Details

Time bar (total: 4.4s)

sample44.0ms

Algorithm
intervals
Results
8.0ms41×body1280valid
7.0ms179×body80valid
6.0ms24×body2560valid
4.0ms111×body80nan
3.0ms17×body640valid
1.0ms9×body320valid
1.0ms2×body5120valid
0.0ms5×body160valid

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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 35.1b

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 b) (* 4.0 (* a c)))
1.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.6b
(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))))

series284.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
47.0ms
(- (* b b) (* 4.0 (* a c)))
72.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(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

prune231.0ms

Filtered
89 candidates to 65 candidates (73.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New80989
Fresh000
Picked101
Done000
Total81990

Merged error: 6.3b

Counts
90 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.4b
(- (* b b) (* 4.0 (* a c)))
1.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite37.0ms

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)))
9.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series290.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
49.0ms
(- (* b b) (* 4.0 (* a c)))
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
68.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify57.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0469991
12048866
25002857

prune200.0ms

Filtered
97 candidates to 65 candidates (67.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New95297
Fresh358
Picked011
Done000
Total988106

Merged error: 6.3b

Counts
106 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.4b
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
9.9b
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
21.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
76×add-sqr-sqrt
63×*-un-lft-identity
52×times-frac
51×add-exp-log
30×add-cube-cbrt associate-*l*
27×add-cbrt-cube
20×prod-exp difference-of-squares
16×div-exp
13×sqrt-prod distribute-lft-out
10×distribute-lft-out--
8×cbrt-undiv cbrt-unprod
7×pow1 associate-*r*
6×associate-/r* add-log-exp
4×rec-exp flip3-- 1-exp associate-/r/ flip-- associate-/l*
3×div-inv
2×sqrt-div associate-/l/ unswap-sqr
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 152
Calls
4 calls:
7.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
23.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
12.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series512.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
161.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
202.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify114.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
07642421
137162067
250012044

prune346.0ms

Filtered
164 candidates to 106 candidates (64.6%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1604164
Fresh336
Picked011
Done011
Total1639172

Merged error: 6.2b

Counts
172 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b b) (* 4.0 (* a c)))
2.2b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
12.1b
(/ (* 4.0 (* a c)) (* 2.0 a))
21.6b
(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
9×prod-exp cbrt-unprod
8×add-log-exp
7×*-un-lft-identity
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 clear-num associate-/r* div-inv associate-/l* distribute-lft-out--
Counts
4 → 67
Calls
4 calls:
4.0ms
(- (* b b) (* 4.0 (* a c)))
7.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
8.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series202.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
10.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify57.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0403576
12221498
25001498

prune178.0ms

Filtered
79 candidates to 54 candidates (68.4%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New78179
Fresh156
Picked011
Done022
Total79988

Merged error: 6.2b

Counts
88 → 9

regimes207.0ms

Accuracy

94.7% (1.3b remaining)

Error of 6.7b against oracle of 5.4b and baseline of 29.8b

bsearch170.0ms

Steps
ItersRangePoint
8
2.8028278488416225e+79
7.17624026241226e+82
9.478602450487487e+81
8
1.375350686157096e-298
7.490097319602105e-296
1.516972353347772e-296
8
-1.0818597257815559e+95
-2.772945999025709e+91
-1.3197886379690183e+93

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04323
14323

end0.0ms

sample1.2s

Algorithm
intervals
Results
259.0ms1053×body2560valid
248.0ms5919×body80valid
187.0ms897×body1280valid
120.0ms3046×body80nan
67.0ms427×body640valid
30.0ms95×body5120valid
25.0ms210×body320valid
9.0ms115×body160valid