Details

Time bar (total: 5.8s)

sample64.0ms

Algorithm
intervals
Results
12.0ms34×body2560valid
12.0ms186×body80valid
8.0ms25×body1280valid
5.0ms88×body80nan
3.0ms14×body640valid
3.0ms13×body320valid
1.0ms2×body5120valid
0.0ms2×body160valid

simplify18.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0299
1659
21219
31519
41609
51649
61649

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b
(- (* b b) (* 4.0 (* a c)))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 157
Calls
4 calls:
45.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
17.0ms
(- (- 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))))

series291.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
48.0ms
(- (* b b) (* 4.0 (* a c)))
68.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify76.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05903305
121012212
250022128

prune356.0ms

Filtered
169 candidates to 89 candidates (52.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b
(- (* b b) (* 4.0 (* a c)))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
88×*-un-lft-identity
68×add-cube-cbrt
67×times-frac
61×prod-diff
38×sqrt-prod
26×distribute-rgt-neg-in
25×add-exp-log
21×distribute-lft-neg-in
13×associate-/r* add-cbrt-cube
12×div-exp
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
7×neg-mul-1 flip3-- flip--
6×pow1
5×cbrt-undiv div-inv
4×expm1-log1p-u log1p-expm1-u
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 205
Calls
4 calls:
26.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
16.0ms
(- (- 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:
113.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
81.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
49.0ms
(- (* b b) (* 4.0 (* a c)))
67.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify102.0ms

Algorithm
egg-herbie
Counts
217 → 217
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
07184222
130992976
250012863

prune559.0ms

Filtered
217 candidates to 98 candidates (45.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b
(- (* b b) (* 4.0 (* a c)))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 157
Calls
4 calls:
47.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
17.0ms
(- (- 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))))

series285.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms
(- (* b b) (* 4.0 (* a c)))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify80.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05903305
121012212
250022128

prune307.0ms

Filtered
169 candidates to 89 candidates (52.7%)
Pruning

10 alts after pruning (10 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)))))))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b
(- (* b b) (* 4.0 (* a c)))
24.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
897×times-frac
569×add-sqr-sqrt
568×*-un-lft-identity
396×add-cube-cbrt
86×distribute-lft-out-- difference-of-squares
76×sqrt-prod
64×distribute-rgt-neg-in
61×prod-diff
43×div-inv
29×associate-/r/
27×associate-/r*
26×add-exp-log
21×distribute-lft-neg-in
17×flip3-- flip--
16×div-exp add-cbrt-cube
13×associate-/l*
11×fma-neg
10×add-log-exp
8×cbrt-undiv
7×neg-mul-1
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×diff-log
2×sub-neg rec-exp sqrt-div 1-exp
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/l/
Counts
4 → 540
Calls
4 calls:
35.0ms
(/ (/ 1 2.0) (/ a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
16.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series302.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ (/ 1 2.0) (/ a (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify133.0ms

Algorithm
egg-herbie
Counts
552 → 552
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0197312206
1500110897

prune940.0ms

Filtered
552 candidates to 242 candidates (43.8%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.9b

regimes314.0ms

Accuracy

83.6% (4.7b remaining)

Error of 10.5b against oracle of 5.8b and baseline of 34.3b

bsearch93.0ms

Steps
ItersRangePoint
5
1.1874868645648804e+84
3.824179182553312e+84
2.4992282662840617e+84
9
-6.219842315709727e-116
-4.3103875869831393e-125
-4.4270058556435274e-117

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03516
13516

end0.0ms

sample1.2s

Algorithm
intervals
Results
253.0ms1089×body2560valid
230.0ms5868×body80valid
162.0ms894×body1280valid
110.0ms2862×body80nan
66.0ms441×body640valid
32.0ms105×body5120valid
23.0ms212×body320valid
9.0ms116×body160valid