Details

Time bar (total: 4.6s)

sample41.0ms

Algorithm
intervals
Results
9.0ms39×body2560valid
6.0ms171×body80valid
5.0ms26×body1280valid
3.0ms74×body80nan
2.0ms9×body5120valid
2.0ms12×body640valid
2.0ms14×body320valid
0.0ms2×body160valid

simplify15.0ms

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: 36.6b

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) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
25.6b
(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:
35.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
13.0ms
(- (- 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))))

series312.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
75.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
48.0ms
(- (* b b) (* 4.0 (* a c)))
73.0ms
(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

prune245.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.3b

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) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
25.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite79.0ms

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:
55.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
14.0ms
(- (- 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))))

series289.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms
(- (* b b) (* 4.0 (* a c)))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify56.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0469992
12048866
25002857

prune233.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.3b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* 4.0 (* a c)))
3.7b
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
10.7b
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
25.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt
61×*-un-lft-identity
52×times-frac
51×add-exp-log
30×add-cube-cbrt associate-*l*
27×add-cbrt-cube
20×prod-exp
18×difference-of-squares
16×div-exp
13×distribute-lft-out
12×sqrt-prod
9×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 → 149
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
67.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
27.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series487.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* 4.0 (* a c)))
164.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
203.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify124.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 2 (104.0ms)

IterNodesCost
07602359
137422008
250011985

prune394.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.2b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* 4.0 (* a c)))
15.5b
(/ (* 4.0 (* a c)) (* 2.0 a))
25.6b
(sqrt (- (* b b) (* 4.0 (* a c))))
25.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
9×prod-exp cbrt-unprod
8×add-sqr-sqrt
6×pow1 cbrt-undiv add-cube-cbrt *-un-lft-identity div-exp sqrt-prod add-log-exp
4×sqrt-div
3×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg frac-2neg times-frac diff-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 67
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series201.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* 4.0 (* a c)))
10.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify53.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0342550
12048477
25002477

prune249.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.2b

regimes207.0ms

Accuracy

88.2% (3.2b remaining)

Error of 8.5b against oracle of 5.3b and baseline of 32.7b

bsearch203.0ms

Steps
ItersRangePoint
8
1.9559514031553493e+101
2.0413668072230428e+104
5.178734871298619e+102
11
-1.2494758591913573e-114
-3.532474056345544e-138
-5.225975318005633e-138
8
-2.334183243992744e+54
-5.015218154388399e+51
-8.343309279866142e+53

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04536
14536

end0.0ms

sample1.1s

Algorithm
intervals
Results
249.0ms1068×body2560valid
217.0ms5808×body80valid
161.0ms853×body1280valid
109.0ms2843×body80nan
70.0ms468×body640valid
31.0ms110×body5120valid
27.0ms246×body320valid
12.0ms143×body160valid