Details

Time bar (total: 5.7s)

sample52.0ms

Algorithm
intervals
Results
23.0ms275×body80valid
6.0ms73×body80nan

simplify23.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03918
18018
214318
317718
418918
519318
619318

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: 20.4b

Counts
2 → 1

localize115.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (* b b) (* (* 4.0 a) c))
2.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
37×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 neg-log
Counts
4 → 140
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series266.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* (* 4.0 a) c))
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify65.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04062988
114311956
250021869

prune352.0ms

Filtered
152 candidates to 80 candidates (52.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1466152
Fresh000
Picked101
Done000
Total1476153

Merged error: 8.4b

Counts
153 → 6

localize117.0ms

Local error

Found 4 expressions with local error:

11.8b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
10×fma-neg prod-diff
9×sqrt-prod
8×add-log-exp
7×pow1
6×distribute-lft-neg-in distribute-rgt-neg-in sqrt-div
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×neg-mul-1 diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 88
Calls
4 calls:
5.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series299.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify181.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
02831391
19981121
247231013
350011013

prune365.0ms

Filtered
100 candidates to 83 candidates (83.0%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New991100
Fresh145
Picked011
Done000
Total1006106

Merged error: 8.4b

Counts
106 → 6

localize123.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
6.5b
(/ (* a c) b)
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
62×*-un-lft-identity
60×prod-diff
55×add-sqr-sqrt
50×add-cube-cbrt
34×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
14×add-exp-log add-cbrt-cube
10×fma-neg
8×times-frac associate-/r* add-log-exp
7×neg-mul-1
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u distribute-lft-out
2×flip3-- frac-2neg sqrt-div diff-log prod-exp clear-num associate-/r/ flip-- cbrt-unprod div-inv associate-/l* distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 159
Calls
4 calls:
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
5.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series353.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
180.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
19.0ms
(/ (* a c) b)
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify83.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06103137
125642048
250011968

prune396.0ms

Filtered
171 candidates to 88 candidates (51.5%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1674171
Fresh044
Picked101
Done011
Total1689177

Merged error: 6.7b

Counts
177 → 9

localize123.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.4b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
5.0b
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
84×add-sqr-sqrt
75×*-un-lft-identity
63×add-cube-cbrt
60×prod-diff
34×sqrt-prod
33×times-frac
30×add-exp-log
24×distribute-rgt-neg-in
23×add-cbrt-cube
22×associate-*r*
21×distribute-lft-neg-in
11×cbrt-prod
10×fma-neg
9×cbrt-undiv div-exp prod-exp cbrt-unprod
8×add-log-exp
7×pow1 neg-mul-1 associate-*l*
6×unswap-sqr
5×associate-/r*
4×expm1-log1p-u log1p-expm1-u distribute-lft-out
3×div-inv
2×flip3-- sqrt-div diff-log associate-/r/ flip-- distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 197
Calls
4 calls:
14.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
22.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series415.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
52.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
212.0ms
(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify112.0ms

Algorithm
egg-herbie
Counts
209 → 209
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
09073855
141342632
250022617

prune640.0ms

Filtered
209 candidates to 128 candidates (61.2%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2063209
Fresh167
Picked101
Done011
Total20810218

Merged error: 6.7b

Counts
218 → 10

regimes217.0ms

Accuracy

92.7% (1.0b remaining)

Error of 7.6b against oracle of 6.7b and baseline of 20.0b

bsearch179.0ms

Steps
ItersRangePoint
8
4.5418805312590315e+84
1.9690305180656607e+89
4.309841870567569e+88
8
-3.270551254255918e+118
-2.131753517190888e+115
-1.169783528148572e+118

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06071
16071

end0.0ms

sample1.1s

Algorithm
intervals
Results
608.0ms8699×body80valid
194.0ms2900×body80nan

Profiling

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