Details

Time bar (total: 5.8s)

sample42.0ms

Algorithm
intervals
Results
8.0ms35×body2560valid
7.0ms180×body80valid
5.0ms29×body1280valid
3.0ms88×body80nan
3.0ms17×body640valid
1.0ms5×body5120valid
1.0ms7×body160valid
0.0ms3×body320valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0299
1659
21219
31519
41609
51649
61649

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b
(- (* b b) (* 4.0 (* a c)))
1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×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 → 157
Calls
4 calls:
44.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
20.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series295.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
49.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify76.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05903305
121012212
250022128

prune346.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.0b
(- (* b b) (* 4.0 (* a c)))
1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
60×add-sqr-sqrt
57×*-un-lft-identity
49×add-cube-cbrt
35×sqrt-prod
23×add-exp-log distribute-rgt-neg-in
21×distribute-lft-neg-in
13×add-cbrt-cube
11×fma-neg
10×prod-exp add-log-exp
7×pow1 neg-mul-1 associate-*r* associate-*l*
5×flip3-- flip--
4×expm1-log1p-u div-exp cbrt-unprod log1p-expm1-u distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp 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 → 165
Calls
4 calls:
56.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
3.0ms
(- (* b b) (* 4.0 (* a c)))
20.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series280.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
47.0ms
(- (* b b) (* 4.0 (* a c)))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
66.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify82.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06563422
125942238
250012193

prune321.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
1.0b
(- (* b b) (* 4.0 (* a c)))
6.0b
(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
204×times-frac
141×prod-diff
101×*-un-lft-identity
98×add-sqr-sqrt
95×add-cube-cbrt
51×sqrt-prod
34×distribute-rgt-neg-in
33×distribute-lft-neg-in
28×div-inv
15×fma-neg
11×neg-mul-1
9×add-exp-log add-cbrt-cube
8×add-log-exp
6×associate-/l*
5×pow1
4×expm1-log1p-u flip3-- sqrt-div flip-- log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv sub-neg diff-log div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-out-- frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* frac-sub cbrt-unprod sub-div difference-of-squares
Counts
4 → 240
Calls
4 calls:
8.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
40.0ms
(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series348.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
49.0ms
(- (* b b) (* 4.0 (* a c)))
104.0ms
(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify122.0ms

Algorithm
egg-herbie
Counts
252 → 252
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
08478136
126765939
250015143

prune400.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* 4.0 (* a c))))))
1.0b
(- (* b b) (* 4.0 (* a c)))
10.3b
(- (/ (- b) (* 2.0 a)) (/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* 4.0 (* a c)))))))
22.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
1238×times-frac
575×prod-diff
514×add-sqr-sqrt
510×*-un-lft-identity
506×add-cube-cbrt
141×sqrt-prod
126×distribute-lft-neg-in distribute-rgt-neg-in
107×associate-/r/
104×div-inv
94×sqrt-div
49×flip3-- flip--
42×neg-mul-1
25×add-exp-log
15×fma-neg
13×add-cbrt-cube
12×div-exp associate-/r*
8×add-log-exp
6×pow1
5×cbrt-undiv
4×expm1-log1p-u log1p-expm1-u
3×rec-exp 1-exp prod-exp associate-/l* difference-of-squares
2×sub-neg diff-log distribute-lft-out--
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 div-sub clear-num frac-sub cbrt-unprod inv-pow
Counts
4 → 720
Calls
4 calls:
12.0ms
(/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
72.0ms
(- (/ (- b) (* 2.0 a)) (/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* 4.0 (* a c)))))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series397.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* 4.0 (* a c))))))
66.0ms
(- (* b b) (* 4.0 (* a c)))
110.0ms
(- (/ (- b) (* 2.0 a)) (/ 1 (/ (* 2.0 a) (sqrt (- (* b b) (* 4.0 (* a c)))))))
109.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify319.0ms

Algorithm
egg-herbie
Counts
732 → 732
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0211739375
1500228113

prune739.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.3b

regimes163.0ms

Accuracy

85.8% (4.1b remaining)

Error of 9.5b against oracle of 5.5b and baseline of 34.2b

bsearch56.0ms

Steps
ItersRangePoint
5
5.10808278574109e+145
1.867402505400959e+146
1.4350402825055232e+146
3
-2.6939693106550122e-64
-1.9710978016715664e-64
-2.648789841343547e-64

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03519
13519

end0.0ms

sample1.4s

Algorithm
intervals
Results
464.0ms1094×body2560valid
243.0ms5855×body80valid
175.0ms919×body1280valid
113.0ms2917×body80nan
62.0ms415×body640valid
31.0ms102×body5120valid
25.0ms222×body320valid
9.0ms112×body160valid