Details

Time bar (total: 5.8s)

sample46.0ms

Algorithm
intervals
Results
8.0ms30×body1280valid
8.0ms193×body80valid
8.0ms33×body2560valid
4.0ms102×body80nan
2.0ms6×body5120valid
1.0ms9×body640valid
1.0ms5×body320valid
0.0ms4×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: 33.4b

localize12.0ms

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)))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite55.0ms

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))
3.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series289.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
48.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0404890
11481801
25001796

prune243.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.8b

localize14.0ms

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)))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
159×times-frac
128×add-sqr-sqrt
127×*-un-lft-identity
75×add-cube-cbrt
26×distribute-lft-out-- difference-of-squares
25×associate-/l*
16×sqrt-prod
13×distribute-rgt-neg-in
10×add-log-exp
9×add-exp-log add-cbrt-cube
5×pow1 div-inv
3×cbrt-undiv flip3-- diff-log div-exp associate-/r* flip--
2×sub-neg sqrt-div div-sub
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/l/
Counts
4 → 164
Calls
4 calls:
36.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
3.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series282.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
46.0ms
(- (* b b) (* 4.0 (* a c)))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
67.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify71.0ms

Algorithm
egg-herbie
Counts
176 → 176
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
06782536
125582441
250012441

prune408.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) (/ 1 a))
0.8b
(- (* b b) (* 4.0 (* a c)))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
41×*-un-lft-identity
37×times-frac
26×add-exp-log
25×associate-*l*
23×add-cube-cbrt
16×add-cbrt-cube
13×associate-*r*
10×add-log-exp
8×div-exp prod-exp distribute-lft-out-- difference-of-squares
7×pow1 sqrt-prod
6×unswap-sqr
4×cbrt-undiv distribute-rgt-neg-in cbrt-unprod
3×flip3-- diff-log flip--
2×sub-neg rec-exp sqrt-div 1-exp div-inv
1×associate--l- neg-sub0 frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ un-div-inv *-commutative
Counts
4 → 114
Calls
4 calls:
54.0ms
(* (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) (/ 1 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
15.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series289.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) (/ 1 a))
47.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify65.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
06351392
124861237
250021224

prune285.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 1) (/ a (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0)))
0.8b
(- (* b b) (* 4.0 (* a c)))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite234.0ms

Algorithm
rewrite-expression-head
Rules
3701×times-frac
1907×add-sqr-sqrt
1906×*-un-lft-identity
1398×add-cube-cbrt
254×distribute-lft-out-- difference-of-squares
138×div-inv
130×sqrt-prod
127×distribute-rgt-neg-in
80×associate-/r*
64×add-exp-log
54×div-exp
25×add-cbrt-cube
15×cbrt-undiv 1-exp associate-/r/
13×associate-/l*
10×add-log-exp
6×rec-exp
5×pow1
3×flip3-- diff-log flip--
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/l/
Counts
4 → 1217
Calls
4 calls:
62.0ms
(/ (/ 1 1) (/ a (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0)))
5.0ms
(- (* b b) (* 4.0 (* a c)))
22.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
6.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series313.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ (/ 1 1) (/ a (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0)))
49.0ms
(- (* b b) (* 4.0 (* a c)))
74.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
78.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify304.0ms

Algorithm
egg-herbie
Counts
1229 → 1229
Iterations

Useful iterations: 1 (66.0ms)

IterNodesCost
0439428221
1500126972

prune1.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.8b

regimes213.0ms

Accuracy

87.3% (3.6b remaining)

Error of 9.3b against oracle of 5.8b and baseline of 34.0b

bsearch165.0ms

Steps
ItersRangePoint
7
7.8930669794294e+68
1.794276654474529e+70
1.3845340503596435e+70
9
-1.1004795362994629e-128
-8.053772428904448e-138
-1.461539579389551e-137
6
-16116865.97641067
-1132915.5505216778
-14858297.008745154

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04128
14128

end0.0ms

sample1.2s

Algorithm
intervals
Results
258.0ms1060×body2560valid
239.0ms5878×body80valid
180.0ms884×body1280valid
107.0ms2868×body80nan
67.0ms444×body640valid
36.0ms116×body5120valid
24.0ms209×body320valid
10.0ms125×body160valid