Details

Time bar (total: 9.0s)

sample74.0ms

Algorithm
intervals
Results
14.0ms270×body80nan
14.0ms114×body320valid
12.0ms526×pre80true
8.0ms105×body160valid
2.0ms15×body640valid
1.0ms22×body80valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

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: 54.5b

Counts
2 → 1

localize11.0ms

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))
28.2b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite149.0ms

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:
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.0ms
(- (* b b) (* (* 4.0 a) c))
41.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
51.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series326.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
46.0ms
(- (* b b) (* (* 4.0 a) c))
117.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
89.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify74.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
06212253
124432157
250022140

prune258.0ms

Filtered
190 candidates to 109 candidates (57.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1864190
Fresh000
Picked101
Done000
Total1874191

Merged error: 0.1b

Counts
191 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* 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)))))

rewrite344.0ms

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:
35.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
26.0ms
(- (* b b) (* (* 4.0 a) c))
108.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
86.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series446.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms
(- (* b b) (* (* 4.0 a) c))
138.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
175.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify255.0ms

Algorithm
egg-herbie
Counts
908 → 908
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0173224064
1500122943

prune1.1s

Filtered
908 candidates to 285 candidates (31.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New9044908
Fresh213
Picked101
Done000
Total9075912

Merged error: 0b

Counts
912 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) 1) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite301.0ms

Algorithm
rewrite-expression-head
Rules
1381×*-un-lft-identity
1217×times-frac
783×add-sqr-sqrt
578×associate-*l*
437×add-cube-cbrt
328×distribute-lft-out
270×associate-*r*
226×distribute-lft-out--
126×unswap-sqr
71×difference-of-squares
57×*-commutative
39×add-exp-log
32×associate-/l*
30×add-cbrt-cube
29×associate-/r*
28×distribute-rgt-neg-in sqrt-prod div-inv
17×associate-/l/
15×div-exp
12×prod-exp
10×add-log-exp
9×pow1 cbrt-undiv cbrt-unprod
4×sub-neg flip3-- associate-*r/ flip--
3×diff-log 1-exp swap-sqr pow-prod-down
2×distribute-rgt-in frac-2neg distribute-lft-in div-sub clear-num associate-/r/
1×associate--l- neg-sub0 associate-+l- flip3-+ neg-log flip-+
Counts
4 → 836
Calls
4 calls:
36.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.0ms
(- (* b b) (* (* 4.0 a) c))
113.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) 1) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series527.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
113.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
51.0ms
(- (* b b) (* (* 4.0 a) c))
282.0ms
(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) 1) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify237.0ms

Algorithm
egg-herbie
Counts
848 → 848
Iterations

Useful iterations: 1 (45.0ms)

IterNodesCost
0229621343
1500120056

prune948.0ms

Filtered
848 candidates to 252 candidates (29.7%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New8471848
Fresh134
Picked011
Done000
Total8485853

Merged error: 0b

Counts
853 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ (* 4.0 (* a c)) 0) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 1))
0.3b
(* (/ 1 (* 2.0 a)) (/ (+ (* 4.0 (* a c)) 0) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 1)))

rewrite328.0ms

Algorithm
rewrite-expression-head
Rules
683×*-un-lft-identity
680×add-sqr-sqrt
676×associate-/r*
486×frac-times
407×associate-*l*
283×add-cube-cbrt
274×associate-*r*
237×times-frac
187×associate-/l*
147×unswap-sqr
115×add-exp-log
110×distribute-lft-out
77×difference-of-squares
68×distribute-lft-out--
65×*-commutative
56×prod-exp
49×clear-num
48×frac-2neg
45×add-cbrt-cube
40×div-exp associate-/l/
31×distribute-rgt-neg-in sqrt-prod
27×associate-*r/
22×associate-*l/
20×flip3-+ flip-+
16×1-exp cbrt-unprod
14×cbrt-undiv
10×add-log-exp
8×rec-exp
6×pow1
4×flip3-- associate-/r/ un-div-inv flip--
3×diff-log swap-sqr div-inv
2×sub-neg
1×associate--l- neg-sub0 pow-prod-down neg-log
Counts
4 → 909
Calls
4 calls:
34.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0ms
(- (* b b) (* (* 4.0 a) c))
62.0ms
(/ (+ (* 4.0 (* a c)) 0) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 1))
138.0ms
(* (/ 1 (* 2.0 a)) (/ (+ (* 4.0 (* a c)) 0) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 1)))

series480.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms
(- (* b b) (* (* 4.0 a) c))
195.0ms
(/ (+ (* 4.0 (* a c)) 0) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 1))
155.0ms
(* (/ 1 (* 2.0 a)) (/ (+ (* 4.0 (* a c)) 0) (* (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 1)))

simplify232.0ms

Algorithm
egg-herbie
Counts
921 → 921
Iterations

Useful iterations: 1 (70.0ms)

IterNodesCost
0347216312
1500115536

prune1.1s

Filtered
921 candidates to 337 candidates (36.6%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New9210921
Fresh033
Picked011
Done011
Total9215926

Merged error: 0b

Counts
926 → 5

regimes89.0ms

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
03217
13217

end0.0ms

sample1.6s

Algorithm
intervals
Results
398.0ms3613×body320valid
297.0ms15982×pre80true
272.0ms7982×body80nan
217.0ms2985×body160valid
74.0ms513×body640valid
34.0ms889×body80valid