Details

Time bar (total: 5.6s)

sample37.0ms

Algorithm
intervals
Results
15.0ms288×body80valid
4.0ms96×body80nan

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03518
16618
211618
314418
415918
516118
616118

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.5b

localize87.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
27.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-sqr-sqrt add-log-exp
7×sqrt-prod
6×pow1 add-cube-cbrt
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 63
Calls
4 calls:
21.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series266.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
63.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
64.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify113.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (106.0ms)

IterNodesCost
0246646
1890606
23702588
35001584

prune280.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 10.7b

localize92.0ms

Local error

Found 4 expressions with local error:

1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0b
(/ (* a c) b)
5.1b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
27.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
13×*-un-lft-identity
10×add-sqr-sqrt
9×add-cube-cbrt
8×add-log-exp
6×times-frac associate-/r*
5×pow1
4×cbrt-undiv div-exp
3×sqrt-prod
2×flip3-- frac-2neg sqrt-div prod-exp clear-num sum-log associate-/r/ flip-- cbrt-unprod div-inv distribute-lft-out associate-/l*
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 74
Calls
4 calls:
23.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(/ (* a c) b)
32.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series214.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms
(/ (* a c) b)
63.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
61.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify54.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0459640
12217559
25001554

prune330.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.5b

localize99.0ms

Local error

Found 4 expressions with local error:

1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.7b
(* (/ a (sqrt b)) (/ c (pow b 1/2)))
2.7b
(/ (* 2.0 c) (- (* 2.0 (* (/ a (sqrt b)) (/ c (pow b 1/2)))) (* 2 b)))
27.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
73×add-sqr-sqrt
59×times-frac
38×*-un-lft-identity
34×add-cube-cbrt
33×add-exp-log
25×associate-*r*
22×associate-*l*
21×add-cbrt-cube
16×sqrt-prod
12×unpow-prod-down div-exp unswap-sqr
9×prod-exp
8×add-log-exp
7×pow1
6×cbrt-undiv sqr-pow
5×cbrt-unprod
3×associate-/r* div-inv
2×pow-to-exp flip3-- sqrt-div pow-exp sum-log associate-/r/ flip-- distribute-lft-out
1×+-commutative neg-sub0 frac-times associate-+l- rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 136
Calls
4 calls:
21.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
36.0ms
(* (/ a (sqrt b)) (/ c (pow b 1/2)))
82.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (sqrt b)) (/ c (pow b 1/2)))) (* 2 b)))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series368.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms
(* (/ a (sqrt b)) (/ c (pow b 1/2)))
190.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (sqrt b)) (/ c (pow b 1/2)))) (* 2 b)))
62.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify112.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (99.0ms)

IterNodesCost
09181365
146041210
250011167

prune661.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.5b

localize96.0ms

Local error

Found 4 expressions with local error:

2.7b
(* (/ a (sqrt b)) (/ c (pow b 1/2)))
2.7b
(/ (* 2.0 c) (- (* 2.0 (* (/ a (sqrt b)) (/ c (pow b 1/2)))) (* 2 b)))
4.8b
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
5.0b
(/ (* a c) b)

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
75×add-sqr-sqrt
65×times-frac
43×add-exp-log
37×add-cube-cbrt *-un-lft-identity
31×add-cbrt-cube
25×associate-*r*
22×associate-*l*
16×div-exp
13×sqrt-prod
12×unpow-prod-down unswap-sqr
11×prod-exp
10×cbrt-undiv
7×associate-/r* cbrt-unprod
6×pow1 sqr-pow
5×div-inv associate-/l*
4×add-log-exp
3×frac-2neg clear-num
2×pow-to-exp flip3-- pow-exp associate-/r/ flip-- associate-/l/
1×frac-times div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 151
Calls
4 calls:
37.0ms
(* (/ a (sqrt b)) (/ c (pow b 1/2)))
80.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (sqrt b)) (/ c (pow b 1/2)))) (* 2 b)))
49.0ms
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
9.0ms
(/ (* a c) b)

series323.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (/ a (sqrt b)) (/ c (pow b 1/2)))
184.0ms
(/ (* 2.0 c) (- (* 2.0 (* (/ a (sqrt b)) (/ c (pow b 1/2)))) (* 2 b)))
75.0ms
(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
18.0ms
(/ (* a c) b)

simplify47.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
09821424
150021153

prune581.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.6b

regimes285.0ms

Accuracy

88.4% (1.9b remaining)

Error of 7.6b against oracle of 5.7b and baseline of 22.4b

bsearch148.0ms

Steps
ItersRangePoint
6
4.231934083523606e+52
2.717919616353272e+53
1.9001138837826174e+53
9
-4.3398659734944224e+136
-6.188138656270848e+129
-4.2975228517561493e+130

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05734
15734

end0.0ms

sample940.0ms

Algorithm
intervals
Results
454.0ms8769×body80valid
132.0ms2813×body80nan