Details

Time bar (total: 5.7s)

sample49.0ms

Algorithm
intervals
Results
11.0ms151×body160valid
9.0ms508×pre80true
9.0ms252×body80nan
4.0ms105×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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.2b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
30.2b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite34.0ms

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))
16.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series303.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
43.0ms
(- (* b b) (* (* 4.0 a) c))
106.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
82.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify51.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0438854
11702750
25002735

prune239.0ms

Filtered
102 candidates to 82 candidates (80.4%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New957102
Fresh000
Picked101
Done000
Total967103

Merged error: 0.3b

Counts
103 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

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:
11.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
21.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series461.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(- (* b b) (* (* 4.0 a) c))
153.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
184.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify163.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (118.0ms)

IterNodesCost
08325099
139673830
250013828

prune539.0ms

Filtered
243 candidates to 137 candidates (56.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New23211243
Fresh606
Picked101
Done000
Total23911250

Merged error: 0.0b

Counts
250 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×add-exp-log add-cbrt-cube
16×associate-/l*
7×cbrt-undiv div-exp
6×add-log-exp
4×pow1 expm1-log1p-u associate-/r* log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg prod-exp clear-num cbrt-unprod
1×sub-neg flip3-- flip3-+ fma-neg diff-log prod-diff flip-- flip-+ fma-udef
Counts
4 → 105
Calls
4 calls:
1.0ms
(fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
9.0ms
(/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

series727.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
50.0ms
(- (* b b) (* (* 4.0 a) c))
226.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
277.0ms
(/ (+ 0 (* 4.0 (* a c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify113.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
05982143
130141804
250021754

prune394.0ms

Filtered
117 candidates to 96 candidates (82.1%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1152117
Fresh2810
Picked101
Done000
Total11810128

Merged error: 0.0b

Counts
128 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
126×times-frac
91×*-un-lft-identity
57×add-sqr-sqrt add-cube-cbrt
32×distribute-lft-neg-in distribute-rgt-neg-in
27×add-exp-log add-cbrt-cube
17×distribute-lft-out
15×associate-/r* div-inv
10×cbrt-undiv div-exp
8×neg-mul-1 associate-/l* add-log-exp
6×prod-exp cbrt-unprod
4×pow1 expm1-log1p-u log1p-expm1-u
3×fma-def
2×frac-2neg flip3-+ clear-num associate-/r/ flip-+ distribute-neg-frac
1×+-commutative sub-neg flip3-- fma-neg diff-log prod-diff sum-log flip-- associate-/l/
Counts
4 → 184
Calls
4 calls:
6.0ms
(/ (* 4.0 (* a c)) a)
6.0ms
(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms
(/ (/ (* 4.0 (* a c)) a) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(- (* b b) (* (* 4.0 a) c))

series289.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(/ (* 4.0 (* a c)) a)
81.0ms
(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
154.0ms
(/ (/ (* 4.0 (* a c)) a) (- (+ b (sqrt (- (* b b) (* (* 4.0 a) c))))))
45.0ms
(- (* b b) (* (* 4.0 a) c))

simplify121.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
08392756
145542476
250022473

prune450.0ms

Filtered
196 candidates to 136 candidates (69.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1933196
Fresh459
Picked101
Done000
Total1988206

Merged error: 0b

Counts
206 → 8

regimes115.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02712
12812
22812

end0.0ms

sample1.4s

Algorithm
intervals
Results
322.0ms4445×body160valid
302.0ms16788×pre80true
299.0ms8788×body80nan
132.0ms3555×body80valid