Details

Time bar (total: 13.9s)

sample35.0ms

Algorithm
intervals
Results
14.0ms279×body80valid
5.0ms110×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03618
16718
212318
316018
417518
517718
617718

prune3.0ms

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: 19.7b

Counts
2 → 1

localize121.0ms

Local error

Found 4 expressions with local error:

1.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
659×add-sqr-sqrt
289×sqrt-prod
270×prod-diff
265×*-un-lft-identity
216×unswap-sqr
182×difference-of-squares
113×add-cube-cbrt
108×associate-*l*
89×distribute-rgt-neg-in
87×distribute-lft-neg-in
74×distribute-lft-out--
36×swap-sqr *-commutative
29×neg-mul-1
12×add-log-exp
10×fma-def fma-neg
6×pow1
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 403
Calls
4 calls:
37.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
46.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
80.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify144.0ms

Algorithm
egg-herbie
Counts
415 → 415
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
073312242
120679625
250019326

prune530.0ms

Filtered
415 candidates to 122 candidates (70.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New4078415
Fresh000
Picked101
Done000
Total4088416

Merged error: 7.2b

Counts
416 → 8

localize123.0ms

Local error

Found 4 expressions with local error:

1.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.2b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
5.3b
(/ (* a c) b)
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite152.0ms

Algorithm
rewrite-expression-head
Rules
303×*-un-lft-identity
181×add-sqr-sqrt
156×times-frac
136×distribute-lft-out--
80×associate-*l*
79×add-cube-cbrt
45×associate-*r*
43×distribute-rgt-neg-in
33×unswap-sqr
28×difference-of-squares
24×sqrt-prod associate-/l*
18×*-commutative
14×add-exp-log add-cbrt-cube
13×associate-/r*
10×fma-def
8×add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×distribute-lft-neg-in swap-sqr
2×flip3-- frac-2neg sqrt-div prod-exp clear-num sum-log associate-/r/ flip-- cbrt-unprod div-inv distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 292
Calls
4 calls:
38.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
41.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
8.0ms
(/ (* a c) b)
50.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series378.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
191.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
22.0ms
(/ (* a c) b)
78.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify121.0ms

Algorithm
egg-herbie
Counts
304 → 304
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
08992908
140502811
250022802

prune728.0ms

Filtered
304 candidates to 169 candidates (44.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2977304
Fresh347
Picked101
Done000
Total30111312

Merged error: 6.7b

Counts
312 → 11

localize132.0ms

Local error

Found 4 expressions with local error:

1.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0b
(* (/ (/ a (cbrt b)) (cbrt b)) (/ c (cbrt b)))
3.2b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ (/ a (cbrt b)) (cbrt b)) (/ c (cbrt b)))))))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite416.0ms

Algorithm
rewrite-expression-head
Rules
781×*-un-lft-identity
736×add-sqr-sqrt
656×times-frac
556×add-cube-cbrt
516×frac-times
478×cbrt-prod
470×associate-/l*
430×associate-/r*
204×associate-*l*
156×associate-/l/
136×distribute-lft-out--
73×add-cbrt-cube
72×clear-num
71×frac-2neg
55×associate-*r*
50×unswap-sqr
46×cbrt-undiv
43×distribute-rgt-neg-in associate-*l/
30×add-exp-log
28×difference-of-squares
24×sqrt-prod
22×cbrt-unprod div-inv
15×*-commutative
12×associate-*r/
11×div-exp
10×fma-def
8×add-log-exp
7×pow1 prod-exp
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in swap-sqr
2×flip3-- sqrt-div sum-log associate-/r/ un-div-inv flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow-prod-down neg-log flip-+
Counts
4 → 1015
Calls
4 calls:
40.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
84.0ms
(* (/ (/ a (cbrt b)) (cbrt b)) (/ c (cbrt b)))
161.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ (/ a (cbrt b)) (cbrt b)) (/ c (cbrt b)))))))
46.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series452.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
56.0ms
(* (/ (/ a (cbrt b)) (cbrt b)) (/ c (cbrt b)))
229.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ (/ a (cbrt b)) (cbrt b)) (/ c (cbrt b)))))))
82.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify202.0ms

Algorithm
egg-herbie
Counts
1027 → 1027
Iterations

Useful iterations: 1 (78.0ms)

IterNodesCost
0416213115
1500112900

prune3.7s

Filtered
1027 candidates to 635 candidates (38.2%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New101891027
Fresh7310
Picked101
Done000
Total1026121038

Merged error: 6.4b

Counts
1038 → 12

localize128.0ms

Local error

Found 4 expressions with local error:

1.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0b
(* (/ (/ a (cbrt b)) (cbrt b)) (/ c (cbrt b)))
3.0b
(/ c (/ (- (- b) (- b (* 2.0 (* (/ (/ a (cbrt b)) (cbrt b)) (/ c (cbrt b)))))) 2.0))
22.4b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite417.0ms

Algorithm
rewrite-expression-head
Rules
828×*-un-lft-identity
761×add-sqr-sqrt
758×times-frac
603×add-cube-cbrt
516×frac-times
478×cbrt-prod
471×associate-/l*
457×associate-/r*
171×associate-*l*
158×associate-/l/
136×distribute-lft-out--
73×clear-num add-cbrt-cube
72×frac-2neg
47×cbrt-undiv
43×distribute-rgt-neg-in associate-*l/
39×unswap-sqr
30×add-exp-log
28×difference-of-squares
26×div-inv
24×sqrt-prod
22×associate-*r*
21×cbrt-unprod
18×associate-/r/
12×associate-*r/ div-exp
10×fma-def
8×add-log-exp
7×pow1
6×prod-exp
4×expm1-log1p-u *-commutative log1p-expm1-u
3×distribute-lft-neg-in swap-sqr
2×flip3-- sqrt-div sum-log un-div-inv flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow-prod-down neg-log flip-+
Counts
4 → 1028
Calls
4 calls:
40.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
84.0ms
(* (/ (/ a (cbrt b)) (cbrt b)) (/ c (cbrt b)))
160.0ms
(/ c (/ (- (- b) (- b (* 2.0 (* (/ (/ a (cbrt b)) (cbrt b)) (/ c (cbrt b)))))) 2.0))
45.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series450.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
55.0ms
(* (/ (/ a (cbrt b)) (cbrt b)) (/ c (cbrt b)))
225.0ms
(/ c (/ (- (- b) (- b (* 2.0 (* (/ (/ a (cbrt b)) (cbrt b)) (/ c (cbrt b)))))) 2.0))
84.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify214.0ms

Algorithm
egg-herbie
Counts
1040 → 1040
Iterations

Useful iterations: 1 (85.0ms)

IterNodesCost
0423913254
1500213041

prune3.8s

Filtered
1040 candidates to 651 candidates (37.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New103281040
Fresh8311
Picked101
Done000
Total1041111052

Merged error: 6.4b

Counts
1052 → 11

regimes262.0ms

Accuracy

93.2% (1.0b remaining)

Error of 7.7b against oracle of 6.7b and baseline of 20.8b

bsearch83.0ms

Steps
ItersRangePoint
0
1.3836563058951246e+50
1.390978468581987e+50
1.3873173872385558e+50
8
-2.283181266341636e+156
-6.52330204454965e+152
-1.337391455611001e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06272
16272

end0.0ms

sample825.0ms

Algorithm
intervals
Results
439.0ms8726×body80valid
141.0ms2780×body80nan