Details

Time bar (total: 6.5s)

sample41.0ms

Algorithm
intervals
Results
7.0ms33×body2560valid
7.0ms186×body80valid
5.0ms28×body1280valid
3.0ms86×body80nan
2.0ms15×body640valid
1.0ms5×body5120valid
1.0ms7×body320valid
0.0ms6×body160valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0229
1439
2839
31109
41189
51189

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b
(- (* b b) (* (* 3.0 a) c))
1.8b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
64.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms
(- (* b b) (* (* 3.0 a) c))
25.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series302.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
43.0ms
(- (* b b) (* (* 3.0 a) c))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
72.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify48.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0433855
11670751
25001736

prune284.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.2b

localize18.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.1b
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.4b
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
124×*-un-lft-identity
90×times-frac
80×add-cube-cbrt
60×prod-diff
44×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
10×fma-neg
8×associate-/r* add-log-exp
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 232
Calls
4 calls:
30.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
85.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
59.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
11.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series488.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
149.0ms
(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
184.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
76.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify140.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 2 (106.0ms)

IterNodesCost
08255119
137383863
250013860

prune527.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.1b

localize19.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.1b
(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
11.3b
(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
22.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt
62×*-un-lft-identity
60×prod-diff
58×add-cube-cbrt
54×add-exp-log add-cbrt-cube
34×sqrt-prod
26×times-frac
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
19×cbrt-undiv div-exp
18×prod-exp cbrt-unprod
10×fma-neg associate-*r/ associate-/r/
8×associate-/l* add-log-exp
7×neg-mul-1 flip3-- flip--
6×div-inv
5×pow1
4×expm1-log1p-u associate-/r* log1p-expm1-u
2×frac-2neg sqrt-div diff-log clear-num distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log associate-/l/
Counts
4 → 194
Calls
4 calls:
30.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
47.0ms
(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
40.0ms
(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
11.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series488.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
150.0ms
(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
183.0ms
(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
73.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify155.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08784475
149663005
250013005

prune430.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.1b

localize18.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.1b
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))) a)
11.5b
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
22.4b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite213.0ms

Algorithm
rewrite-expression-head
Rules
337×times-frac
220×add-sqr-sqrt
219×*-un-lft-identity
159×add-cube-cbrt
60×prod-diff
48×sqrt-prod
45×associate-/l*
41×add-exp-log
36×distribute-rgt-neg-in
30×distribute-lft-out-- difference-of-squares
24×div-exp
23×add-cbrt-cube
21×distribute-lft-neg-in
18×div-inv
11×cbrt-undiv
10×fma-neg
8×add-log-exp
7×neg-mul-1
5×pow1
4×expm1-log1p-u prod-exp associate-/r* associate-/r/ log1p-expm1-u
3×rec-exp flip3-- 1-exp flip-- associate-/l/
2×frac-2neg sqrt-div diff-log clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 div-sub neg-log
Counts
4 → 323
Calls
4 calls:
30.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
77.0ms
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))) a)
77.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
11.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series387.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
127.0ms
(/ (/ 1 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))) a)
104.0ms
(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
75.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify83.0ms

Algorithm
egg-herbie
Counts
335 → 335
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
013286748
150015443

prune621.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.1b

regimes497.0ms

Accuracy

90.6% (2.5b remaining)

Error of 8.1b against oracle of 5.7b and baseline of 31.8b

bsearch156.0ms

Steps
ItersRangePoint
7
7.363656180201337e+60
1.0503009045500217e+63
5.354608489416471e+62
7
1.3148169546496053e-135
1.6902561201493824e-133
2.4967447941335268e-135
10
-1.6375536470903724e+107
-1.9877314958440015e+97
-1.2574766781276779e+107

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04932
14932

end0.0ms

sample1.1s

Algorithm
intervals
Results
217.0ms1051×body2560valid
213.0ms5865×body80valid
155.0ms933×body1280valid
91.0ms2815×body80nan
58.0ms452×body640valid
30.0ms113×body5120valid
25.0ms237×body320valid
8.0ms117×body160valid