Details

Time bar (total: 4.7s)

sample43.0ms

Algorithm
intervals
Results
8.0ms34×body2560valid
8.0ms186×body80valid
6.0ms32×body1280valid
4.0ms94×body80nan
3.0ms17×body640valid
1.0ms7×body320valid
0.0ms5×body160valid
0.0ms1×body5120valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1649
21149
31359
41449
51489
61489

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

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:
11.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* 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))))

series288.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
45.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0404890
11481801
25001796

prune256.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
67×times-frac
48×add-sqr-sqrt
47×*-un-lft-identity
27×add-cube-cbrt
25×add-exp-log
13×associate-/r* add-cbrt-cube
12×div-exp
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
8×sqrt-prod
7×flip3-- flip--
6×pow1
5×cbrt-undiv distribute-rgt-neg-in div-inv
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 125
Calls
4 calls:
14.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
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))))

series311.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
49.0ms
(- (* b b) (* 4.0 (* a c)))
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify71.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05331804
125441605
250021531

prune284.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.8b
(- (* b b) (* 4.0 (* a c)))
1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

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))))

series294.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
44.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify63.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0469991
12048866
25002857

prune239.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.0b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.8b
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
12.0b
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite49.0ms

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)
20.0ms
(* (/ (+ 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))))

series531.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
170.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
205.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify122.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
07642421
137162067
250012044

prune398.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.0b

regimes199.0ms

Accuracy

86.8% (3.4b remaining)

Error of 9.2b against oracle of 5.7b and baseline of 31.9b

bsearch150.0ms

Steps
ItersRangePoint
3
5.062782482725967e+112
6.853081242536654e+112
6.293612880095814e+112
7
-2.1605152142522817e-113
-1.8017938791730603e-115
-2.125553485370055e-113
5
-1.1619433740097673e-94
-3.191731313316827e-95
-6.180620892104376e-95
4
-2.1402528215307472e+20
-1.2933083028149787e+20
-1.8507408941501855e+20

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05534
15534

end0.0ms

sample1.2s

Algorithm
intervals
Results
267.0ms1069×body2560valid
241.0ms5857×body80valid
187.0ms907×body1280valid
116.0ms2908×body80nan
72.0ms468×body640valid
33.0ms244×body320valid
29.0ms95×body5120valid
11.0ms115×body160valid