Details

Time bar (total: 6.4s)

sample1.1s

Algorithm
intervals
Results
15.0ms158×body160valid
8.0ms270×pre80true
6.0ms43×body320valid
3.0ms55×body80valid
1.0ms14×body80nan

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune151.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 45.4b

Counts
2 → 1

localize14.0ms

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
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
42.0b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-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 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series66.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(- (* b b) (* (* 4.0 a) c))
28.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
16.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0396773
11550683
25001673

prune126.0ms

Filtered
82 candidates to 63 candidates (23.2%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New79382
Fresh000
Picked101
Done000
Total80383

Merged error: 0.2b

Counts
83 → 3

localize16.0ms

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

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 148
Calls
4 calls:
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
14.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series122.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(- (* b b) (* (* 4.0 a) c))
42.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
58.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify116.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
06372580
131912340
250012327

prune317.0ms

Filtered
160 candidates to 106 candidates (33.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1519160
Fresh112
Picked101
Done000
Total15310163

Merged error: 0.0b

Counts
163 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b))))
0.4b
(* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2)))
0.6b
(* (* b b) (* b b))
0.7b
(pow (* (* 4.0 a) c) 3)

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
130×pow1
49×add-sqr-sqrt
36×pow-prod-up
33×add-exp-log add-cbrt-cube
32×pow-prod-down
30×times-frac
29×*-un-lft-identity
24×difference-of-squares
22×pow-sqr
21×add-cube-cbrt sqr-pow
18×pow-plus
17×prod-exp cbrt-unprod
13×pow2
10×associate-/l*
9×unpow-prod-down
4×associate-*r* distribute-lft-out-- add-log-exp
3×pow-unpow pow-pow pow-exp associate-/r* rem-cube-cbrt
2×flip3-+ associate-*r/ associate-*l* associate-/r/ *-commutative flip-+ associate-/l/
1×cbrt-undiv distribute-rgt-in cube-mult pow-to-exp flip3-- frac-2neg distribute-lft-in unpow3 div-sub cube-prod swap-sqr div-exp clear-num flip-- div-inv unswap-sqr
Counts
4 → 173
Calls
4 calls:
22.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b))))
12.0ms
(* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2)))
8.0ms
(* (* b b) (* b b))
6.0ms
(pow (* (* 4.0 a) c) 3)

series60.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b))))
17.0ms
(* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2)))
3.0ms
(* (* b b) (* b b))
8.0ms
(pow (* (* 4.0 a) c) 3)

simplify153.0ms

Algorithm
egg-herbie
Counts
185 → 185
Iterations

Useful iterations: 2 (128.0ms)

IterNodesCost
07022185
138502049
250012035

prune444.0ms

Filtered
185 candidates to 96 candidates (48.1%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1850185
Fresh099
Picked011
Done000
Total18510195

Merged error: 0.0b

Counts
195 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite103.0ms

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×add-log-exp
3×frac-2neg clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 360
Calls
4 calls:
6.0ms
(/ 4.0 (/ 2.0 (* a c)))
4.0ms
(/ 2.0 (* a c))
54.0ms
(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))
14.0ms
(/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)

series83.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(/ 4.0 (/ 2.0 (* a c)))
3.0ms
(/ 2.0 (* a c))
44.0ms
(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))
33.0ms
(/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)

simplify77.0ms

Algorithm
egg-herbie
Counts
372 → 372
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
014785494
150014891

prune651.0ms

Filtered
372 candidates to 218 candidates (41.4%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New3693372
Fresh358
Picked011
Done101
Total3739382

Merged error: 0b

Counts
382 → 9

regimes208.0ms

Accuracy

0% (0.5b 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 (1.0ms)

IterNodesCost
02513
12513

end0.0ms

sample2.4s

Algorithm
intervals
Results
477.0ms4798×body160valid
245.0ms8373×pre80true
209.0ms1386×body320valid
90.0ms1816×body80valid
18.0ms373×body80nan

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