Details

Time bar (total: 10.1s)

sample62.0ms

Algorithm
intervals
Results
12.0ms117×body320valid
9.0ms515×pre80true
9.0ms259×body80nan
6.0ms94×body160valid
6.0ms21×body640valid
1.0ms24×body80valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 54.3b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(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))
25.9b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
139×add-sqr-sqrt
116×*-un-lft-identity
60×times-frac
42×unswap-sqr
36×add-cube-cbrt associate-*l*
30×difference-of-squares
28×distribute-lft-out
24×sqrt-prod
18×associate-*r*
14×distribute-rgt-neg-in
12×associate-/r* *-commutative distribute-lft-out--
10×add-log-exp
9×add-exp-log add-cbrt-cube
6×swap-sqr
5×pow1 associate-/l*
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num cbrt-unprod div-inv
Counts
4 → 178
Calls
4 calls:
22.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms
(- (* b b) (* (* 4.0 a) c))
41.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
38.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series325.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
47.0ms
(- (* b b) (* (* 4.0 a) c))
117.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
86.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify76.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
06212253
124432157
250022140

prune239.0ms

Filtered
190 candidates to 109 candidates (42.6%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1882190
Fresh000
Picked101
Done000
Total1892191

Merged error: 0.1b

Counts
191 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite347.0ms

Algorithm
rewrite-expression-head
Rules
1801×*-un-lft-identity
1346×times-frac
946×add-sqr-sqrt
408×distribute-lft-out--
400×distribute-lft-out
385×add-cube-cbrt
377×associate-*l*
217×difference-of-squares
168×associate-*r*
101×distribute-rgt-neg-in sqrt-prod
74×unswap-sqr
69×associate-/l*
59×*-commutative
28×associate-/r/
26×associate-/r*
23×associate-/l/
18×add-exp-log add-cbrt-cube
16×flip3-- flip--
15×div-inv
10×add-log-exp
7×cbrt-undiv div-exp
4×pow1
3×frac-2neg diff-log div-sub swap-sqr clear-num
2×associate-+l- sub-neg flip3-+ prod-exp cbrt-unprod flip-+
1×associate--l- neg-sub0 neg-log
Counts
4 → 896
Calls
4 calls:
22.0ms
(- (* b b) (* (* 4.0 a) c))
35.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
115.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
89.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series442.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b b) (* (* 4.0 a) c))
82.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
136.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
177.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify250.0ms

Algorithm
egg-herbie
Counts
908 → 908
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0173224064
1500122943

prune1.2s

Filtered
908 candidates to 285 candidates (68.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New9026908
Fresh011
Picked101
Done000
Total9037910

Merged error: 0b

Counts
910 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1)))
0.3b
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1)))) (* 2.0 a))
0.3b
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1))))

rewrite390.0ms

Algorithm
rewrite-expression-head
Rules
2151×*-un-lft-identity
1710×times-frac
1347×add-sqr-sqrt
512×distribute-lft-out
475×associate-*l*
464×distribute-lft-out--
455×add-cube-cbrt
419×difference-of-squares
303×sqrt-prod
210×associate-*r*
101×unpow-prod-down distribute-rgt-neg-in sqr-pow
88×unswap-sqr
83×associate-/l*
73×*-commutative
30×associate-/r*
28×associate-/r/
25×associate-/l/
18×add-exp-log add-cbrt-cube
16×flip3-- flip--
15×div-inv
10×add-log-exp
7×cbrt-undiv div-exp
4×pow1
3×frac-2neg diff-log div-sub swap-sqr clear-num
2×associate-+l- sub-neg flip3-+ prod-exp cbrt-unprod flip-+
1×associate--l- neg-sub0 neg-log
Counts
4 → 1098
Calls
4 calls:
23.0ms
(- (* b b) (* (* 4.0 a) c))
43.0ms
(- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1)))
120.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1)))) (* 2.0 a))
89.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1))))

series440.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1)))
133.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1)))) (* 2.0 a))
177.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1))))

simplify325.0ms

Algorithm
egg-herbie
Counts
1110 → 1110
Iterations

Useful iterations: 1 (45.0ms)

IterNodesCost
0217431610
1500230665

prune1.2s

Filtered
1110 candidates to 298 candidates (73.2%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New110821110
Fresh246
Picked011
Done000
Total111071117

Merged error: 0b

Counts
1117 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) a)
0.3b
(* (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) a) (/ (/ 1 (- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1)))) 2.0))

rewrite391.0ms

Algorithm
rewrite-expression-head
Rules
1398×*-un-lft-identity
1057×add-sqr-sqrt
971×associate-/l*
810×frac-times
668×times-frac
466×add-cube-cbrt
360×associate-/r*
355×associate-/l/
311×difference-of-squares
278×distribute-lft-out--
248×distribute-lft-out
222×sqrt-prod
158×associate-*l*
103×associate-*r*
90×clear-num
88×frac-2neg
74×unpow-prod-down distribute-rgt-neg-in sqr-pow
56×flip3-+ flip-+
54×associate-*r/
41×add-exp-log
38×associate-/r/
27×add-cbrt-cube
26×unswap-sqr
23×div-inv
21×flip3-- flip--
18×div-exp
15×associate-*l/
10×cbrt-undiv prod-exp add-log-exp
6×pow1 un-div-inv cbrt-unprod
4×*-commutative
3×diff-log swap-sqr
2×sub-neg rec-exp 1-exp
1×associate--l- neg-sub0 associate-+l- div-sub pow-prod-down neg-log
Counts
4 → 1145
Calls
4 calls:
38.0ms
(- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1)))
25.0ms
(- (* b b) (* (* 4.0 a) c))
47.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) a)
168.0ms
(* (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) a) (/ (/ 1 (- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1)))) 2.0))

series288.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1)))
51.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) a)
141.0ms
(* (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) a) (/ (/ 1 (- (- b) (sqrt (pow (- (* b b) (* (* 4.0 a) c)) 1)))) 2.0))

simplify338.0ms

Algorithm
egg-herbie
Counts
1157 → 1157
Iterations

Useful iterations: 1 (72.0ms)

IterNodesCost
0389329363
1500227531

prune1.8s

Filtered
1157 candidates to 397 candidates (65.7%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New115431157
Fresh325
Picked011
Done011
Total115771164

Merged error: 0b

Counts
1164 → 7

regimes130.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03218
13218

end0.0ms

sample1.7s

Algorithm
intervals
Results
386.0ms3646×body320valid
315.0ms16479×pre80true
284.0ms8479×body80nan
205.0ms2922×body160valid
70.0ms501×body640valid
33.0ms931×body80valid