Details

Time bar (total: 7.6s)

sample77.0ms

Algorithm
intervals
Results
17.0ms518×pre80true
17.0ms121×body320valid
12.0ms262×body80nan
9.0ms96×body160valid
2.0ms13×body640valid
1.0ms26×body80valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 52.6b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
27.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite30.0ms

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:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series299.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
43.0ms
(- (* b b) (* (* 4.0 a) c))
108.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify50.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0438855
11702750
25002735

prune230.0ms

Filtered
102 candidates to 82 candidates (80.4%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1002102
Fresh000
Picked101
Done000
Total1012103

Merged error: 0.1b

Counts
103 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
123×add-sqr-sqrt *-un-lft-identity
90×times-frac
79×add-cube-cbrt
61×prod-diff
41×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
11×fma-neg
10×add-log-exp
8×associate-/r*
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 expm1-log1p-u log1p-expm1-u div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 231
Calls
4 calls:
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series457.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(- (* b b) (* (* 4.0 a) c))
146.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
183.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify156.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (118.0ms)

IterNodesCost
08325099
139673830
250013828

prune500.0ms

Filtered
243 candidates to 137 candidates (56.4%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2385243
Fresh011
Picked011
Done000
Total2387245

Merged error: 0.0b

Counts
245 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.4b
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
181×prod-diff
133×add-sqr-sqrt
131×*-un-lft-identity
123×add-cube-cbrt
92×sqrt-prod
62×distribute-rgt-in distribute-lft-in
59×distribute-rgt-neg-in
57×distribute-lft-neg-in
27×add-exp-log add-cbrt-cube
19×neg-mul-1
11×fma-neg
10×prod-exp cbrt-unprod add-log-exp
7×associate-*r*
6×pow1 cbrt-undiv div-exp
4×expm1-log1p-u sub-neg flip3-- associate-*r/ flip-- log1p-expm1-u distribute-lft-out-- difference-of-squares
3×diff-log associate-*l*
2×associate-/r/
1×associate--l- neg-sub0 frac-2neg times-frac pow-prod-down neg-log clear-num associate-/r* *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 285
Calls
4 calls:
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
18.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series388.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(- (* b b) (* (* 4.0 a) c))
108.0ms
(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
155.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify168.0ms

Algorithm
egg-herbie
Counts
297 → 297
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
07978337
143945185
250015161

prune387.0ms

Filtered
297 candidates to 105 candidates (35.4%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New2961297
Fresh235
Picked011
Done011
Total2986304

Merged error: 0b

Counts
304 → 6

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(* a (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)))
0.3b
(/ (* 4.0 (* a c)) (* a (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))))
0.3b
(* (/ (* 4.0 (* a c)) (* a (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)))) (+ (* (- b) (- b)) (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
27.7b
(+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite270.0ms

Algorithm
rewrite-expression-head
Rules
936×prod-diff
694×unpow-prod-down cube-prod
562×add-sqr-sqrt
538×*-un-lft-identity
520×add-cube-cbrt
471×distribute-rgt-in distribute-lft-in
320×sqrt-prod
220×distribute-rgt-neg-in
216×distribute-lft-neg-in
98×sqr-pow
88×cube-mult unpow3
72×neg-mul-1
56×add-exp-log add-cbrt-cube
40×sqrt-div associate-*r*
28×associate-*r/
26×prod-exp cbrt-unprod
24×difference-of-squares
23×flip3-- flip--
16×frac-add
12×cbrt-undiv div-exp
10×frac-times associate-*l*
9×distribute-lft-out--
8×pow1
6×add-log-exp
5×associate-*l/
4×expm1-log1p-u associate-/r/ log1p-expm1-u
3×flip3-+ flip-+
2×distribute-lft-neg-out sub-neg times-frac pow-prod-down *-commutative div-inv unswap-sqr
1×difference-cubes +-commutative distribute-rgt-out fma-def frac-2neg unsub-neg clear-num associate-/r* sum-log associate-/l*
Counts
4 → 1101
Calls
4 calls:
70.0ms
(* a (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)))
36.0ms
(/ (* 4.0 (* a c)) (* a (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))))
47.0ms
(* (/ (* 4.0 (* a c)) (* a (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)))) (+ (* (- b) (- b)) (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
13.0ms
(+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
322.0ms
(* a (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)))
290.0ms
(/ (* 4.0 (* a c)) (* a (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))))
381.0ms
(* (/ (* 4.0 (* a c)) (* a (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)))) (+ (* (- b) (- b)) (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
119.0ms
(+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify413.0ms

Algorithm
egg-herbie
Counts
1113 → 1113
Iterations

Useful iterations: 1 (52.0ms)

IterNodesCost
0206742197
1500233449

prune641.0ms

Filtered
1113 candidates to 113 candidates (10.2%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New111301113
Fresh033
Picked011
Done022
Total111361119

Merged error: 0b

Counts
1119 → 6

regimes89.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02513
12713
22713

end0.0ms

sample2.1s

Algorithm
intervals
Results
505.0ms3640×body320valid
439.0ms16059×pre80true
379.0ms8059×body80nan
278.0ms2946×body160valid
101.0ms519×body640valid
44.0ms895×body80valid