Details

Time bar (total: 3.8s)

sample38.0ms

Algorithm
intervals
Results
7.0ms189×body80valid
6.0ms34×body1280valid
6.0ms28×body2560valid
3.0ms92×body80nan
2.0ms16×body640valid
2.0ms7×body5120valid
0.0ms4×body160valid
0.0ms2×body320valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0219
1429
2769
3949
41029
51029

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.1b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.4b
(- (* b b) (* (* 3.0 a) c))
25.1b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite30.0ms

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:
14.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
7.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms
(- (* b b) (* (* 3.0 a) c))
3.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series316.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
51.0ms
(- (* b b) (* (* 3.0 a) c))
72.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify48.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0400780
11529686
25002675

prune226.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
1.1b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.4b
(- (* b b) (* (* 3.0 a) c))
25.1b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 *-un-lft-identity add-log-exp
9×add-exp-log add-cbrt-cube
7×add-sqr-sqrt
6×add-cube-cbrt
3×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×flip3-- sqrt-div sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 diff-log associate-*l* neg-log *-commutative flip-+
Counts
4 → 60
Calls
4 calls:
5.0ms
(* (* 3.0 a) c)
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series219.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (* 3.0 a) c)
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
49.0ms
(- (* b b) (* (* 3.0 a) c))
68.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify41.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0307469
11303428
25001417

prune180.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (* 3.0 a))
1.1b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.4b
(- (* b b) (* (* 3.0 a) c))
25.1b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
15×add-exp-log
11×*-un-lft-identity
10×add-log-exp
9×add-cbrt-cube
8×pow1 add-sqr-sqrt
7×add-cube-cbrt
4×div-exp
3×times-frac prod-exp sqrt-prod associate-/l*
2×cbrt-undiv rec-exp flip3-- pow-flip sqrt-div 1-exp sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log pow-prod-down neg-log clear-num associate-/r* cbrt-unprod flip-+ div-inv inv-pow
Counts
4 → 70
Calls
4 calls:
4.0ms
(/ 1 (* 3.0 a))
7.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms
(- (* b b) (* (* 3.0 a) c))
7.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series214.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ 1 (* 3.0 a))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
45.0ms
(- (* b b) (* (* 3.0 a) c))
72.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify40.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0338493
11380446
25001430

prune192.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.9b

localize14.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* (* 3.0 a) c))
1.4b
(- (* b b) (* (* 3.0 a) c))
25.1b
(sqrt (- (* b b) (* (* 3.0 a) c)))
25.1b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 54
Calls
4 calls:
3.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series242.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* (* 3.0 a) c))
50.0ms
(- (* b b) (* (* 3.0 a) c))
69.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
74.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify80.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (74.0ms)

IterNodesCost
0149476
1576446
22486444
35001440

prune218.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 6.9b

regimes424.0ms

Accuracy

85.3% (4.2b remaining)

Error of 10.1b against oracle of 5.9b and baseline of 34.3b

bsearch94.0ms

Steps
ItersRangePoint
7
1.9426594712364374e-87
2.1051237392284573e-85
1.667046824505827e-85
8
-3.734333779790662e+128
-2.2987999557012895e+125
-5.238946631357967e+127

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03416
13416

end0.0ms

sample1.1s

Algorithm
intervals
Results
222.0ms1050×body2560valid
220.0ms5876×body80valid
166.0ms905×body1280valid
95.0ms2862×body80nan
62.0ms459×body640valid
26.0ms98×body5120valid
22.0ms215×body320valid
8.0ms122×body160valid