Details

Time bar (total: 5.4s)

sample55.0ms

Algorithm
intervals
Results
13.0ms279×body80nan
11.0ms146×body160valid
10.0ms535×pre80true
4.0ms110×body80valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.6b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.3b
(- (* b b) (* (* 4.0 a) c))
28.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
4.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series293.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
102.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
45.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify51.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0438854
11702750
25001735

prune256.0ms

Filtered
102 candidates to 82 candidates (80.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New975102
Fresh000
Picked101
Done000
Total985103

Merged error: 0.3b

Counts
103 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
123×add-sqr-sqrt *-un-lft-identity
90×times-frac
79×add-cube-cbrt
61×prod-diff
41×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
11×fma-neg
10×add-log-exp
8×associate-/r*
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 expm1-log1p-u log1p-expm1-u div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 231
Calls
4 calls:
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
4.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series441.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
142.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
45.0ms
(- (* b b) (* (* 4.0 a) c))
179.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify153.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (113.0ms)

IterNodesCost
08325099
139673830
250013828

prune541.0ms

Filtered
243 candidates to 137 candidates (56.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2349243
Fresh404
Picked101
Done000
Total2399248

Merged error: 0.0b

Counts
248 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
181×prod-diff
133×add-sqr-sqrt
131×*-un-lft-identity
123×add-cube-cbrt
92×sqrt-prod
62×distribute-rgt-in distribute-lft-in
59×distribute-rgt-neg-in
57×distribute-lft-neg-in
27×add-exp-log add-cbrt-cube
19×neg-mul-1
11×fma-neg
10×prod-exp cbrt-unprod add-log-exp
7×associate-*r*
6×pow1 cbrt-undiv div-exp
4×expm1-log1p-u sub-neg flip3-- associate-*r/ flip-- log1p-expm1-u distribute-lft-out-- difference-of-squares
3×diff-log associate-*l*
2×associate-/r/
1×associate--l- neg-sub0 frac-2neg times-frac pow-prod-down neg-log clear-num associate-/r* *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 285
Calls
4 calls:
16.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series369.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
75.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(- (* b b) (* (* 4.0 a) c))
146.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify154.0ms

Algorithm
egg-herbie
Counts
297 → 297
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
07978337
143945185
250015161

prune437.0ms

Filtered
297 candidates to 105 candidates (35.4%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2952297
Fresh268
Picked011
Done000
Total2979306

Merged error: 0b

Counts
306 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(/ (/ (* c 4.0) 1) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b
(- (* b b) (* (* 4.0 a) c))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
107×add-sqr-sqrt
106×*-un-lft-identity
73×times-frac
70×add-cube-cbrt
61×prod-diff
42×sqrt-prod
30×distribute-rgt-neg-in
21×distribute-lft-neg-in
18×add-exp-log distribute-lft-out-- difference-of-squares
13×add-cbrt-cube
11×fma-neg
10×add-log-exp
9×div-exp div-inv
7×neg-mul-1 associate-/r* associate-/l*
5×pow1 cbrt-undiv
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×sub-neg sqrt-div 1-exp prod-exp associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num cbrt-unprod associate-/l/
Counts
4 → 209
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
13.0ms
(/ (/ (* c 4.0) 1) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))

series360.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
172.0ms
(/ (/ (* c 4.0) 1) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(- (* b b) (* (* 4.0 a) c))

simplify97.0ms

Algorithm
egg-herbie
Counts
221 → 221
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
07574284
131833087
250013006

prune398.0ms

Filtered
221 candidates to 109 candidates (49.3%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2174221
Fresh437
Picked101
Done011
Total2228230

Merged error: 0b

Counts
230 → 8

regimes119.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02812
13612
23612

end0.0ms

sample1.4s

Algorithm
intervals
Results
322.0ms4394×body160valid
304.0ms16499×pre80true
297.0ms8499×body80nan
135.0ms3606×body80valid