Details

Time bar (total: 4.3s)

sample47.0ms

Algorithm
intervals
Results
9.0ms32×body1280valid
8.0ms34×body2560valid
7.0ms179×body80valid
3.0ms86×body80nan
2.0ms15×body640valid
2.0ms7×body5120valid
1.0ms7×body320valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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: 33.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.3b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b
(- (* b b) (* 4.0 (* a c)))
22.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite56.0ms

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)))))
35.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series278.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
91.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
43.0ms
(- (* b b) (* 4.0 (* a c)))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0404890
11481801
25001796

prune249.0ms

Filtered
89 candidates to 65 candidates (73.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.3b
(/ (pow (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 1) (* 2.0 a))
0.4b
(- (* b b) (* 4.0 (* a c)))
22.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
21×*-un-lft-identity
17×add-exp-log
14×unpow-prod-down
11×times-frac associate-/l*
10×add-log-exp
9×add-cube-cbrt add-cbrt-cube
6×div-exp sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
3×flip3-- distribute-rgt-neg-in diff-log prod-exp flip--
2×cbrt-undiv pow-to-exp sub-neg sqrt-div pow-exp sqr-pow
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 86
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
64.0ms
(/ (pow (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 1) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series286.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
101.0ms
(/ (pow (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 1) (* 2.0 a))
43.0ms
(- (* b b) (* 4.0 (* a c)))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
04241032
11620943
25001931

prune234.0ms

Filtered
98 candidates to 63 candidates (64.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.4b
(- (* b b) (* 4.0 (* a c)))
0.5b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
22.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite76.0ms

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:
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
55.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series276.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms
(- (* b b) (* 4.0 (* a c)))
91.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify55.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0469991
12048866
25002857

prune227.0ms

Filtered
97 candidates to 64 candidates (66.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.8b
(* (/ 1 (* 2.0 a)) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))))
19.3b
(- (pow b 2) (pow b 2))
22.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite210.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
24×*-un-lft-identity
23×add-exp-log
22×unpow-prod-down
16×add-cube-cbrt difference-of-squares
13×add-cbrt-cube
12×unpow2 sqr-pow
10×distribute-rgt-out-- prod-exp add-log-exp
8×distribute-lft-out--
7×pow1 associate-*l*
4×div-exp cbrt-unprod
3×flip3-+ times-frac associate-*r* sqrt-prod flip-+
2×cbrt-undiv frac-times rec-exp flip3-- sqrt-div 1-exp associate-*r/ sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 distribute-rgt-in associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in distribute-lft-in sqrt-pow1 pow1/2 +-inverses diff-log pow-prod-down neg-log associate-*l/ *-commutative div-inv unswap-sqr
Counts
4 → 114
Calls
4 calls:
12.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
177.0ms
(* (/ 1 (* 2.0 a)) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))))
13.0ms
(- (pow b 2) (pow b 2))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series158.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms
(* (/ 1 (* 2.0 a)) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))))
1.0ms
(- (pow b 2) (pow b 2))
67.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify37.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
0663841
15001626

prune308.0ms

Filtered
126 candidates to 80 candidates (63.5%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.3b

regimes159.0ms

Accuracy

96.1% (0.9b remaining)

Error of 6.2b against oracle of 5.3b and baseline of 29.4b

bsearch195.0ms

Steps
ItersRangePoint
10
2.531505514381809e+64
2.4051897841780437e+82
1.3017976234533476e+80
10
1.3073375047174026e-281
5.2835940265373795e-264
1.4997509575725276e-267
7
-4.788437381304621e+112
-4.459607117755996e+110
-3.8738438305427415e+112

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04425
14425

end0.0ms

sample1.2s

Algorithm
intervals
Results
253.0ms1046×body2560valid
247.0ms5910×body80valid
177.0ms896×body1280valid
121.0ms2839×body80nan
65.0ms420×body640valid
39.0ms133×body5120valid
28.0ms236×body320valid
10.0ms126×body160valid