Details

Time bar (total: 4.1s)

sample43.0ms

Algorithm
intervals
Results
7.0ms189×body80valid
6.0ms34×body1280valid
6.0ms28×body2560valid
6.0ms92×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
0249
1459
2799
3979
41059
51059

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(- (* b b) (* (* 4.0 a) c))
25.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

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:
11.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series310.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
76.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(- (* b b) (* (* 4.0 a) c))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify47.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0405779
11563685
25001674

prune365.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(- (* b b) (* (* 4.0 a) c))
25.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
53×times-frac
45×*-un-lft-identity
26×add-sqr-sqrt
25×add-exp-log add-cube-cbrt
13×add-cbrt-cube
12×div-exp
11×associate-/r*
10×distribute-lft-out add-log-exp
9×associate-/r/
6×pow1
5×cbrt-undiv distribute-rgt-neg-in flip3-+ flip-+ div-inv
3×rec-exp 1-exp prod-exp sqrt-prod associate-/l*
2×flip3-- sqrt-div sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 diff-log neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 114
Calls
4 calls:
16.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
75.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms
(- (* b b) (* (* 4.0 a) c))
65.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify67.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05251588
125701375
250011308

prune252.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 (* 2.0 a)) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
1.1b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b
(- (* b b) (* (* 4.0 a) c))
25.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
16×*-un-lft-identity
13×add-cbrt-cube
11×add-sqr-sqrt
10×prod-exp add-log-exp
8×add-cube-cbrt
7×pow1 associate-*l*
5×associate-*r*
4×div-exp cbrt-unprod distribute-lft-out
3×flip3-+ times-frac sqrt-prod flip-+
2×cbrt-undiv frac-times rec-exp flip3-- distribute-rgt-neg-in sqrt-div 1-exp associate-*r/ sum-log flip--
1×+-commutative neg-sub0 distribute-rgt-in associate-+l- sub-neg rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 diff-log pow-prod-down neg-log associate-*l/ *-commutative div-inv unswap-sqr
Counts
4 → 81
Calls
4 calls:
17.0ms
(* (/ 1 (* 2.0 a)) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series322.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(* (/ 1 (* 2.0 a)) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
76.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms
(- (* b b) (* (* 4.0 a) c))
65.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify64.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
0509923
12707795
25001787

prune222.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.8b

localize14.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (* b b) (* (* 4.0 a) c))
25.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
25.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

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

series223.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 4.0 a) c))
43.0ms
(- (* b b) (* (* 4.0 a) c))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify79.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (73.0ms)

IterNodesCost
0149476
1576446
22486444
35001440

prune209.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.8b

regimes215.0ms

Accuracy

85% (4.3b remaining)

Error of 10.0b against oracle of 5.7b and baseline of 34.2b

bsearch96.0ms

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
03716
13716

end0.0ms

sample1.1s

Algorithm
intervals
Results
250.0ms1050×body2560valid
228.0ms5875×body80valid
173.0ms905×body1280valid
103.0ms2863×body80nan
68.0ms457×body640valid
28.0ms99×body5120valid
23.0ms212×body320valid
10.0ms128×body160valid