Details

Time bar (total: 5.9s)

sample277.0ms

Algorithm
intervals
Results
7.0ms37×body2560valid
6.0ms180×body80valid
4.0ms75×body80nan
3.0ms23×body1280valid
2.0ms17×body640valid
1.0ms9×body320valid
1.0ms3×body5120valid
0.0ms3×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1237
2307
3327
4347
5347

prune4.0ms

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: 35.0b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b
(- (* b_2 b_2) (* a c))
1.3b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
19×add-sqr-sqrt
18×add-cube-cbrt
15×times-frac
10×fma-def distribute-lft-out add-log-exp
8×distribute-rgt-neg-in
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in associate-/r* sqrt-prod
2×neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub div-exp prod-diff neg-log clear-num div-inv
Counts
4 → 100
Calls
4 calls:
24.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms
(- (* b_2 b_2) (* a c))
8.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series260.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms
(- (* b_2 b_2) (* a c))
72.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
66.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify49.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0389850
11366779
25001753

prune264.0ms

Filtered
112 candidates to 88 candidates (78.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1048112
Fresh000
Picked101
Done000
Total1058113

Merged error: 5.9b

Counts
113 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.4b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.7b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
199×add-sqr-sqrt
198×*-un-lft-identity
186×times-frac
130×add-cube-cbrt
60×prod-diff
50×sqrt-prod
38×distribute-rgt-neg-in
34×distribute-lft-out-- difference-of-squares
30×associate-/l*
21×distribute-lft-neg-in
11×add-exp-log add-cbrt-cube
10×fma-neg associate-/r* associate-/r/
8×add-log-exp
7×neg-mul-1 flip3-- flip--
6×div-inv
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×associate-/l/
2×frac-2neg sqrt-div diff-log clear-num
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 284
Calls
4 calls:
13.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series431.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
139.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
162.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify142.0ms

Algorithm
egg-herbie
Counts
296 → 296
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
09195579
139184508
250014505

prune523.0ms

Filtered
296 candidates to 172 candidates (58.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2933296
Fresh347
Picked011
Done000
Total2968304

Merged error: 5.8b

Counts
304 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.4b
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
23.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
951×times-frac
630×add-sqr-sqrt
629×*-un-lft-identity
433×add-cube-cbrt
98×distribute-lft-out-- difference-of-squares
83×associate-/l*
82×sqrt-prod
70×distribute-rgt-neg-in
60×prod-diff
28×associate-/r*
22×div-inv
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
10×fma-neg
9×cbrt-undiv div-exp
8×add-log-exp
7×neg-mul-1
5×pow1 associate-/r/
4×expm1-log1p-u log1p-expm1-u
2×flip3-- frac-2neg sqrt-div diff-log clear-num flip--
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log associate-/l/
Counts
4 → 569
Calls
4 calls:
13.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
10.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
26.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series462.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
65.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
154.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
64.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify130.0ms

Algorithm
egg-herbie
Counts
581 → 581
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0175510832
150029428

prune1.0s

Filtered
581 candidates to 328 candidates (56.5%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New5801581
Fresh156
Picked011
Done011
Total5818589

Merged error: 5.8b

Counts
589 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.6b
(- (* b_2 b_2) (* a c))
1.3b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.1b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
137×add-sqr-sqrt
110×*-un-lft-identity
84×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
24×associate-/r*
19×prod-diff
15×add-exp-log
13×distribute-lft-out--
9×associate-/r/ add-cbrt-cube
8×add-log-exp
7×flip3-- fma-neg div-exp flip--
6×pow1
5×div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv associate-/l*
2×sub-neg rec-exp sqrt-div diff-log 1-exp
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num inv-pow
Counts
4 → 196
Calls
4 calls:
13.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
4.0ms
(- (* b_2 b_2) (* a c))
12.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series285.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
36.0ms
(- (* b_2 b_2) (* a c))
67.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify83.0ms

Algorithm
egg-herbie
Counts
208 → 208
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06582519
129432155
250012004

prune263.0ms

Filtered
208 candidates to 104 candidates (50.0%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New2080208
Fresh055
Picked011
Done022
Total2088216

Merged error: 5.8b

Counts
216 → 8

regimes257.0ms

Accuracy

87.6% (3.3b remaining)

Error of 8.6b against oracle of 5.4b and baseline of 31.5b

bsearch155.0ms

Steps
ItersRangePoint
10
8.485467515044765e-21
0.011261476250181132
0.000518782715372617
10
-4.4782599006234366e-147
-2.1964053429920463e-160
-2.2271387790640654e-160
10
-1.5021501144069279e+69
-2.501148282372368e+59
-1.2963688795759268e+64

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04023
14023

end0.0ms

sample972.0ms

Algorithm
intervals
Results
199.0ms1050×body2560valid
193.0ms5824×body80valid
140.0ms884×body1280valid
88.0ms2907×body80nan
58.0ms490×body640valid
22.0ms243×body320valid
21.0ms92×body5120valid
8.0ms130×body160valid