Details

Time bar (total: 4.6s)

sample50.0ms

Algorithm
intervals
Results
14.0ms189×body80valid
8.0ms26×body2560valid
6.0ms256×pre80true
5.0ms20×body1280valid
3.0ms15×body640valid
1.0ms4×body320valid
0.0ms2×body160valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0289
1409
2489
3509
4529
5539
6539

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: 14.8b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.4b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
22×add-sqr-sqrt
21×add-cube-cbrt
18×times-frac
16×sqrt-prod
8×pow1
6×add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u
3×fma-def sqrt-pow1 associate-/l*
2×pow1/2 associate-*r/ associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg div-exp pow-prod-down clear-num sum-log div-inv distribute-lft-out
Counts
4 → 92
Calls
4 calls:
13.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
7.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series449.0ms

Counts
4 → 12
Calls
4 calls:
263.0ms
(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
54.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
74.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
58.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify79.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 3 (69.0ms)

IterNodesCost
0297948
1884898
22732885
35001883

prune273.0ms

Filtered
104 candidates to 82 candidates (78.8%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New9212104
Fresh000
Picked101
Done000
Total9312105

Merged error: 14.6b

Counts
105 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.4b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.4b
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
24×add-sqr-sqrt
23×add-cube-cbrt
18×times-frac
15×sqrt-prod
6×pow1 add-exp-log associate-/r* add-cbrt-cube add-log-exp
5×log-pow
4×expm1-log1p-u log-prod exp-prod sqrt-div log1p-expm1-u
3×fma-def flip3-+ flip-+ associate-/l*
2×associate-/r/ distribute-lft-out
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp exp-sum clear-num sum-log div-inv
Counts
4 → 96
Calls
4 calls:
7.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series278.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
88.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
78.0ms
(log (exp (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
57.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify79.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
0286956
1875889
22480876
35002874

prune315.0ms

Filtered
108 candidates to 83 candidates (76.9%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1071108
Fresh01111
Picked101
Done000
Total10812120

Merged error: 14.6b

Counts
120 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.1b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
12.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
24×associate-*r*
22×*-un-lft-identity times-frac
20×add-cube-cbrt
15×sqrt-prod
13×add-exp-log
10×pow1
9×add-cbrt-cube
6×sqrt-div add-log-exp
5×unswap-sqr
4×expm1-log1p-u flip3-+ prod-exp flip-+ log1p-expm1-u
3×fma-def sqrt-pow1 associate-*r/ associate-*l*
2×pow1/2 div-exp pow-prod-down associate-/r/ cbrt-unprod
1×cbrt-undiv +-commutative rem-sqrt-square rec-exp 1-exp sum-log un-div-inv *-commutative div-inv
Counts
4 → 99
Calls
4 calls:
4.0ms
(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
13.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series476.0ms

Counts
4 → 12
Calls
4 calls:
293.0ms
(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
56.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
75.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
52.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify50.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0407969
11772880
25001845

prune261.0ms

Filtered
111 candidates to 82 candidates (73.9%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1074111
Fresh6511
Picked101
Done000
Total1149123

Merged error: 14.5b

Counts
123 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0b
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
2.1b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
12.8b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
24×*-un-lft-identity associate-*r*
22×add-cube-cbrt times-frac
15×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×pow1
6×add-log-exp
5×log-pow unswap-sqr
4×expm1-log1p-u exp-prod sqrt-div prod-exp log1p-expm1-u
3×log-prod fma-def flip3-+ associate-*l* flip-+
2×div-exp associate-/r/ cbrt-unprod
1×cbrt-undiv +-commutative rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ rem-log-exp pow-prod-down sum-log un-div-inv *-commutative div-inv
Counts
4 → 102
Calls
4 calls:
14.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
3.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
9.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series452.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
271.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
75.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
52.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify50.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04161032
11721918
25001881

prune297.0ms

Filtered
114 candidates to 87 candidates (76.3%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1077114
Fresh358
Picked101
Done000
Total11112123

Merged error: 14.5b

Counts
123 → 12

regimes167.0ms

Accuracy

0% (0.6b remaining)

Error of 13.6b against oracle of 13.0b and baseline of 13.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02814
12814

end0.0ms

sample1.2s

Algorithm
intervals
Results
317.0ms6019×body80valid
260.0ms827×body2560valid
154.0ms8000×pre80true
147.0ms593×body1280valid
63.0ms311×body640valid
27.0ms167×body320valid
8.0ms83×body160valid

Profiling

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