Details

Time bar (total: 7.0s)

sample14.0ms

Algorithm
intervals
Results
6.0ms339×body80valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0143
1233
2303
3313
4313

prune2.0ms

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: 5.6b

Counts
2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

5.2b
(* x (+ 1.0 (* y y)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
7×*-un-lft-identity
5×add-sqr-sqrt associate-*r*
4×associate-*l*
3×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
2×+-commutative distribute-rgt-in distribute-lft-in associate-*r/ distribute-lft-out
1×expm1-log1p-u flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ log1p-expm1-u add-log-exp unswap-sqr
Counts
1 → 28
Calls
1 calls:
9.0ms
(* x (+ 1.0 (* y y)))

series59.0ms

Counts
1 → 3
Calls
1 calls:
59.0ms
(* x (+ 1.0 (* y y)))

simplify94.0ms

Algorithm
egg-herbie
Counts
31 → 31
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0144129
1714109
23295106
35001106

prune44.0ms

Filtered
31 candidates to 23 candidates (25.8%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New27431
Fresh000
Picked011
Done000
Total27532

Merged error: 5.4b

Counts
32 → 5

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (sqrt (+ 1.0 (* y y))))
0.1b
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
5.2b
(sqrt (+ 1.0 (* y y)))
5.2b
(sqrt (+ 1.0 (* y y)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
35×*-un-lft-identity
32×sqrt-prod
29×associate-*l*
24×associate-*r*
18×sqrt-div
16×unswap-sqr
15×add-cube-cbrt
13×pow1
11×add-exp-log add-cbrt-cube
10×associate-*r/ hypot-def distribute-lft-out
9×flip3-+ flip-+
5×*-commutative
4×expm1-log1p-u frac-times pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 swap-sqr associate-*l/
Counts
4 → 132
Calls
4 calls:
10.0ms
(* x (sqrt (+ 1.0 (* y y))))
25.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
7.0ms
(sqrt (+ 1.0 (* y y)))
7.0ms
(sqrt (+ 1.0 (* y y)))

series216.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(* x (sqrt (+ 1.0 (* y y))))
57.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
44.0ms
(sqrt (+ 1.0 (* y y)))
50.0ms
(sqrt (+ 1.0 (* y y)))

simplify59.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0337978
11389827
25001760

prune245.0ms

Filtered
144 candidates to 102 candidates (29.2%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1404144
Fresh303
Picked011
Done011
Total1436149

Merged error: 5.4b

Counts
149 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sqrt (sqrt (+ 1.0 (* y y)))) 3)
2.2b
(* (* (pow (sqrt (sqrt (+ 1.0 (* y y)))) 3) 1) x)
5.2b
(sqrt (+ 1.0 (* y y)))
5.2b
(sqrt (+ 1.0 (* y y)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
77×add-sqr-sqrt
54×associate-*l*
48×sqrt-prod
43×*-un-lft-identity
34×unpow-prod-down
33×unswap-sqr
20×add-exp-log
17×add-cube-cbrt
14×pow1
13×prod-exp
10×add-cbrt-cube hypot-def
8×distribute-lft-out
6×sqrt-pow1 associate-*r* sqr-pow
5×pow-pow
4×expm1-log1p-u pow1/2 sqrt-div *-commutative log1p-expm1-u add-log-exp
3×pow-to-exp pow-unpow 1-exp pow-prod-down pow-exp cbrt-unprod
2×rem-sqrt-square flip3-+ unpow3 swap-sqr flip-+
1×sqrt-pow2 rem-cube-cbrt
Counts
4 → 151
Calls
4 calls:
8.0ms
(pow (sqrt (sqrt (+ 1.0 (* y y)))) 3)
23.0ms
(* (* (pow (sqrt (sqrt (+ 1.0 (* y y)))) 3) 1) x)
8.0ms
(sqrt (+ 1.0 (* y y)))
7.0ms
(sqrt (+ 1.0 (* y y)))

series654.0ms

Counts
4 → 12
Calls
4 calls:
248.0ms
(pow (sqrt (sqrt (+ 1.0 (* y y)))) 3)
311.0ms
(* (* (pow (sqrt (sqrt (+ 1.0 (* y y)))) 3) 1) x)
44.0ms
(sqrt (+ 1.0 (* y y)))
52.0ms
(sqrt (+ 1.0 (* y y)))

simplify84.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
06061159
125811039
25002992

prune345.0ms

Filtered
163 candidates to 103 candidates (36.8%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1630163
Fresh033
Picked011
Done022
Total1636169

Merged error: 5.4b

Counts
169 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

4.4b
(- (* (* y y) (* y y)) (* 1.0 (* y y)))
5.2b
(sqrt (+ 1.0 (* y y)))
6.6b
(sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y)))))
8.0b
(/ (* x (hypot (pow (pow y 2) 3/2) (pow 1.0 3/2))) (sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y))))))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
5072×add-sqr-sqrt
2425×associate-*r*
2268×prod-diff
2260×unswap-sqr
2049×*-un-lft-identity
1859×swap-sqr
1772×associate-*l*
1285×add-cube-cbrt
947×*-commutative
243×sqrt-prod
240×times-frac
222×difference-of-squares
198×distribute-lft-out
184×distribute-lft-out--
81×fma-neg
79×distribute-rgt-out--
20×associate-/r*
12×associate-/l*
10×hypot-def
9×add-exp-log add-cbrt-cube
6×pow1 sqrt-div add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×flip3-+ flip-+
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-/r/
1×sub-neg flip3-- frac-2neg diff-log prod-exp clear-num flip-- cbrt-unprod div-inv
Counts
4 → 3030
Calls
4 calls:
155.0ms
(- (* (* y y) (* y y)) (* 1.0 (* y y)))
9.0ms
(sqrt (+ 1.0 (* y y)))
484.0ms
(sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y)))))
272.0ms
(/ (* x (hypot (pow (pow y 2) 3/2) (pow 1.0 3/2))) (sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y))))))

series685.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(- (* (* y y) (* y y)) (* 1.0 (* y y)))
43.0ms
(sqrt (+ 1.0 (* y y)))
81.0ms
(sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y)))))
462.0ms
(/ (* x (hypot (pow (pow y 2) 3/2) (pow 1.0 3/2))) (sqrt (+ (* 1.0 1.0) (- (* (* y y) (* y y)) (* 1.0 (* y y))))))

simplify629.0ms

Algorithm
egg-herbie
Counts
3042 → 3042
Iterations

Useful iterations: 1 (73.0ms)

IterNodesCost
0337755109
1500140569

prune1.8s

Filtered
3042 candidates to 338 candidates (88.9%)
Pruning

6 alts after pruning (2 fresh and 4 done)

PrunedKeptTotal
New304203042
Fresh022
Picked011
Done033
Total304263048

Merged error: 5.4b

Counts
3048 → 6

regimes112.0ms

Accuracy

0% (0.2b remaining)

Error of 5.2b against oracle of 5.0b and baseline of 5.2b

bsearch0.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
083
183

end0.0ms

sample345.0ms

Algorithm
intervals
Results
190.0ms10603×body80valid