Details

Time bar (total: 7.6s)

sample79.0ms

Algorithm
intervals
Results
16.0ms248×body80nan
15.0ms105×body320valid
14.0ms504×pre80true
9.0ms98×body160valid
5.0ms25×body640valid
2.0ms28×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: 52.2b

Counts
2 → 1

localize11.0ms

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))
25.3b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite33.0ms

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))
14.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
9.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series310.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms
(- (* b b) (* (* 4.0 a) c))
109.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
85.0ms
(+ (- 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

prune236.0ms

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

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:
13.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series459.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(- (* b b) (* (* 4.0 a) c))
151.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
185.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify161.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (118.0ms)

IterNodesCost
08325099
139673830
250013828

prune527.0ms

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

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 2.0 (* a c))
0.3b
(/ 4.0 (/ 2.0 (* a c)))
0.3b
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
0.4b
(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
389×times-frac
281×add-sqr-sqrt
255×*-un-lft-identity
169×add-cube-cbrt
117×add-exp-log
85×associate-*r*
77×add-cbrt-cube
62×div-exp
42×distribute-lft-out-- difference-of-squares
37×cbrt-undiv
33×associate-/l*
27×prod-exp
26×associate-*l*
21×distribute-rgt-neg-in sqrt-prod
19×div-inv
17×cbrt-unprod
16×associate-/r/
11×associate-/r*
8×unswap-sqr
7×flip3-- flip--
6×pow1
5×rec-exp 1-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 368
Calls
4 calls:
8.0ms
(/ 2.0 (* a c))
11.0ms
(/ 4.0 (/ 2.0 (* a c)))
28.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
107.0ms
(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series326.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(/ 2.0 (* a c))
20.0ms
(/ 4.0 (/ 2.0 (* a c)))
125.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
159.0ms
(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify87.0ms

Algorithm
egg-herbie
Counts
380 → 380
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
014915557
150014952

prune860.0ms

Filtered
380 candidates to 226 candidates (59.5%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New3800380
Fresh066
Picked011
Done000
Total3807387

Merged error: 0b

Counts
387 → 7

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (* (- b) (- b)) (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) a)
0.3b
(/ (* 4.0 (* a c)) (* 2.0 (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))))
0.4b
(* (/ (* 4.0 (* a c)) (* 2.0 (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)))) (/ (+ (* (- b) (- b)) (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) a))
25.3b
(+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
92×add-exp-log add-cbrt-cube
41×prod-exp cbrt-unprod
40×sqrt-div
26×cbrt-undiv div-exp
25×add-sqr-sqrt associate-*r/
22×flip3-- flip--
21×times-frac
20×add-cube-cbrt *-un-lft-identity
16×frac-add
13×associate-*r*
9×frac-times
7×associate-*l*
6×pow1 add-log-exp
5×associate-*l/
4×distribute-lft-neg-out expm1-log1p-u associate-/r* associate-/r/ log1p-expm1-u div-inv associate-/l*
2×associate-+r- frac-2neg flip3-+ div-sub unsub-neg clear-num flip-+ associate-/l/ unswap-sqr
1×+-commutative distribute-rgt-out fma-def pow-prod-down sum-log *-commutative
Counts
4 → 159
Calls
4 calls:
15.0ms
(/ (+ (* (- b) (- b)) (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) a)
35.0ms
(/ (* 4.0 (* a c)) (* 2.0 (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))))
48.0ms
(* (/ (* 4.0 (* a c)) (* 2.0 (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)))) (/ (+ (* (- b) (- b)) (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) a))
13.0ms
(+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ (+ (* (- b) (- b)) (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) a)
359.0ms
(/ (* 4.0 (* a c)) (* 2.0 (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3))))
386.0ms
(* (/ (* 4.0 (* a c)) (* 2.0 (- (pow (- b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)))) (/ (+ (* (- b) (- b)) (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) a))
126.0ms
(+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify76.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
011976830
150014956

prune622.0ms

Filtered
171 candidates to 117 candidates (68.4%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1710171
Fresh055
Picked011
Done011
Total1717178

Merged error: 0b

Counts
178 → 7

regimes107.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02513
12513

end0.0ms

sample2.2s

Algorithm
intervals
Results
513.0ms3511×body320valid
457.0ms16247×pre80true
399.0ms8247×body80nan
297.0ms3027×body160valid
103.0ms540×body640valid
46.0ms922×body80valid