Details

Time bar (total: 5.9s)

sample51.0ms

Algorithm
intervals
Results
12.0ms165×body160valid
9.0ms467×pre80true
7.0ms211×body80nan
5.0ms43×body320valid
2.0ms48×body80valid

simplify12.0ms

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: 45.2b

localize12.0ms

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))
0.1b
(- (* b b) (* (* 4.0 a) c))
40.0b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite60.0ms

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)))
34.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series314.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
109.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
49.0ms
(- (* b b) (* (* 4.0 a) c))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify51.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0438854
11702750
25001735

prune267.0ms

Filtered
102 candidates to 82 candidates (80.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(- (- b) (sqrt (- (* 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)))))

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))))
46.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
27.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series472.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
151.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
191.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify156.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (120.0ms)

IterNodesCost
08325099
139673830
250013828

prune583.0ms

Filtered
243 candidates to 137 candidates (56.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize21.0ms

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))
0.2b
(- (- 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))))))

rewrite109.0ms

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))))
22.0ms
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series392.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
44.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
157.0ms
(/ (+ 0 (* 4.0 (* a c))) (* (* 2.0 a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify88.0ms

Algorithm
egg-herbie
Counts
297 → 297
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
010108635
150015618

prune476.0ms

Filtered
297 candidates to 108 candidates (36.4%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-*r*
12×times-frac
11×add-exp-log add-cbrt-cube
9×pow1
8×add-log-exp
6×distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod
5×distribute-rgt-neg-out distribute-lft-out
4×expm1-log1p-u associate-/r* log1p-expm1-u
3×flip3-+ pow-prod-down prod-exp cbrt-unprod flip-+ associate-/l*
2×flip3-- sqrt-div associate-*r/ associate-/r/ flip-- associate-/l/ distribute-neg-frac
1×cbrt-undiv +-commutative neg-mul-1 sub-neg distribute-neg-out fma-def frac-2neg fma-neg diff-log div-exp associate-*l* unsub-neg prod-diff clear-num sum-log *-commutative div-inv
Counts
4 → 107
Calls
4 calls:
20.0ms
(* (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
7.0ms
(+ (* (* 2.0 a) (- b)) (* (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
22.0ms
(/ (+ 0 (* 4.0 (* a c))) (+ (* (* 2.0 a) (- b)) (* (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))

series517.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(* (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
121.0ms
(+ (* (* 2.0 a) (- b)) (* (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))
44.0ms
(- (* b b) (* (* 4.0 a) c))
261.0ms
(/ (+ 0 (* 4.0 (* a c))) (+ (* (* 2.0 a) (- b)) (* (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))

simplify131.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (118.0ms)

IterNodesCost
06181615
135291390
250011384

prune380.0ms

Filtered
119 candidates to 95 candidates (79.8%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes115.0ms

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
03416
14716
25516
35516

end0.0ms

sample1.5s

Algorithm
intervals
Results
352.0ms4834×body160valid
309.0ms16413×pre80true
290.0ms8413×body80nan
143.0ms1317×body320valid
70.0ms1849×body80valid