Details

Time bar (total: 6.5s)

sample52.0ms

Algorithm
intervals
Results
14.0ms169×body160valid
9.0ms489×pre80true
8.0ms233×body80nan
3.0ms31×body320valid
2.0ms56×body80valid

simplify10.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b
(- (* b b) (* (* 4.0 a) c))
38.7b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite55.0ms

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)))
36.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
2.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series372.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
150.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
47.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0405779
11563685
25002674

prune190.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

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:
14.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0ms
(- (* b b) (* (* 4.0 a) c))
42.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
26.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series462.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms
(- (* b b) (* (* 4.0 a) c))
152.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
184.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify116.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
06422664
131752400
250032388

prune434.0ms

Filtered
163 candidates to 106 candidates (65.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
0.4b
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
0.6b
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
130×add-sqr-sqrt times-frac
118×pow1
92×*-un-lft-identity
66×pow-prod-down
56×add-exp-log add-cbrt-cube
52×add-cube-cbrt
42×difference-of-squares
39×associate-/l*
29×prod-exp cbrt-unprod
20×sqrt-prod distribute-lft-out--
12×associate-/r*
10×distribute-rgt-neg-in
9×pow-sqr pow-prod-up
8×cbrt-undiv div-exp associate-/r/
5×div-inv associate-/l/
4×unpow-prod-down flip3-- flip-- add-log-exp sqr-pow
3×frac-2neg pow-plus clear-num
2×flip3-+ flip-+
1×pow2 div-sub swap-sqr associate-*r* associate-*l* *-commutative
Counts
4 → 235
Calls
4 calls:
112.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
74.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
19.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
30.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series555.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
234.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
92.0ms
(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
41.0ms
(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify73.0ms

Algorithm
egg-herbie
Counts
247 → 247
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09935277
150014702

prune716.0ms

Filtered
247 candidates to 145 candidates (58.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (pow b 2) (* 4.0 (* a c)))
0.2b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (+ (pow b 2) (* 4.0 (* a c))) (/ (- (pow b 2) (* 4.0 (* a c))) (+ (* b b) (* (* 4.0 a) c))))))) (* 2.0 a))
0.3b
(/ (- (pow b 2) (* 4.0 (* a c))) (+ (* b b) (* (* 4.0 a) c)))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (+ (pow b 2) (* 4.0 (* a c))) (/ (- (pow b 2) (* 4.0 (* a c))) (+ (* b b) (* (* 4.0 a) c)))))))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
87×times-frac
83×*-un-lft-identity
63×add-sqr-sqrt
43×add-cube-cbrt
30×associate-/l*
20×add-exp-log add-cbrt-cube distribute-lft-out--
10×distribute-rgt-neg-in associate-/r* difference-of-squares
8×cbrt-undiv div-exp associate-/r/
6×add-log-exp
5×flip3-- flip-- div-inv associate-/l/
4×pow1
3×frac-2neg clear-num
2×flip3-+ prod-exp cbrt-unprod flip-+
1×sub-neg diff-log div-sub
Counts
4 → 155
Calls
4 calls:
7.0ms
(- (pow b 2) (* 4.0 (* a c)))
30.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (+ (pow b 2) (* 4.0 (* a c))) (/ (- (pow b 2) (* 4.0 (* a c))) (+ (* b b) (* (* 4.0 a) c))))))) (* 2.0 a))
19.0ms
(/ (- (pow b 2) (* 4.0 (* a c))) (+ (* b b) (* (* 4.0 a) c)))
17.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (+ (pow b 2) (* 4.0 (* a c))) (/ (- (pow b 2) (* 4.0 (* a c))) (+ (* b b) (* (* 4.0 a) c)))))))

series432.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (pow b 2) (* 4.0 (* a c)))
155.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (+ (pow b 2) (* 4.0 (* a c))) (/ (- (pow b 2) (* 4.0 (* a c))) (+ (* b b) (* (* 4.0 a) c))))))) (* 2.0 a))
40.0ms
(/ (- (pow b 2) (* 4.0 (* a c))) (+ (* b b) (* (* 4.0 a) c)))
187.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (+ (pow b 2) (* 4.0 (* a c))) (/ (- (pow b 2) (* 4.0 (* a c))) (+ (* b b) (* (* 4.0 a) c)))))))

simplify139.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 2 (104.0ms)

IterNodesCost
07464282
138273831
250013806

prune754.0ms

Filtered
167 candidates to 120 candidates (71.9%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes138.0ms

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
03423
13823
23823

end0.0ms

sample1.5s

Algorithm
intervals
Results
341.0ms4813×body160valid
316.0ms16514×pre80true
285.0ms8514×body80nan
138.0ms1340×body320valid
67.0ms1847×body80valid