Details

Time bar (total: 8.2s)

sample38.0ms

Algorithm
intervals
Results
15.0ms277×body80valid
4.0ms84×body80nan

simplify94.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (8.0ms)

IterNodesCost
02038
13838
27837
313637
415637
516537
616837
done16837

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.8b

localize116.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

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:
15.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series290.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
75 → 75
Iterations

Useful iterations: 3 (485.0ms)

IterNodesCost
01001330
12461186
27661089
329201070
done50011070

prune289.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.2b

localize121.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.2b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
4.5b
(/ (* a c) b)
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
14×add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt
8×times-frac associate-/r* add-log-exp
5×pow1
4×cbrt-undiv div-exp sqrt-prod distribute-lft-out
3×distribute-rgt-neg-in
2×flip3-- frac-2neg sqrt-div diff-log prod-exp clear-num associate-/r/ flip-- cbrt-unprod div-inv associate-/l* distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 81
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
40.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
3.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series345.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
178.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
19.0ms
(/ (* a c) b)
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify605.0ms

Counts
93 → 93
Iterations

Useful iterations: 2 (170.0ms)

IterNodesCost
01761500
14401404
216061207
done50001207

prune325.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.4b

localize120.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.7b
(* a (/ c b))
3.2b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* a (/ c b))) b)))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
25×add-sqr-sqrt
15×add-cube-cbrt times-frac
14×add-exp-log add-cbrt-cube
13×associate-*r*
8×add-log-exp
7×pow1
5×associate-/r*
4×sqrt-prod distribute-lft-out
3×cbrt-undiv distribute-rgt-neg-in div-exp associate-*l* prod-exp cbrt-unprod
2×flip3-- sqrt-div diff-log associate-/r/ flip-- div-inv distribute-lft-out-- difference-of-squares unswap-sqr
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log clear-num *-commutative flip-+ associate-/l*
Counts
4 → 92
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms
(* a (/ c b))
59.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* a (/ c b))) b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series342.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms
(* a (/ c b))
177.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* a (/ c b))) b)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify603.0ms

Counts
104 → 104
Iterations

Useful iterations: 2 (196.0ms)

IterNodesCost
02001591
15051485
216461288
done50011288

prune400.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.4b

localize126.0ms

Local error

Found 4 expressions with local error:

20.3b
(cbrt (* a (/ c b)))
20.3b
(cbrt (* a (/ c b)))
20.3b
(cbrt (* a (/ c b)))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×cbrt-prod cbrt-div pow1/3 associate-*r/ sqrt-prod
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 45
Calls
4 calls:
3.0ms
(cbrt (* a (/ c b)))
3.0ms
(cbrt (* a (/ c b)))
3.0ms
(cbrt (* a (/ c b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series321.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(cbrt (* a (/ c b)))
82.0ms
(cbrt (* a (/ c b)))
83.0ms
(cbrt (* a (/ c b)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify923.0ms

Counts
57 → 57
Iterations

Useful iterations: done (921.0ms)

IterNodesCost
097675
1210633
2631574
32243550
done5000549

prune310.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.4b

regimes188.0ms

Accuracy

90.4% (1.4b remaining)

Error of 7.8b against oracle of 6.4b and baseline of 21.4b

bsearch178.0ms

Steps
ItersRangePoint
9
1.790439840991813e+53
4.6520850645607246e+61
4.581932003920303e+61
7
-2.4291110075415274e+53
-8.95268880325176e+51
-2.3219741201870814e+53

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
051145
164145
done64145

end0.0ms

sample861.0ms

Algorithm
intervals
Results
465.0ms8710×body80valid
138.0ms2882×body80nan