Details

Time bar (total: 4.5s)

sample43.0ms

Algorithm
intervals
Results
10.0ms42×body2560valid
8.0ms191×body80valid
4.0ms20×body1280valid
4.0ms96×body80nan
3.0ms17×body640valid
1.0ms4×body5120valid
1.0ms7×body320valid
0.0ms3×body160valid

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0289
1649
21149
31359
41449
51489
61489

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b
(- (* b b) (* 4.0 (* a c)))
0.8b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 77
Calls
4 calls:
12.0ms
(/ (- (- 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)))))
6.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series292.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
48.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify48.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0404890
11481801
25001796

prune256.0ms

Filtered
89 candidates to 65 candidates (73.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.6b
(- (* b b) (* 4.0 (* a c)))
0.8b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
19×add-sqr-sqrt
16×*-un-lft-identity
13×add-cbrt-cube
10×prod-exp add-log-exp
8×add-cube-cbrt
7×pow1 associate-*r* associate-*l*
5×flip3-- sqrt-prod flip--
4×div-exp cbrt-unprod distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp distribute-rgt-neg-in sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 85
Calls
4 calls:
15.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
4.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series302.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
46.0ms
(- (* b b) (* 4.0 (* a c)))
80.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify58.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0469991
12048866
25002857

prune257.0ms

Filtered
97 candidates to 65 candidates (67.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.6b
(- (* b b) (* 4.0 (* a c)))
15.9b
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
25.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log *-un-lft-identity add-cbrt-cube
10×add-log-exp
8×add-sqr-sqrt
7×add-cube-cbrt
5×pow1
4×times-frac distribute-lft-out associate-/l*
3×cbrt-undiv flip3-+ div-exp prod-exp sqrt-prod cbrt-unprod flip-+
2×flip3-- sqrt-div associate-*l/ sum-log associate-/r/ flip-- associate-/l/
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 diff-log neg-log clear-num associate-/r* div-inv
Counts
4 → 71
Calls
4 calls:
8.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
15.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series361.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
165.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify101.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
0502969
13079812
25002794

prune233.0ms

Filtered
83 candidates to 63 candidates (75.9%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* 4.0 (* a c)))
4.4b
(/ (/ 4.0 (/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* a c))) (* 2.0 a))
10.7b
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* a c))
25.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
121×times-frac
71×*-un-lft-identity
41×add-exp-log add-cbrt-cube
40×add-sqr-sqrt
39×add-cube-cbrt
37×associate-/l*
20×cbrt-undiv div-exp
16×distribute-lft-out
10×div-inv
8×distribute-rgt-neg-in
7×prod-exp cbrt-unprod
6×add-log-exp
5×pow1
3×sqrt-prod associate-/l/
2×flip3-- frac-2neg sqrt-div clear-num associate-/r* associate-/r/ flip--
1×neg-sub0 associate-+l- sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log div-sub flip-+
Counts
4 → 147
Calls
4 calls:
4.0ms
(- (* b b) (* 4.0 (* a c)))
18.0ms
(/ (/ 4.0 (/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* a c))) (* 2.0 a))
11.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* a c))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series343.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* 4.0 (* a c)))
113.0ms
(/ (/ 4.0 (/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* a c))) (* 2.0 a))
113.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* a c))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify103.0ms

Algorithm
egg-herbie
Counts
159 → 159
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
08792281
142791955
250021954

prune362.0ms

Filtered
159 candidates to 109 candidates (68.6%)
Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.2b

regimes196.0ms

Accuracy

88.3% (3.2b remaining)

Error of 8.9b against oracle of 5.7b and baseline of 33.1b

bsearch160.0ms

Steps
ItersRangePoint
7
9.786063674806627e+75
3.1345211132670796e+77
3.0892781849035615e+77
9
-2.1802019263390548e-262
-2.6517018216343976e-267
-2.682647159074029e-267
7
-1.5740426810714466e-25
-6.855473855303728e-27
-1.55602287666915e-25

simplify5.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
04628
14628

end0.0ms

sample1.2s

Algorithm
intervals
Results
260.0ms1079×body2560valid
235.0ms5913×body80valid
177.0ms912×body1280valid
112.0ms2982×body80nan
60.0ms399×body640valid
33.0ms114×body5120valid
31.0ms212×body320valid
8.0ms97×body160valid