Details

Time bar (total: 5.1s)

sample187.0ms

Algorithm
intervals
Results
147.0ms265×body80nan
10.0ms521×pre80true
9.0ms128×body160valid
4.0ms128×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

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.3b
(- (* b b) (* (* 4.0 a) c))
25.2b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite56.0ms

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)))
37.0ms
(/ (+ (- 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))))

series303.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
107.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
44.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify47.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0405779
11563685
25002674

prune209.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (* b b) (* (* 4.0 a) c))
0.3b
(- (- 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)))))

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:
2.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(/ (/ (+ 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)))))

series456.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* (* 4.0 a) c))
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
151.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
181.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify119.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
06422664
131752400
250032388

prune441.0ms

Filtered
163 candidates to 106 candidates (65.0%)
Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
54×add-exp-log add-cbrt-cube
25×prod-exp cbrt-unprod
16×add-sqr-sqrt
14×*-un-lft-identity
12×cbrt-undiv div-exp
10×add-log-exp
7×associate-*r*
6×pow1 add-cube-cbrt
5×associate-*l*
4×sub-neg flip3-- flip-- distribute-lft-out-- difference-of-squares
3×diff-log
2×distribute-rgt-in frac-times distribute-rgt-neg-in distribute-lft-in times-frac associate-*r/ sqrt-prod div-inv
1×associate--l- neg-sub0 frac-2neg pow-prod-down neg-log associate-*l/ clear-num associate-/r* *-commutative associate-/l* unswap-sqr
Counts
4 → 100
Calls
4 calls:
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
2.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
66.0ms
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series226.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
49.0ms
(- (* b b) (* (* 4.0 a) c))
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
86.0ms
(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify109.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
06031333
139971032
250011002

prune290.0ms

Filtered
112 candidates to 66 candidates (58.9%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b
(- (* b b) (* (* 4.0 a) c))
0.3b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b
(* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
327×add-exp-log
174×div-exp
136×prod-exp
78×add-cbrt-cube
66×1-exp
36×rec-exp
31×times-frac
30×cbrt-undiv
27×add-sqr-sqrt *-un-lft-identity cbrt-unprod
22×frac-times
19×add-cube-cbrt
14×associate-*l/ associate-/r/
13×associate-/l*
12×flip3-- flip--
10×associate-*r/ add-log-exp
9×pow1
7×associate-*r*
6×un-div-inv
4×sub-neg distribute-lft-out-- difference-of-squares
3×diff-log pow-prod-down div-inv
2×distribute-rgt-in distribute-rgt-neg-in distribute-lft-in sqrt-prod
1×associate--l- neg-sub0 frac-2neg associate-*l* neg-log clear-num associate-/r* *-commutative associate-/l/
Counts
4 → 214
Calls
4 calls:
35.0ms
(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
2.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
52.0ms
(* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series415.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(/ (/ 1 1) (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
45.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
111.0ms
(* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify57.0ms

Algorithm
egg-herbie
Counts
226 → 226
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012753261
150012524

prune342.0ms

Filtered
226 candidates to 92 candidates (40.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes144.0ms

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
02111
12111

end0.0ms

sample1.4s

Algorithm
intervals
Results
305.0ms4404×body160valid
297.0ms16698×pre80true
288.0ms8698×body80nan
130.0ms3596×body80valid