Details

Time bar (total: 4.3s)

sample44.0ms

Algorithm
intervals
Results
8.0ms33×body2560valid
7.0ms183×body80valid
6.0ms31×body1280valid
6.0ms85×body80nan
3.0ms17×body640valid
1.0ms9×body320valid
0.0ms1×body5120valid
0.0ms2×body160valid

simplify11.0ms

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: 35.4b

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))
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(- (* b b) (* (* 4.0 a) c))
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

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

series292.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
75.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms
(- (* b b) (* (* 4.0 a) c))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0405779
11563685
25001674

prune215.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New74882
Fresh000
Picked011
Done000
Total74983

Merged error: 7.9b

Counts
83 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
3.6b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.2b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 148
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series429.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
142.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
174.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify112.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
06402581
131552333
250012320

prune372.0ms

Filtered
160 candidates to 106 candidates (66.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1573160
Fresh257
Picked101
Done011
Total1609169

Merged error: 7.8b

Counts
169 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(- (* b b) (* (* 4.0 a) c))
15.3b
(/ (* 2.0 a) (* 4.0 (* a c)))
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt add-log-exp
9×*-un-lft-identity prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 70
Calls
4 calls:
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series199.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify65.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
0429637
12471542
25003534

prune186.0ms

Filtered
82 candidates to 55 candidates (67.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New81182
Fresh167
Picked101
Done011
Total83891

Merged error: 7.8b

Counts
91 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b
(- (* b b) (* (* 4.0 a) c))
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×*-un-lft-identity
13×add-cube-cbrt associate-*l*
10×times-frac add-log-exp
9×add-exp-log add-cbrt-cube
7×pow1 associate-*r*
5×flip3-- sqrt-prod flip--
4×sub-neg distribute-lft-out-- difference-of-squares
3×diff-log
2×distribute-rgt-in frac-times distribute-rgt-neg-in distribute-lft-in sqrt-div associate-*r/ prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 div-exp pow-prod-down neg-log associate-*l/ *-commutative div-inv
Counts
4 → 89
Calls
4 calls:
14.0ms
(* (/ 0.5 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
11.0ms
(- (- 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)))

series293.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(* (/ 0.5 c) (- (- 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))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify54.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0445997
11857906
25001896

prune217.0ms

Filtered
101 candidates to 73 candidates (72.3%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New992101
Fresh156
Picked101
Done011
Total1018109

Merged error: 7.8b

Counts
109 → 8

regimes165.0ms

Accuracy

95.3% (1.1b remaining)

Error of 6.9b against oracle of 5.8b and baseline of 30.0b

bsearch193.0ms

Steps
ItersRangePoint
8
3.182319375801986e+130
1.3165557463351014e+133
3.29571176074688e+130
11
-2.847532546532628e-300
1.5391744236734674e-294
-1.0623739899498678e-305
7
-2.129980745276144e+116
-9.287529331322677e+113
-9.597540061084627e+115

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05328
16428
26828
36828

end0.0ms

sample1.2s

Algorithm
intervals
Results
252.0ms1068×body2560valid
237.0ms5876×body80valid
181.0ms882×body1280valid
109.0ms2898×body80nan
68.0ms446×body640valid
31.0ms103×body5120valid
25.0ms220×body320valid
9.0ms115×body160valid