Details

Time bar (total: 4.3s)

sample38.0ms

Algorithm
intervals
Results
8.0ms39×body2560valid
6.0ms36×body1280valid
6.0ms165×body80valid
3.0ms86×body80nan
2.0ms13×body640valid
1.0ms8×body320valid
1.0ms2×body5120valid
0.0ms4×body160valid

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: 33.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
1.0b
(- (* b b) (* (* 3.0 a) c))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.6b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite30.0ms

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:
10.0ms
(* (* 3.0 a) c)
3.0ms
(- (* b b) (* (* 3.0 a) c))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series213.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (* 3.0 a) c)
47.0ms
(- (* b b) (* (* 3.0 a) c))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
69.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify42.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0307469
11303428
25001417

prune187.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 3.0 (* a c))
1.0b
(- (* b b) (pow (* 3.0 (* a c)) 1))
1.4b
(+ (- b) (sqrt (- (* b b) (pow (* 3.0 (* a c)) 1))))
22.6b
(sqrt (- (* b b) (pow (* 3.0 (* a c)) 1)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 *-un-lft-identity add-log-exp
9×add-exp-log add-sqr-sqrt add-cbrt-cube
6×add-cube-cbrt
5×sqrt-prod
4×difference-of-squares
3×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×flip3-- sqrt-div sum-log flip-- distribute-lft-out sqr-pow
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r* neg-log *-commutative flip-+
Counts
4 → 64
Calls
4 calls:
6.0ms
(* 3.0 (* a c))
4.0ms
(- (* b b) (pow (* 3.0 (* a c)) 1))
24.0ms
(+ (- b) (sqrt (- (* b b) (pow (* 3.0 (* a c)) 1))))
10.0ms
(sqrt (- (* b b) (pow (* 3.0 (* a c)) 1)))

series224.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* 3.0 (* a c))
43.0ms
(- (* b b) (pow (* 3.0 (* a c)) 1))
79.0ms
(+ (- b) (sqrt (- (* b b) (pow (* 3.0 (* a c)) 1))))
78.0ms
(sqrt (- (* b b) (pow (* 3.0 (* a c)) 1)))

simplify39.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0316556
11196502
25002494

prune204.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt 3.0) (* (sqrt 3.0) (* a c)))
1.0b
(- (* b b) (pow (* (sqrt 3.0) (* (sqrt 3.0) (* a c))) 1))
1.4b
(+ (- b) (sqrt (- (* b b) (pow (* (sqrt 3.0) (* (sqrt 3.0) (* a c))) 1))))
22.6b
(sqrt (- (* b b) (pow (* (sqrt 3.0) (* (sqrt 3.0) (* a c))) 1)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1
13×add-exp-log add-cbrt-cube
11×*-un-lft-identity
10×add-sqr-sqrt add-log-exp
8×sqrt-prod
7×add-cube-cbrt
6×associate-*l* pow-prod-down prod-exp cbrt-unprod
4×difference-of-squares
2×flip3-- sqrt-div sum-log flip-- distribute-lft-out sqr-pow
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r* neg-log *-commutative flip-+
Counts
4 → 70
Calls
4 calls:
21.0ms
(* (sqrt 3.0) (* (sqrt 3.0) (* a c)))
4.0ms
(- (* b b) (pow (* (sqrt 3.0) (* (sqrt 3.0) (* a c))) 1))
16.0ms
(+ (- b) (sqrt (- (* b b) (pow (* (sqrt 3.0) (* (sqrt 3.0) (* a c))) 1))))
6.0ms
(sqrt (- (* b b) (pow (* (sqrt 3.0) (* (sqrt 3.0) (* a c))) 1)))

series650.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(* (sqrt 3.0) (* (sqrt 3.0) (* a c)))
121.0ms
(- (* b b) (pow (* (sqrt 3.0) (* (sqrt 3.0) (* a c))) 1))
224.0ms
(+ (- b) (sqrt (- (* b b) (pow (* (sqrt 3.0) (* (sqrt 3.0) (* a c))) 1))))
226.0ms
(sqrt (- (* b b) (pow (* (sqrt 3.0) (* (sqrt 3.0) (* a c))) 1)))

simplify48.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0367849
11531703
25002690

prune240.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 14.3b

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.6b
(sqrt (- (* b b) (* (* 3.0 a) c)))
22.6b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-log-exp
8×add-sqr-sqrt
6×pow1 add-cube-cbrt sqrt-prod
4×add-exp-log sqrt-div sum-log add-cbrt-cube distribute-lft-out
2×+-commutative neg-sub0 associate-+l- rem-sqrt-square flip3-- distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 neg-log flip-- flip-+
Counts
4 → 60
Calls
4 calls:
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
15.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series311.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
81.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify99.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (93.0ms)

IterNodesCost
0217598
1808556
23289534
35001530

prune239.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 14.3b

regimes303.0ms

Accuracy

95.4% (1.0b remaining)

Error of 13.1b against oracle of 12.1b and baseline of 33.8b

bsearch191.0ms

Steps
ItersRangePoint
8
2.1878188410446244e+107
3.8616146939177386e+111
5.80649981292105e+110
9
2.365685850767504e-168
1.2053288471691685e-161
1.7270734494037783e-162
10
-2.699314103090194e+180
-2.227381996671495e+165
-2.272454186637281e+165

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05539
16139
26139

end0.0ms

sample1.0s

Algorithm
intervals
Results
210.0ms1025×body2560valid
209.0ms5915×body80valid
156.0ms893×body1280valid
101.0ms2995×body80nan
59.0ms447×body640valid
27.0ms107×body5120valid
21.0ms210×body320valid
7.0ms103×body160valid