Details

Time bar (total: 6.1s)

sample52.0ms

Algorithm
intervals
Results
12.0ms169×body160valid
11.0ms489×pre80true
8.0ms233×body80nan
3.0ms31×body320valid
2.0ms56×body80valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b
(- (* b b) (* (* 4.0 a) c))
38.7b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite59.0ms

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)))
35.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series288.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
100.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
45.0ms
(- (* b b) (* (* 4.0 a) c))
75.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify50.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0438854
11702750
25001735

prune241.0ms

Filtered
102 candidates to 82 candidates (80.4%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

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:
19.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
44.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
30.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series444.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(- (* b b) (* (* 4.0 a) c))
146.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
179.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify152.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (115.0ms)

IterNodesCost
08325099
139673830
250013828

prune532.0ms

Filtered
243 candidates to 137 candidates (56.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
124×*-un-lft-identity
90×times-frac
80×add-cube-cbrt
60×prod-diff
44×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
10×fma-neg
8×associate-/r* add-log-exp
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 230
Calls
4 calls:
1.0ms
(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
12.0ms
(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
34.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
20.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

series497.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
87.0ms
(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
151.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
181.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

simplify123.0ms

Algorithm
egg-herbie
Counts
242 → 242
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
07675082
131663826
250013733

prune512.0ms

Filtered
242 candidates to 132 candidates (54.5%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
109×add-sqr-sqrt
103×*-un-lft-identity
71×add-cube-cbrt
60×prod-diff
51×add-exp-log
46×times-frac
41×sqrt-prod
29×distribute-rgt-neg-in
27×associate-*l* add-cbrt-cube
21×distribute-lft-neg-in
20×prod-exp
16×div-exp distribute-lft-out-- difference-of-squares
10×fma-neg
8×cbrt-undiv cbrt-unprod add-log-exp
7×pow1 neg-mul-1 associate-*r* associate-/r*
4×expm1-log1p-u rec-exp 1-exp associate-/r/ log1p-expm1-u
3×flip3-- flip-- div-inv associate-/l*
2×diff-log associate-/l/ unswap-sqr
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 225
Calls
4 calls:
1.0ms
(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
12.0ms
(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
54.0ms
(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))) (/ 1 (* 2.0 a)))
20.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

series508.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(sqrt (fma b b (- 0 (* 4.0 (* a c)))))
88.0ms
(- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))
152.0ms
(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c))))))) (/ 1 (* 2.0 a)))
188.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma b b (- 0 (* 4.0 (* a c)))))))

simplify139.0ms

Algorithm
egg-herbie
Counts
237 → 237
Iterations

Useful iterations: 2 (103.0ms)

IterNodesCost
08594807
139533431
250013428

prune502.0ms

Filtered
237 candidates to 128 candidates (54.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes121.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02614
13814
24414
34414

end0.0ms

sample1.5s

Algorithm
intervals
Results
346.0ms4813×body160valid
305.0ms16514×pre80true
296.0ms8514×body80nan
143.0ms1340×body320valid
70.0ms1847×body80valid