Details

Time bar (total: 6.8s)

sample73.0ms

Algorithm
intervals
Results
16.0ms114×body320valid
13.0ms490×pre80true
11.0ms234×body80nan
9.0ms90×body160valid
4.0ms20×body640valid
2.0ms32×body80valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

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: 52.0b

Counts
2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(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))
26.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite28.0ms

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:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
4.0ms
(- (* b b) (* (* 4.0 a) c))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series317.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
115.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
46.0ms
(- (* b b) (* (* 4.0 a) c))
86.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify50.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0405779
11563685
25002674

prune186.0ms

Filtered
82 candidates to 63 candidates (76.8%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New80282
Fresh000
Picked011
Done000
Total80383

Merged error: 0.1b

Counts
83 → 3

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
82×add-sqr-sqrt *-un-lft-identity
38×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
11×distribute-rgt-neg-in sqrt-prod
10×add-log-exp
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 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 → 151
Calls
4 calls:
9.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
13.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
17.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series487.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms
(- (* b b) (* (* 4.0 a) c))
195.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
161.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify120.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
06422664
131752400
250022388

prune422.0ms

Filtered
163 candidates to 106 candidates (65.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1576163
Fresh011
Picked101
Done101
Total1597166

Merged error: 0b

Counts
166 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
166×add-sqr-sqrt
138×times-frac
96×*-un-lft-identity
60×difference-of-squares
56×add-cube-cbrt
52×cbrt-prod
50×sqrt-prod
42×associate-/l*
20×distribute-lft-out--
19×add-exp-log add-cbrt-cube
16×unpow-prod-down cube-prod
12×associate-/r* sqr-pow
10×distribute-rgt-neg-in
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×cube-div div-inv add-log-exp
3×pow-unpow associate-/l/
2×cube-mult cbrt-div frac-2neg unpow3 prod-exp clear-num cbrt-unprod
1×pow-to-exp pow-pow flip3-+ pow1/3 pow-exp rem-cbrt-cube flip-+ rem-cube-cbrt
Counts
4 → 209
Calls
4 calls:
24.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
25.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
5.0ms
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
5.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

series507.0ms

Counts
4 → 12
Calls
4 calls:
197.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3)))))
162.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))))) (* 2.0 a))
47.0ms
(cbrt (pow (- (* b b) (* (* 4.0 a) c)) 3))
101.0ms
(pow (- (* b b) (* (* 4.0 a) c)) 3)

simplify164.0ms

Algorithm
egg-herbie
Counts
221 → 221
Iterations

Useful iterations: 2 (124.0ms)

IterNodesCost
08564185
144263809
250013728

prune600.0ms

Filtered
221 candidates to 128 candidates (57.9%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2210221
Fresh066
Picked011
Done000
Total2217228

Merged error: 0b

Counts
228 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 4.0 (/ 2.0 (* a c)))
0.3b
(/ 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))

rewrite112.0ms

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))
15.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
61.0ms
(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

series340.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(/ 4.0 (/ 2.0 (* a c)))
22.0ms
(/ 2.0 (* a c))
129.0ms
(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a)
168.0ms
(* (/ 4.0 (/ 2.0 (* a c))) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))

simplify87.0ms

Algorithm
egg-herbie
Counts
372 → 372
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
014745495
150024888

prune834.0ms

Filtered
372 candidates to 218 candidates (58.6%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New3711372
Fresh145
Picked101
Done011
Total3736379

Merged error: 0b

Counts
379 → 6

regimes100.0ms

Accuracy

0% (0.4b 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
02512
12512

end0.0ms

sample2.2s

Algorithm
intervals
Results
518.0ms3584×body320valid
453.0ms16173×pre80true
400.0ms8173×body80nan
289.0ms2990×body160valid
100.0ms523×body640valid
45.0ms903×body80valid