Details

Time bar (total: 6.8s)

sample76.0ms

Algorithm
intervals
Results
16.0ms114×body320valid
14.0ms519×pre80true
13.0ms263×body80nan
9.0ms91×body160valid
3.0ms16×body640valid
2.0ms35×body80valid

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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 51.8b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
27.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite30.0ms

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:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
9.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series305.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
49.0ms
(- (* b b) (* (* 4.0 a) c))
108.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify57.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0438854
11702750
25002735

prune225.0ms

Filtered
102 candidates to 82 candidates (80.4%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New993102
Fresh000
Picked101
Done000
Total1003103

Merged error: 0.1b

Counts
103 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
123×add-sqr-sqrt *-un-lft-identity
90×times-frac
79×add-cube-cbrt
61×prod-diff
41×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
11×fma-neg
10×add-log-exp
8×associate-/r*
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 expm1-log1p-u log1p-expm1-u div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 231
Calls
4 calls:
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series456.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(- (* b b) (* (* 4.0 a) c))
179.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
148.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify162.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (118.0ms)

IterNodesCost
08325099
139673830
250013828

prune516.0ms

Filtered
243 candidates to 137 candidates (56.4%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2376243
Fresh112
Picked101
Done000
Total2397246

Merged error: 0b

Counts
246 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))))) (* 2.0 a))
0.3b
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
0.3b
(* (* a c) (fma b b (* (* 4.0 a) c)))
0.7b
(pow (* (* 4.0 a) c) 3)

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
115×add-sqr-sqrt
114×times-frac
77×*-un-lft-identity
45×add-cube-cbrt
42×difference-of-squares
40×associate-/l*
29×add-exp-log add-cbrt-cube
21×sqr-pow
16×distribute-lft-out--
15×pow1
12×sqrt-prod
9×unpow-prod-down
8×prod-exp cbrt-unprod
7×cbrt-undiv div-exp
6×distribute-rgt-neg-in pow-prod-down
4×expm1-log1p-u associate-/r* associate-/r/ log1p-expm1-u div-inv add-log-exp
3×pow-unpow flip3-- pow-pow associate-*r* pow-exp flip-- associate-/l/ rem-cube-cbrt
2×frac-2neg clear-num fma-udef
1×distribute-rgt-in cube-mult pow-to-exp distribute-lft-in unpow3 div-sub cube-prod associate-*l* *-commutative
Counts
4 → 191
Calls
4 calls:
37.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))))) (* 2.0 a))
18.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
5.0ms
(* (* a c) (fma b b (* (* 4.0 a) c)))
6.0ms
(pow (* (* 4.0 a) c) 3)

series475.0ms

Counts
4 → 12
Calls
4 calls:
222.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))))) (* 2.0 a))
129.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (fma 4.0 (* (* a c) (fma b b (* (* 4.0 a) c))) (pow b 4)))
65.0ms
(* (* a c) (fma b b (* (* 4.0 a) c)))
59.0ms
(pow (* (* 4.0 a) c) 3)

simplify164.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09604391
147324015
250014015

prune813.0ms

Filtered
203 candidates to 141 candidates (69.5%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2030203
Fresh066
Picked011
Done000
Total2037210

Merged error: 0b

Counts
210 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.3b
(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt
57×*-un-lft-identity
52×add-exp-log
45×times-frac
32×add-cbrt-cube
28×add-cube-cbrt
27×associate-*r*
18×div-exp
17×prod-exp
14×distribute-lft-out-- difference-of-squares
10×cbrt-undiv
9×cbrt-unprod
8×associate-/r*
7×pow1 distribute-rgt-neg-in sqrt-prod
6×associate-/l/ add-log-exp
4×expm1-log1p-u frac-times rec-exp flip3-+ 1-exp associate-*l/ associate-/r/ flip-+ log1p-expm1-u associate-/l*
3×flip3-- associate-*l* flip-- div-inv unswap-sqr
2×frac-2neg associate-*r/ clear-num un-div-inv
1×sub-neg pow-flip fma-neg diff-log prod-diff pow-prod-down *-commutative inv-pow
Counts
4 → 160
Calls
4 calls:
11.0ms
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
23.0ms
(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series494.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
44.0ms
(- (* b b) (* (* 4.0 a) c))
155.0ms
(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
187.0ms
(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify47.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
07602276
150011908

prune367.0ms

Filtered
172 candidates to 105 candidates (61.0%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1711172
Fresh145
Picked011
Done011
Total1727179

Merged error: 0b

Counts
179 → 7

regimes112.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03522
13722
23722

end0.0ms

sample2.2s

Algorithm
intervals
Results
537.0ms3675×body320valid
446.0ms16166×pre80true
399.0ms8166×body80nan
288.0ms2913×body160valid
100.0ms520×body640valid
46.0ms892×body80valid