Details

Time bar (total: 5.8s)

sample56.0ms

Algorithm
intervals
Results
13.0ms500×pre80true
11.0ms156×body160valid
8.0ms244×body80nan
6.0ms55×body320valid
2.0ms45×body80valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 47.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
41.1b
(+ (- 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:
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
37.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series313.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
49.0ms
(- (* b b) (* (* 4.0 a) c))
110.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
83.0ms
(+ (- 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
25002735

prune262.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 4.0 a) c))
0.1b
(- (- b) (sqrt (- (* 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))

rewrite103.0ms

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:
3.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
45.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series475.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
188.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
156.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify152.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (115.0ms)

IterNodesCost
08325099
139673830
250013828

prune550.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
181×prod-diff
132×add-sqr-sqrt *-un-lft-identity
124×add-cube-cbrt
92×sqrt-prod
62×distribute-rgt-in distribute-lft-in
59×distribute-rgt-neg-in
57×distribute-lft-neg-in
19×neg-mul-1
18×add-exp-log add-cbrt-cube
11×fma-neg
10×add-log-exp
9×pow1
7×associate-*r*
6×prod-exp cbrt-unprod
4×expm1-log1p-u sub-neg flip3-- associate-*r/ flip-- log1p-expm1-u distribute-lft-out-- difference-of-squares
3×cbrt-undiv times-frac diff-log div-exp pow-prod-down associate-/l*
2×associate-/r/ associate-/l/
1×associate--l- neg-sub0 frac-2neg flip3-+ associate-*l* neg-log clear-num associate-/r* *-commutative flip-+ div-inv
Counts
4 → 285
Calls
4 calls:
52.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.0ms
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series399.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
46.0ms
(- (* b b) (* (* 4.0 a) c))
82.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
158.0ms
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify90.0ms

Algorithm
egg-herbie
Counts
297 → 297
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010108634
150015618

prune467.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (/ (- (pow (* b b) 3) (pow (* (* 4.0 a) c) 3)) (fma (* 4.0 (* a c)) (fma b b (* (* 4.0 a) c)) (* (* b b) (* b b))))))))
0.5b
(* (* b b) (* b b))
0.7b
(pow (* b b) 3)
0.8b
(pow (* (* 4.0 a) c) 3)

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
129×pow1
37×pow-prod-up
34×add-exp-log add-cbrt-cube
27×pow-prod-down
23×pow-sqr
19×pow-plus
15×prod-exp cbrt-unprod
14×pow2
9×pow-pow
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow-unpow
5×pow-exp rem-cube-cbrt
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv times-frac div-exp associate-/l*
2×cube-mult pow-to-exp unpow-prod-down unpow3 cube-prod associate-*r/ associate-/r/ associate-/l/ sqr-pow
1×flip3-- frac-2neg flip3-+ swap-sqr associate-*r* associate-*l* clear-num associate-/r* *-commutative flip-- flip-+ div-inv unswap-sqr
Counts
4 → 149
Calls
4 calls:
60.0ms
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (/ (- (pow (* b b) 3) (pow (* (* 4.0 a) c) 3)) (fma (* 4.0 (* a c)) (fma b b (* (* 4.0 a) c)) (* (* b b) (* b b))))))))
13.0ms
(* (* b b) (* b b))
3.0ms
(pow (* b b) 3)
7.0ms
(pow (* (* 4.0 a) c) 3)

series378.0ms

Counts
4 → 12
Calls
4 calls:
233.0ms
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (/ (- (pow (* b b) 3) (pow (* (* 4.0 a) c) 3)) (fma (* 4.0 (* a c)) (fma b b (* (* 4.0 a) c)) (* (* b b) (* b b))))))))
33.0ms
(* (* b b) (* b b))
50.0ms
(pow (* b b) 3)
61.0ms
(pow (* (* 4.0 a) c) 3)

simplify140.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 2 (126.0ms)

IterNodesCost
05881230
13773964
25001963

prune425.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes117.0ms

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
03325
13525
23525

end0.0ms

sample1.5s

Algorithm
intervals
Results
336.0ms4726×body160valid
296.0ms16316×pre80true
275.0ms8316×body80nan
142.0ms1398×body320valid
67.0ms1876×body80valid