Details

Time bar (total: 6.7s)

sample47.0ms

Algorithm
intervals
Results
10.0ms198×body80valid
6.0ms27×body1280valid
5.0ms17×body2560valid
5.0ms256×pre80true
2.0ms10×body640valid
1.0ms4×body320valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0279
1349
2389
3409
4419
5419

prune4.0ms

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: 13.1b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
0.0b
(+ (* (* 4.0 p) p) (* x x))
0.0b
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
21×add-sqr-sqrt
20×add-cube-cbrt
18×times-frac
15×sqrt-prod
8×add-log-exp
6×add-exp-log associate-/r* add-cbrt-cube
5×pow1
4×flip3-+ sqrt-div flip-+
3×associate-/l*
2×+-commutative sum-log associate-/r/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv distribute-lft-out
Counts
4 → 79
Calls
4 calls:
12.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms
(+ (* (* 4.0 p) p) (* x x))
12.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series273.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
40.0ms
(+ (* (* 4.0 p) p) (* x x))
68.0ms
(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
73.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify148.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0278822
11014772
24232757
35001757

prune696.0ms

Filtered
91 candidates to 67 candidates (26.4%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New791291
Fresh000
Picked101
Done000
Total801292

Merged error: 12.9b

Counts
92 → 12

localize12.0ms

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)))))
2.9b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
24×associate-*r*
22×times-frac
21×*-un-lft-identity
19×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×flip3-+ prod-exp flip-+
3×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 → 88
Calls
4 calls:
4.0ms
(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
14.0ms
(* 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)))

series571.0ms

Counts
4 → 12
Calls
4 calls:
340.0ms
(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
67.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
92.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
71.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify47.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0390900
11684818
25001784

prune619.0ms

Filtered
100 candidates to 71 candidates (29.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New964100
Fresh3811
Picked101
Done000
Total10012112

Merged error: 12.9b

Counts
112 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
8.5b
(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
39×sqrt-prod
27×associate-*r*
22×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
18×times-frac
11×pow1
10×sqrt-div
9×add-exp-log add-cbrt-cube
6×add-log-exp
4×flip3-+ flip-+
3×associate-*r/ pow-prod-down prod-exp cbrt-unprod
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×+-commutative frac-times associate-*l* associate-*l/ sum-log *-commutative div-inv
Counts
4 → 86
Calls
4 calls:
26.0ms
(* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
3.0ms
(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series292.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
94.0ms
(+ 1.0 (* (* x (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (sqrt (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
69.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))
65.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify55.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03861299
115091123
250011062

prune821.0ms

Filtered
98 candidates to 72 candidates (26.5%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New94498
Fresh4711
Picked011
Done000
Total9812110

Merged error: 12.9b

Counts
110 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
2.9b
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
2.9b
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
14.5b
(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
24×associate-*r*
23×*-un-lft-identity
22×times-frac
21×add-cube-cbrt
15×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×pow1
6×add-log-exp
5×log-pow unswap-sqr
4×exp-prod sqrt-div prod-exp
3×log-prod 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 → 91
Calls
4 calls:
14.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms
(+ 1.0 (* 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))))))))))
5.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

series543.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
88.0ms
(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
321.0ms
(log (exp (sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))))
68.0ms
(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify44.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0399962
11650851
25002816

prune884.0ms

Filtered
103 candidates to 76 candidates (26.2%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New9310103
Fresh5510
Picked101
Done101
Total10015115

Merged error: 12.9b

Counts
115 → 15

regimes324.0ms

Accuracy

0% (1.4b remaining)

Error of 14.5b against oracle of 13.1b and baseline of 14.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02921
12921

end0.0ms

sample1.1s

Algorithm
intervals
Results
291.0ms6019×body80valid
237.0ms803×body2560valid
151.0ms648×body1280valid
123.0ms8000×pre80true
58.0ms296×body640valid
23.0ms171×body320valid
6.0ms63×body160valid

Profiling

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