Details

Time bar (total: 4.8s)

sample41.0ms

Algorithm
intervals
Results
8.0ms206×body80valid
7.0ms32×body2560valid
4.0ms23×body1280valid
4.0ms103×body80nan
3.0ms19×body640valid
0.0ms3×body320valid
0.0ms2×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

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: 33.7b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b
(- (* b b) (* (* 4.0 a) c))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-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 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
12.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
85.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms
(- (* b b) (* (* 4.0 a) c))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify49.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0405779
11563685
25001674

prune234.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New73982
Fresh000
Picked101
Done000
Total74983

Merged error: 6.1b

Counts
83 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b
(- (* b b) (* (* 4.0 a) c))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
16×*-un-lft-identity
13×add-cbrt-cube
11×add-sqr-sqrt
10×prod-exp add-log-exp
8×add-cube-cbrt
7×pow1 associate-*r*
5×associate-*l*
4×div-exp cbrt-unprod distribute-lft-out
3×flip3-+ times-frac sqrt-prod flip-+
2×cbrt-undiv frac-times rec-exp flip3-- distribute-rgt-neg-in sqrt-div 1-exp associate-*l/ sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 80
Calls
4 calls:
15.0ms
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series511.0ms

Counts
4 → 12
Calls
4 calls:
300.0ms
(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
51.0ms
(- (* b b) (* (* 4.0 a) c))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify62.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0481921
12189790
25001777

prune214.0ms

Filtered
92 candidates to 66 candidates (71.7%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New90292
Fresh358
Picked101
Done000
Total947101

Merged error: 6.1b

Counts
101 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b
(- (* b b) (* (* 4.0 a) c))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
53×times-frac
45×*-un-lft-identity
26×add-sqr-sqrt
25×add-exp-log add-cube-cbrt
13×add-cbrt-cube
12×div-exp
11×associate-/r*
10×distribute-lft-out add-log-exp
9×associate-/r/
6×pow1
5×cbrt-undiv distribute-rgt-neg-in flip3-+ flip-+ div-inv
3×rec-exp 1-exp prod-exp sqrt-prod associate-/l*
2×flip3-- sqrt-div sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 diff-log neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 114
Calls
4 calls:
13.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
10.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series343.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms
(- (* b b) (* (* 4.0 a) c))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify71.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
05251588
125701375
250011308

prune228.0ms

Filtered
126 candidates to 72 candidates (57.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1251126
Fresh066
Picked011
Done000
Total1258133

Merged error: 6.0b

Counts
133 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.8b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.9b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 154
Calls
4 calls:
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series489.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
153.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
185.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify117.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
06512692
131392439
250022426

prune391.0ms

Filtered
166 candidates to 110 candidates (66.3%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1660166
Fresh066
Picked011
Done011
Total1668174

Merged error: 6.0b

Counts
174 → 8

regimes204.0ms

Accuracy

82.2% (5.1b remaining)

Error of 10.5b against oracle of 5.4b and baseline of 33.9b

bsearch110.0ms

Steps
ItersRangePoint
10
2.319058093766752e-122
4.8666627780759835e-109
1.0023817224401286e-110
5
-2.6938476684742574e+82
-9.311037300204504e+81
-2.657139070341684e+82

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03716
13716

end0.0ms

sample1.2s

Algorithm
intervals
Results
244.0ms1055×body2560valid
240.0ms5771×body80valid
182.0ms952×body1280valid
111.0ms2946×body80nan
71.0ms483×body640valid
33.0ms115×body5120valid
25.0ms228×body320valid
8.0ms110×body160valid