Details

Time bar (total: 4.6s)

sample38.0ms

Algorithm
intervals
Results
8.0ms201×body80valid
6.0ms31×body1280valid
5.0ms21×body2560valid
4.0ms103×body80nan
2.0ms13×body640valid
1.0ms3×body5120valid
1.0ms7×body320valid
0.0ms5×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-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 neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
33.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms
(+ (- 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)))

series301.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms
(- (* b b) (* (* 4.0 a) c))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify48.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0438854
11702750
25001735

prune278.0ms

Filtered
102 candidates to 82 candidates (80.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0) a)
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
117×times-frac
116×*-un-lft-identity
65×add-sqr-sqrt
64×add-cube-cbrt
26×distribute-lft-out
19×associate-/l*
16×distribute-rgt-neg-in
10×fma-def add-log-exp
9×add-exp-log add-cbrt-cube
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv distribute-lft-neg-in div-exp associate-/r* sqrt-prod
2×neg-sub0 associate-+l- flip3-- sqrt-div div-sub sum-log flip--
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff neg-log clear-num flip-+ associate-/l/
Counts
4 → 157
Calls
4 calls:
37.0ms
(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0) a)
12.0ms
(+ (- 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)))

series311.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0) a)
76.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
55.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify67.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
06462036
124951928
250011904

prune394.0ms

Filtered
169 candidates to 121 candidates (71.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-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 neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
33.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
16.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series302.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
86.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
45.0ms
(- (* b b) (* (* 4.0 a) c))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0438854
11702750
25001735

prune248.0ms

Filtered
102 candidates to 79 candidates (77.5%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (* (/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)) 2.0))
1.0b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.2b
(- (* b b) (* (* 4.0 a) c))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
25×add-exp-log
23×*-un-lft-identity
21×add-cube-cbrt
19×prod-diff
16×sqrt-prod
13×add-cbrt-cube
9×div-exp
8×pow1 add-log-exp
7×fma-neg
6×prod-exp
4×cbrt-undiv expm1-log1p-u log1p-expm1-u
3×rec-exp flip3-- times-frac 1-exp flip-- associate-/l*
2×sub-neg pow-flip sqrt-div diff-log cbrt-unprod difference-of-squares
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*l/ clear-num associate-/r* associate-/r/ div-inv distribute-lft-out-- inv-pow
Counts
4 → 109
Calls
4 calls:
28.0ms
(/ 1 (* (/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)) 2.0))
21.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series323.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ 1 (* (/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)) 2.0))
76.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
42.0ms
(- (* b b) (* (* 4.0 a) c))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify62.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04811250
11985982
25001949

prune236.0ms

Filtered
121 candidates to 74 candidates (61.2%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.4b

regimes279.0ms

Accuracy

87.2% (3.7b remaining)

Error of 9.2b against oracle of 5.5b and baseline of 34.1b

bsearch165.0ms

Steps
ItersRangePoint
2
3.9431530817676045e+109
4.557375181159837e+109
4.019930844191633e+109
10
9.294290849485744e-131
6.48544897696183e-121
1.9238883452280037e-130
10
-1.5405955983178716e+163
-1.402598515452623e+153
-2.3044033969831823e+153

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04628
14828
24828

end0.0ms

sample1.2s

Algorithm
intervals
Results
260.0ms1101×body2560valid
248.0ms5850×body80valid
173.0ms921×body1280valid
109.0ms2888×body80nan
70.0ms450×body640valid
29.0ms103×body5120valid
27.0ms228×body320valid
9.0ms121×body160valid