Details

Time bar (total: 7.1s)

sample34.0ms

Algorithm
intervals
Results
13.0ms281×body80valid
4.0ms77×body80nan

simplify15.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03918
18018
214318
317718
418918
519318
619318
done19318

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.6b

localize86.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square 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 → 151
Calls
4 calls:
29.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series313.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
85.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify61.0ms

Counts
163 → 163
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04183056
114712008
250011917
done50011917

prune432.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.4b

localize89.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
6.2b
(/ (* a c) b)
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
62×*-un-lft-identity
60×prod-diff
55×add-sqr-sqrt
50×add-cube-cbrt
34×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
14×add-exp-log add-cbrt-cube
10×fma-neg
8×times-frac associate-/r* add-log-exp
7×neg-mul-1
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u distribute-lft-out
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 → 159
Calls
4 calls:
28.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
85.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
9.0ms
(/ (* a c) b)
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
177.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
19.0ms
(/ (* a c) b)
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify76.0ms

Counts
171 → 171
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
06103137
125642048
250011968
done50011968

prune452.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.9b

localize109.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.8b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.0b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite595.0ms

Algorithm
rewrite-expression-head
Rules
84×add-sqr-sqrt
75×*-un-lft-identity
63×add-cube-cbrt
60×prod-diff
34×sqrt-prod
33×times-frac
30×add-exp-log
24×distribute-rgt-neg-in
23×add-cbrt-cube
22×associate-*r*
21×distribute-lft-neg-in
11×cbrt-prod
10×fma-neg
9×cbrt-undiv div-exp prod-exp cbrt-unprod
8×add-log-exp
7×pow1 neg-mul-1 associate-*l*
6×unswap-sqr
5×associate-/r*
4×expm1-log1p-u log1p-expm1-u distribute-lft-out
3×div-inv
2×flip3-- sqrt-div diff-log associate-/r/ flip-- distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 197
Calls
4 calls:
29.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
40.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
503.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series431.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
54.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
207.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
86.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify119.0ms

Counts
209 → 209
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
09073856
141342632
250022617
done50022617

prune900.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.9b

localize98.0ms

Local error

Found 4 expressions with local error:

3.0b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
13.3b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite459.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
17×add-sqr-sqrt
14×add-cube-cbrt
10×fma-neg prod-diff
9×add-exp-log add-cbrt-cube
8×distribute-rgt-neg-in add-log-exp
6×pow1 distribute-lft-neg-in sqrt-prod
5×times-frac associate-/r*
4×expm1-log1p-u sqrt-div log1p-expm1-u distribute-lft-out
3×flip3-- flip--
2×cbrt-undiv neg-mul-1 rem-sqrt-square sqrt-pow1 pow1/2 diff-log div-exp associate-/r/
1×associate--l- neg-sub0 sub-neg frac-2neg flip3-+ neg-log prod-exp clear-num cbrt-unprod flip-+ div-inv associate-/l* difference-of-squares
Counts
4 → 100
Calls
4 calls:
420.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
14.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series424.0ms

Counts
4 → 12
Calls
4 calls:
203.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
78.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify56.0ms

Counts
112 → 112
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04451758
117881408
250021383
done50021383

prune508.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

regimes225.0ms

Accuracy

93.6% (1.0b remaining)

Error of 7.9b against oracle of 7.0b and baseline of 21.9b

bsearch114.0ms

Steps
ItersRangePoint
5
3.355600980676121e+98
1.2784432988208537e+99
1.1125484838729303e+99
6
-4.2638646006519825e+105
-4.3760586339396263e+104
-4.2041496511092447e+105

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06272
16272
done6272

end0.0ms

sample896.0ms

Algorithm
intervals
Results
438.0ms8756×body80valid
128.0ms2874×body80nan