5×cbrt-undiv div-exp
4×sqrt-prod insert-posit16
3×flip3-- associate-*r* associate-*l/ flip--
2×sqrt-div diff-log associate-/r/ div-inv distribute-lft-out-- difference-of-squares unswap-sqr
1×associate--l- neg-sub0 rem-sqrt-square clear-num associate-/r* sub-neg distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 pow-prod-down neg-log *-commutative associate-/l*
Counts
4 → 92
Calls
4 calls:
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
26.0ms
(/ (* 2 c) (* (- (* (/ a b) c) b) 2))
18.0ms
(* (/ a b) c)
13.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series337.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
91.0ms
(/ (* 2 c) (* (- (* (/ a b) c) b) 2))
31.0ms
(* (/ a b) c)
91.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify930.0ms

Counts
104 → 104
Iterations
IterNodes
22143
1523
0202

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.0b

localize189.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt a)
1.1b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
3.8b
(/ (* 2 c) (* (- (* (/ (* (cbrt a) (cbrt a)) (* (cbrt b) (cbrt b))) (* (/ (cbrt a) (cbrt b)) c)) b) 2))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
16×add-cbrt-cube add-exp-log
11×add-sqr-sqrt
10×*-un-lft-identity
8×add-log-exp
6×add-cube-cbrt
5×pow1
4×cbrt-undiv div-exp prod-exp sqrt-prod cbrt-unprod insert-posit16
3×cbrt-prod flip3-- flip--
2×sqrt-div diff-log associate-*l/ associate-/r/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square clear-num associate-/r* sub-neg distribute-rgt-neg-in frac-2neg sqrt-pow1 times-frac pow1/2 pow1/3 neg-log div-inv associate-/l*
Counts
4 → 71
Calls
4 calls:
1.0ms
(cbrt a)
15.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
120.0ms
(/ (* 2 c) (* (- (* (/ (* (cbrt a) (cbrt a)) (* (cbrt b) (cbrt b))) (* (/ (cbrt a) (cbrt b)) c)) b) 2))
16.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series534.0ms

Counts
4 → 12
Calls
4 calls:
237.0ms
(cbrt a)
107.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
97.0ms
(/ (* 2 c) (* (- (* (/ (* (cbrt a) (cbrt a)) (* (cbrt b) (cbrt b))) (* (/ (cbrt a) (cbrt b)) c)) b) 2))
93.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify22.2s

Counts
83 → 83
Iterations
IterNodes
311351
21906
1463
0174

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.0b

localize221.0ms

Local error

Found 4 expressions with local error:

3.8b
(/ (* 2 c) (* (- (* (/ (* (cbrt a) (cbrt a)) (* (cbrt b) (cbrt b))) (* (/ (cbrt a) (cbrt b)) c)) b) 2))
12.8b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))
22.9b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
16×add-cbrt-cube add-exp-log
9×add-sqr-sqrt
8×add-log-exp
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×cbrt-undiv flip3-- sqrt-div div-exp prod-exp cbrt-unprod insert-posit16 flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-*l/ associate-/r/
1×associate--l- neg-sub0 clear-num associate-/r* sub-neg frac-2neg times-frac neg-log div-inv associate-/l* difference-of-squares
Counts
4 → 72
Calls
4 calls:
92.0ms
(/ (* 2 c) (* (- (* (/ (* (cbrt a) (cbrt a)) (* (cbrt b) (cbrt b))) (* (/ (cbrt a) (cbrt b)) c)) b) 2))
14.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
7.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(/ (* 2 c) (* (- (* (/ (* (cbrt a) (cbrt a)) (* (cbrt b) (cbrt b))) (* (/ (cbrt a) (cbrt b)) c)) b) 2))
98.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4 a) c))))))
111.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
86.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify40.5s

Counts
84 → 84
Iterations
IterNodes
311166
21834
1433
0156

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.0b

regimes523.0ms

Accuracy

93.5% (1.0b remaining)

Error of 6.5b against oracle of 5.6b and baseline of 20.4b

bsearch290.0ms

Steps
ItersRangePoint
8
6.45623811977989e+97
1.5556153764929518e+101
1.6529445176198465e+100
7
-1.8217288728729631e+111
-6.606823090402082e+109
-5.148407540792454e+110

simplify41.0ms

Iterations
IterNodes
270
170
056

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.2s8769×body80valid
556.0ms2978×body80nan