Details

Time bar (total: 6.7s)

sample72.0ms

Algorithm
intervals
Results
16.0ms38×body2560valid
16.0ms181×body80valid
11.0ms31×body1280valid
8.0ms66×body80nan
4.0ms14×body640valid
2.0ms5×body5120valid
2.0ms9×body320valid
1.0ms4×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite54.0ms

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:
34.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series286.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
45.0ms
(- (* 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)))

simplify47.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0438854
11702750
25001735

prune288.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.0b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite97.0ms

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:
15.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
25.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series476.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
149.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
177.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify141.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
08295119
137633863
250013860

prune566.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.2b
(/ (* 2.0 a) (* 4.0 (* a c)))
24.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
123×add-exp-log
63×add-cbrt-cube
60×prod-diff
57×prod-exp
53×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
40×div-exp
34×sqrt-prod
25×cbrt-unprod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
20×cbrt-undiv
10×fma-neg
8×pow1 rec-exp 1-exp add-log-exp
7×neg-mul-1
5×associate-/r/
4×expm1-log1p-u flip3-- times-frac flip-- log1p-expm1-u associate-/l*
2×frac-times pow-flip frac-2neg sqrt-div diff-log associate-*r/ clear-num associate-/r* div-inv distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down neg-log associate-*l/ inv-pow
Counts
4 → 193
Calls
4 calls:
61.0ms
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series306.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify129.0ms

Algorithm
egg-herbie
Counts
205 → 205
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
09153955
148362570
250012570

prune356.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ (* (/ 2.0 4.0) 1) c))
1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.8b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
441×times-frac
291×add-sqr-sqrt
290×*-un-lft-identity
190×add-cube-cbrt
94×add-exp-log
64×div-exp
61×prod-diff
58×sqrt-prod
50×distribute-lft-out-- difference-of-squares
46×distribute-rgt-neg-in
37×div-inv
36×add-cbrt-cube
27×associate-/l*
21×distribute-lft-neg-in
20×cbrt-undiv
17×associate-/r/
16×prod-exp
14×1-exp
11×flip3-- fma-neg flip--
10×add-log-exp
7×neg-mul-1 associate-/r*
6×rec-exp
5×pow1
4×expm1-log1p-u cbrt-unprod log1p-expm1-u
3×diff-log
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 → 392
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
41.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ (* (/ 2.0 4.0) 1) c))
18.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series316.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* (* 4.0 a) c))
126.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ (* (/ 2.0 4.0) 1) c))
74.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify98.0ms

Algorithm
egg-herbie
Counts
404 → 404
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
015978817
150027331

prune695.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.8b

regimes154.0ms

Accuracy

79% (5.0b remaining)

Error of 11.0b against oracle of 6.0b and baseline of 30.0b

bsearch332.0ms

Steps
ItersRangePoint
10
9.168682727753708e+124
1.4581761209996442e+140
6.972127475937741e+134
10
-4.4698229087150014e-60
-7.90650715848996e-79
-3.097985126053574e-61
10
-1.003617951747773e+25
-9531903230471.172
-9.847501781463365e+24
7
-1.4072277076308412e+56
-5.8205596871901896e+54
-5.874864305580093e+54

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06042
16642
26642

end0.0ms

sample2.0s

Algorithm
intervals
Results
513.0ms5833×body80valid
472.0ms1077×body2560valid
314.0ms856×body1280valid
219.0ms2698×body80nan
139.0ms464×body640valid
51.0ms96×body5120valid
50.0ms223×body320valid
16.0ms104×body160valid