Details

Time bar (total: 19.4s)

sample37.0ms

Algorithm
intervals
Results
7.0ms36×body2560valid
7.0ms192×body80valid
4.0ms26×body1280valid
3.0ms83×body80nan
2.0ms12×body640valid
1.0ms9×body320valid
1.0ms3×body5120valid
0.0ms2×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0219
1429
2769
3949
41029
51029

prune5.0ms

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: 31.1b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.2b
(- (* b b) (* (* 3.0 a) c))
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.5b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
139×add-sqr-sqrt
116×*-un-lft-identity
60×times-frac
42×unswap-sqr
36×add-cube-cbrt associate-*l*
30×difference-of-squares
28×distribute-lft-out
24×sqrt-prod
18×associate-*r*
14×distribute-rgt-neg-in
12×associate-/r* *-commutative distribute-lft-out--
10×add-log-exp
9×add-exp-log add-cbrt-cube
6×swap-sqr
5×pow1 associate-/l*
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 cbrt-unprod div-inv
Counts
4 → 178
Calls
4 calls:
43.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
23.0ms
(- (* b b) (* (* 3.0 a) c))
37.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series332.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
48.0ms
(- (* b b) (* (* 3.0 a) c))
86.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
78.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify78.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
06122254
124072158
250012141

prune317.0ms

Filtered
190 candidates to 109 candidates (57.4%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1837190
Fresh000
Picked011
Done000
Total1838191

Merged error: 4.4b

Counts
191 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 3.0 a) c))
0.2b
(* (/ 1 a) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0))
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.5b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
177×add-sqr-sqrt
156×*-un-lft-identity
117×frac-times
95×associate-/l*
72×associate-/r*
69×add-cube-cbrt
42×unswap-sqr
31×times-frac associate-*l*
30×distribute-lft-out difference-of-squares
26×add-exp-log
25×clear-num
24×frac-2neg sqrt-prod
20×associate-/l/
19×associate-*r*
16×add-cbrt-cube
15×distribute-rgt-neg-in
13×associate-*r/
12×distribute-lft-out--
11×flip3-+ flip-+
10×add-log-exp
9×associate-*l/
8×div-exp prod-exp
7×pow1 *-commutative
6×swap-sqr
4×cbrt-undiv un-div-inv cbrt-unprod
2×rec-exp flip3-- sqrt-div 1-exp sum-log flip-- div-inv
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log pow-prod-down neg-log
Counts
4 → 286
Calls
4 calls:
22.0ms
(- (* b b) (* (* 3.0 a) c))
56.0ms
(* (/ 1 a) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0))
38.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series371.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (* b b) (* (* 3.0 a) c))
154.0ms
(* (/ 1 a) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0))
85.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
79.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify66.0ms

Algorithm
egg-herbie
Counts
298 → 298
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
012213597
150013358

prune423.0ms

Filtered
298 candidates to 145 candidates (48.7%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2935298
Fresh246
Picked101
Done011
Total29610306

Merged error: 4.3b

Counts
306 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 3.0 a) c))
0.2b
(/ (* (cbrt 1) (cbrt 1)) (* (/ a (cbrt 1)) (/ 3.0 (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.5b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite445.0ms

Algorithm
rewrite-expression-head
Rules
3211×times-frac
2906×add-sqr-sqrt
2224×*-un-lft-identity
1833×cbrt-prod
1339×add-cube-cbrt
1086×associate-*l*
1035×associate-*r*
813×unswap-sqr
348×swap-sqr
226×distribute-lft-out
223×associate-/r/
193×associate-/r*
132×frac-times
129×add-cbrt-cube
113×distribute-rgt-neg-in
108×associate-/l*
96×*-commutative
70×cbrt-undiv
67×div-inv
58×cbrt-unprod
45×add-exp-log
34×flip3-+ flip-+
30×difference-of-squares
27×clear-num
26×frac-2neg
24×sqrt-prod
18×div-exp
13×prod-exp
12×associate-*l/ distribute-lft-out--
11×associate-*r/
10×add-log-exp
5×pow1
2×flip3-- sqrt-div sum-log un-div-inv flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log neg-log
Counts
4 → 2176
Calls
4 calls:
24.0ms
(- (* b b) (* (* 3.0 a) c))
123.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (/ a (cbrt 1)) (/ 3.0 (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
39.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series378.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* (* 3.0 a) c))
162.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (/ a (cbrt 1)) (/ 3.0 (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))))
87.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
80.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify518.0ms

Algorithm
egg-herbie
Counts
2188 → 2188
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
0500155896

prune5.9s

Filtered
2188 candidates to 1340 candidates (61.2%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New218802188
Fresh088
Picked011
Done011
Total2188102198

Merged error: 4.3b

Counts
2198 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 3.0 a) c))
0.3b
(/ (/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (cbrt 3.0) (cbrt 3.0))) a) (cbrt 3.0))
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.5b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite710.0ms

Algorithm
rewrite-expression-head
Rules
8415×times-frac
5854×*-un-lft-identity
4425×add-sqr-sqrt
3446×add-cube-cbrt
3042×cbrt-prod
1192×distribute-lft-out
684×associate-*l*
672×swap-sqr
666×associate-*r*
596×distribute-rgt-neg-in
565×associate-/l*
480×unswap-sqr
221×associate-/l/
117×*-commutative
47×add-cbrt-cube
36×cbrt-undiv associate-/r*
30×div-inv difference-of-squares
24×sqrt-prod
18×add-exp-log
12×distribute-lft-out--
10×add-log-exp
9×div-exp
8×cbrt-unprod
5×pow1
3×frac-2neg div-sub clear-num
2×neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+
1×+-commutative sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log neg-log prod-exp
Counts
4 → 3248
Calls
4 calls:
22.0ms
(- (* b b) (* (* 3.0 a) c))
193.0ms
(/ (/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (cbrt 3.0) (cbrt 3.0))) a) (cbrt 3.0))
37.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series387.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (* b b) (* (* 3.0 a) c))
176.0ms
(/ (/ (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* (cbrt 3.0) (cbrt 3.0))) a) (cbrt 3.0))
83.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
79.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify794.0ms

Algorithm
egg-herbie
Counts
3260 → 3260
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
0500187789

prune6.8s

Filtered
3260 candidates to 1554 candidates (47.7%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New325823260
Fresh167
Picked011
Done022
Total3259113270

Merged error: 4.3b

Counts
3270 → 11

regimes368.0ms

Accuracy

82.8% (4.7b remaining)

Error of 10.6b against oracle of 5.8b and baseline of 33.4b

bsearch74.0ms

Steps
ItersRangePoint
6
5.170278655164064e-52
2.1804079894200568e-51
5.4422572916334605e-52
6
-9.354797223898085e+144
-1.633197596261116e+144
-2.1415042714212705e+144

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02913
12913

end0.0ms

sample1.1s

Algorithm
intervals
Results
221.0ms1029×body2560valid
212.0ms5955×body80valid
153.0ms853×body1280valid
101.0ms2985×body80nan
61.0ms463×body640valid
24.0ms221×body320valid
22.0ms87×body5120valid
7.0ms102×body160valid