Details

Time bar (total: 5.7s)

sample55.0ms

Algorithm
intervals
Results
12.0ms157×body160valid
10.0ms501×pre80true
8.0ms245×body80nan
5.0ms43×body320valid
2.0ms56×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 (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 45.6b

Counts
2 → 1

localize13.0ms

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))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
41.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-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 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series306.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms
(- (* b b) (* (* 4.0 a) c))
106.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify47.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0405779
11563685
25002674

prune197.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New77582
Fresh000
Picked101
Done000
Total78583

Merged error: 0.2b

Counts
83 → 5

localize21.0ms

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
(/ (/ (+ 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)))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
82×add-sqr-sqrt *-un-lft-identity
38×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
11×distribute-rgt-neg-in sqrt-prod
10×add-log-exp
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 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 → 151
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(/ (/ (+ 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)))))

series470.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
155.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
190.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify123.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
06422664
131752400
250032388

prune429.0ms

Filtered
163 candidates to 106 candidates (65.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1549163
Fresh314
Picked101
Done000
Total15810168

Merged error: 0.0b

Counts
168 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
0.5b
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
0.7b
(pow (- (* b b) (* (* 4.0 a) c)) 3)

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
166×add-sqr-sqrt
138×times-frac
96×*-un-lft-identity
60×difference-of-squares
56×add-cube-cbrt
52×cbrt-prod
50×sqrt-prod
42×associate-/l*
20×distribute-lft-out--
19×add-exp-log add-cbrt-cube
16×unpow-prod-down cube-prod
12×associate-/r* sqr-pow
10×distribute-rgt-neg-in
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×cube-div div-inv add-log-exp
3×pow-unpow associate-/l/
2×cube-mult cbrt-div frac-2neg unpow3 prod-exp clear-num cbrt-unprod
1×pow-to-exp pow-pow flip3-+ pow1/3 pow-exp rem-cbrt-cube flip-+ rem-cube-cbrt
Counts
4 → 209
Calls
4 calls:
29.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
19.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
5.0ms
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
5.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

series475.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
184.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
48.0ms
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
93.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

simplify169.0ms

Algorithm
egg-herbie
Counts
221 → 221
Iterations

Useful iterations: 2 (128.0ms)

IterNodesCost
08564185
144263809
250013728

prune606.0ms

Filtered
221 candidates to 128 candidates (57.9%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2156221
Fresh639
Picked101
Done000
Total2229231

Merged error: 0b

Counts
231 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
163×add-exp-log
89×add-cbrt-cube
73×prod-exp
56×div-exp
37×cbrt-unprod
28×cbrt-undiv
24×*-un-lft-identity
20×add-sqr-sqrt times-frac
18×add-cube-cbrt
12×associate-*l*
10×rec-exp 1-exp
7×pow1
6×associate-*l/ associate-/r* div-inv add-log-exp
4×distribute-lft-neg-in distribute-rgt-neg-in distribute-neg-frac associate-/l*
3×distribute-lft-neg-out flip3-+ associate-*r* flip-+ distribute-lft-out
2×frac-2neg clear-num associate-/l/
1×+-commutative neg-mul-1 pow-flip distribute-frac-neg pow-prod-down sum-log associate-/r/ *-commutative inv-pow unswap-sqr
Counts
4 → 152
Calls
4 calls:
6.0ms
(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(* (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
14.0ms
(/ (* (* (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))) a) 2.0) (* 4.0 (* a c)))
15.0ms
(/ 1 (/ (* (* (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))) a) 2.0) (* 4.0 (* a c))))

series383.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
91.0ms
(* (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
92.0ms
(/ (* (* (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))) a) 2.0) (* 4.0 (* a c)))
122.0ms
(/ 1 (/ (* (* (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))) a) 2.0) (* 4.0 (* a c))))

simplify136.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (114.0ms)

IterNodesCost
08282583
148522014
250011983

prune309.0ms

Filtered
164 candidates to 85 candidates (51.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1631164
Fresh178
Picked011
Done000
Total1649173

Merged error: 0b

Counts
173 → 9

regimes143.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03413
14313
24713
34713

end0.0ms

sample1.5s

Algorithm
intervals
Results
349.0ms4801×body160valid
303.0ms16220×pre80true
288.0ms8220×body80nan
153.0ms1369×body320valid
68.0ms1830×body80valid