Details

Time bar (total: 2.5s)

sample17.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
1.0ms57×body80nan

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
084
184

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.2b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.2b
(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
13×add-sqr-sqrt
12×add-cube-cbrt times-frac
5×distribute-lft-out
4×add-exp-log associate-/r* sqrt-prod add-cbrt-cube
3×pow1 associate-/l*
2×flip3-+ sqrt-div associate-/r/ flip-+ add-log-exp
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
2 → 49
Calls
2 calls:
3.0ms
(sqrt (+ x 1.0))
7.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series24.0ms

Counts
2 → 6
Calls
2 calls:
7.0ms
(sqrt (+ x 1.0))
17.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify43.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0412473
11774450
25002447

prune106.0ms

Filtered
42 candidates to 55 candidates (-31.0%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New51455
Fresh000
Picked101
Done000
Total52456

Merged error: 0b

Counts
56 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ x (+ 1.0 (/ (sqrt (+ (pow x 3) (pow 1.0 3))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))))
7.0b
(/ (sqrt (+ (pow x 3) (pow 1.0 3))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))
7.5b
(sqrt (+ (pow x 3) (pow 1.0 3)))
11.0b
(sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
143×*-un-lft-identity
114×sqrt-prod
84×times-frac
57×add-sqr-sqrt
55×add-cube-cbrt
44×distribute-lft-out
32×unpow-prod-down cube-prod
15×associate-/l*
10×associate-/r*
8×add-exp-log sqrt-div sum-cubes add-cbrt-cube
6×pow1
5×flip3-+ flip-+
4×associate-/r/ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv associate-/l/
1×sqrt-undiv
Counts
4 → 176
Calls
4 calls:
33.0ms
(/ x (+ 1.0 (/ (sqrt (+ (pow x 3) (pow 1.0 3))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))))
19.0ms
(/ (sqrt (+ (pow x 3) (pow 1.0 3))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))
10.0ms
(sqrt (+ (pow x 3) (pow 1.0 3)))
5.0ms
(sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

series36.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(/ x (+ 1.0 (/ (sqrt (+ (pow x 3) (pow 1.0 3))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))))
7.0ms
(/ (sqrt (+ (pow x 3) (pow 1.0 3))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))
4.0ms
(sqrt (+ (pow x 3) (pow 1.0 3)))
4.0ms
(sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

simplify90.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
06993257
130473043
250023032

prune381.0ms

Filtered
104 candidates to 188 candidates (-80.8%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1880188
Fresh033
Picked011
Done000
Total1884192

Merged error: 0b

Counts
192 → 4

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
66×*-un-lft-identity
55×add-sqr-sqrt
52×times-frac
39×sqrt-prod
38×add-cube-cbrt
30×associate-*r*
14×distribute-lft-out
10×add-exp-log add-cbrt-cube
6×pow1 associate-*l* associate-/l* unswap-sqr
4×associate-/r* associate-/r/
3×flip3-+ flip-+ add-log-exp
2×cbrt-undiv sqrt-div div-exp prod-exp cbrt-unprod div-inv
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num *-commutative
Counts
3 → 120
Calls
3 calls:
3.0ms
(sqrt (+ x 1.0))
8.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
18.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series48.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(sqrt (+ x 1.0))
28.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
16.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify101.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
08081382
140051273
250011249

prune182.0ms

Filtered
81 candidates to 129 candidates (-59.3%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1290129
Fresh022
Picked011
Done011
Total1294133

Merged error: 0b

Counts
133 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (/ x (+ 1.0 (sqrt (+ x 1.0)))))
0.2b
(/ x (+ 1.0 (sqrt (+ x 1.0))))
0.2b
(/ x (+ 1.0 (sqrt (+ x 1.0))))
0.3b
(* (sqrt (/ x (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (/ x (+ 1.0 (sqrt (+ x 1.0))))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
134×*-un-lft-identity
116×sqrt-prod
103×times-frac
101×add-sqr-sqrt
70×add-cube-cbrt
29×swap-sqr distribute-lft-out
21×associate-*r* associate-*l*
20×pow1
14×associate-/r/
10×add-exp-log add-cbrt-cube
9×sqrt-pow1 pow1/2 unswap-sqr
8×associate-/r*
7×flip3-+ flip-+ div-inv
6×associate-/l*
5×sqrt-div pow-prod-up
4×add-log-exp
3×pow-prod-down pow-sqr
2×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ associate-*l/ prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 204
Calls
4 calls:
10.0ms
(sqrt (/ x (+ 1.0 (sqrt (+ x 1.0)))))
7.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))
7.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))
24.0ms
(* (sqrt (/ x (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (/ x (+ 1.0 (sqrt (+ x 1.0))))))

series87.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(sqrt (/ x (+ 1.0 (sqrt (+ x 1.0)))))
19.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))
16.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))
26.0ms
(* (sqrt (/ x (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (/ x (+ 1.0 (sqrt (+ x 1.0))))))

simplify126.0ms

Algorithm
egg-herbie
Counts
216 → 216
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
08112434
144642291
250032262

prune449.0ms

Filtered
138 candidates to 216 candidates (-56.5%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New2160216
Fresh011
Picked011
Done022
Total2164220

Merged error: 0b

Counts
220 → 4

regimes115.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.4b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03324
13324

end0.0ms

sample460.0ms

Algorithm
intervals
Results
225.0ms7999×body80valid
66.0ms2627×body80nan
0.0ms1×body1280valid

Profiling

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