Details

Time bar (total: 18.6s)

sample132.0ms

Algorithm
intervals
Results
84.0ms277×body80valid
20.0ms86×body80nan

simplify183.0ms

Counts
1 → 1
Iterations
IterNodes
8152
7152
6151
5144
4132
3101
262
135
020

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.5b

localize152.0ms

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))))
23.5b
(sqrt (- (* b b) (* (* 4 a) c)))
23.5b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite63.0ms

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))))
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
12.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
19.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series381.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
88.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
88.0ms
(sqrt (- (* b b) (* (* 4 a) c)))
112.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify912.0ms

Counts
79 → 79
Iterations
IterNodes
32441
2760
1248
0102

prune715.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.2b

localize173.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
3.2b
(* (/ a b) c)
4.8b
(/ (* (- (* (/ a b) c) b) 2) (* 2 a))
23.5b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite102.0ms

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 div-inv distribute-lft-out-- difference-of-squares unswap-sqr associate-/l/
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:
17.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
24.0ms
(* (/ a b) c)
44.0ms
(/ (* (- (* (/ a b) c) b) 2) (* 2 a))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series275.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
35.0ms
(* (/ a b) c)
51.0ms
(/ (* (- (* (/ a b) c) b) 2) (* 2 a))
89.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.5s

Counts
104 → 104
Iterations
IterNodes
22250
1532
0202

prune773.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.2b

localize155.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))))
0.8b
(- (* b b) (* (* 4 a) c))
1.2b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
23.5b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite132.0ms

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:
70.0ms
(/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))))
15.0ms
(- (* b b) (* (* 4 a) c))
30.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
15.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series522.0ms

Counts
4 → 12
Calls
4 calls:
241.0ms
(/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))))
73.0ms
(- (* b b) (* (* 4 a) c))
115.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
93.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.4s

Counts
92 → 92
Iterations
IterNodes
34239
21193
1377
0152

prune765.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.2b

localize130.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 2 c) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))))
0.8b
(- (* b b) (* (* 4 a) c))
1.2b
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
23.5b
(sqrt (- (* b b) (* (* 4 a) c)))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
32×*-un-lft-identity
27×associate-*r*
26×add-exp-log
21×times-frac
16×add-cbrt-cube add-cube-cbrt
12×prod-exp
10×pow1 add-log-exp
8×distribute-lft-out-- difference-of-squares
7×sqrt-prod
6×cbrt-unprod
4×distribute-rgt-neg-in flip3-- div-exp insert-posit16 flip--
3×diff-log pow-prod-down
2×cbrt-undiv rec-exp sub-neg sqrt-div 1-exp associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*l* neg-log associate-*r/ un-div-inv *-commutative div-inv
Counts
4 → 101
Calls
4 calls:
106.0ms
(* (* 2 c) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))))
14.0ms
(- (* b b) (* (* 4 a) c))
31.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
14.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

series452.0ms

Counts
4 → 12
Calls
4 calls:
212.0ms
(* (* 2 c) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))))
58.0ms
(- (* b b) (* (* 4 a) c))
93.0ms
(- (- b) (sqrt (- (* b b) (* (* 4 a) c))))
89.0ms
(sqrt (- (* b b) (* (* 4 a) c)))

simplify3.7s

Counts
113 → 113
Iterations
IterNodes
34733
21484
1513
0189

prune633.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.2b

regimes531.0ms

Accuracy

92.8% (1.1b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 20.9b

bsearch307.0ms

Steps
ItersRangePoint
8
2.231296991249122e+66
2.5939819947174796e+69
2.559678284282607e+69
9
-2.2464591800446616e+91
-3.153507839293123e+86
-1.3599228730895225e+90

simplify17.0ms

Iterations
IterNodes
248
148
040

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.3s8699×body80valid
632.0ms2954×body80nan