Details

Time bar (total: 15.5s)

sample104.0ms

Algorithm
intervals
Results
34.0ms273×body80valid
13.0ms103×body80nan

simplify153.0ms

Counts
1 → 1
Iterations
IterNodes
done179
6179
5175
4163
3136
278
138
020

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.6b

localize130.0ms

Local error

Found 4 expressions with local error:

1.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b
(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-cbrt-cube sqrt-div add-exp-log
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 → 63
Calls
4 calls:
18.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series472.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
131.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
116.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
119.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify677.0ms

Counts
75 → 75
Iterations
IterNodes
done5000
21036
1254
0100

prune696.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.6b

localize166.0ms

Local error

Found 4 expressions with local error:

1.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.5b
(/ (+ (* -2 b) (/ (* a 2.0) (/ b c))) (* 2.0 a))
6.8b
(/ (* a 2.0) (/ b c))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
34×times-frac
25×*-un-lft-identity
22×add-sqr-sqrt
21×add-cbrt-cube add-exp-log add-cube-cbrt
14×associate-/r*
8×cbrt-undiv div-exp add-log-exp
5×pow1
4×div-inv associate-/l*
3×prod-exp sqrt-prod cbrt-unprod
2×clear-num sum-log frac-2neg flip3-+ sqrt-div flip-+ distribute-lft-out associate-/l/
1×neg-sub0 +-commutative rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-- pow1/2 neg-log associate-/r/ associate-+l- flip--
Counts
4 → 99
Calls
4 calls:
29.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms
(/ (+ (* -2 b) (/ (* a 2.0) (/ b c))) (* 2.0 a))
16.0ms
(/ (* a 2.0) (/ b c))
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series368.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
92.0ms
(/ (+ (* -2 b) (/ (* a 2.0) (/ b c))) (* 2.0 a))
36.0ms
(/ (* a 2.0) (/ b c))
104.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts
111 → 111
Iterations
IterNodes
done5001
23877
1683
0244

prune939.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize143.0ms

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))
1.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-cbrt-cube add-exp-log
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 associate-/r* times-frac
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv sum-log flip3-+ flip3-- sqrt-div div-exp associate-/r/ flip-+ flip--
1×neg-sub0 +-commutative rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log neg-log prod-exp associate-+l- cbrt-unprod div-inv associate-/l*
Counts
4 → 69
Calls
4 calls:
49.0ms
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
18.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series704.0ms

Counts
4 → 12
Calls
4 calls:
353.0ms
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
81.0ms
(- (* b b) (* (* 4.0 a) c))
142.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
127.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.0s

Counts
81 → 81
Iterations
IterNodes
done5001
21894
1393
0144

prune610.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize183.0ms

Local error

Found 4 expressions with local error:

1.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.1b
(* (/ (* 2.0 a) (* (cbrt b) (cbrt b))) (* (cbrt c) (cbrt c)))
4.5b
(/ (+ (* -2 b) (/ (* (/ (* 2.0 a) (* (cbrt b) (cbrt b))) (* (cbrt c) (cbrt c))) (/ (cbrt b) (cbrt c)))) (* 2.0 a))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite207.0ms

Algorithm
rewrite-expression-head
Rules
50×add-exp-log
32×add-cbrt-cube
24×prod-exp cbrt-unprod
12×*-un-lft-identity
10×add-sqr-sqrt pow1 cbrt-undiv div-exp
8×add-cube-cbrt add-log-exp
5×associate-*l*
4×times-frac
3×pow-prod-down sqrt-prod associate-/l*
2×sum-log flip3-+ sqrt-div flip-+ div-inv distribute-lft-out associate-/l/
1×neg-sub0 +-commutative rem-sqrt-square clear-num associate-/r* distribute-rgt-neg-in frac-2neg sqrt-pow1 flip3-- pow1/2 associate-*r* neg-log associate-*l/ *-commutative associate-+l- flip-- unswap-sqr
Counts
4 → 91
Calls
4 calls:
27.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms
(* (/ (* 2.0 a) (* (cbrt b) (cbrt b))) (* (cbrt c) (cbrt c)))
117.0ms
(/ (+ (* -2 b) (/ (* (/ (* 2.0 a) (* (cbrt b) (cbrt b))) (* (cbrt c) (cbrt c))) (/ (cbrt b) (cbrt c)))) (* 2.0 a))
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series468.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
141.0ms
(* (/ (* 2.0 a) (* (cbrt b) (cbrt b))) (* (cbrt c) (cbrt c)))
94.0ms
(/ (+ (* -2 b) (/ (* (/ (* 2.0 a) (* (cbrt b) (cbrt b))) (* (cbrt c) (cbrt c))) (/ (cbrt b) (cbrt c)))) (* 2.0 a))
127.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts
103 → 103
Iterations
IterNodes
done5000
23664
1729
0244

prune833.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

regimes454.0ms

Accuracy

93.3% (1.1b remaining)

Error of 6.5b against oracle of 5.5b and baseline of 21.4b

bsearch516.0ms

Steps
ItersRangePoint
9
6.258218916731328e+93
1.8883840965187804e+99
3.256132414529083e+96
8
1.8451777477141087e-282
1.805639974384451e-278
2.6001952372348532e-282
10
-8.831205444333401e+160
-1.4178648401840193e+143
-7.722472254682146e+145

simplify17.0ms

Iterations
IterNodes
done70
270
169
057

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.6s8730×body80valid
297.0ms2931×body80nan