Details

Time bar (total: 36.6s)

sample24.0ms

Algorithm
intervals
Results
7.0ms47×body1280valid
5.0ms46×body640valid
4.0ms136×body80valid
1.0ms17×body320valid
1.0ms10×body160valid

simplify17.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0126
1166
2196
3216
4276
5396
6586
7796
81076
91606
102776
113036
123036

prune6.0ms

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: 28.3b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ x (+ x 1.0))
3.2b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
65×*-un-lft-identity
32×times-frac
23×add-sqr-sqrt
13×distribute-lft-out--
12×distribute-lft-out
11×add-cube-cbrt
4×add-exp-log associate-/r* add-cbrt-cube add-log-exp difference-of-squares
3×associate-/l*
2×pow1 associate-/r/
1×cbrt-undiv sub-neg flip3-- frac-2neg flip3-+ diff-log div-exp clear-num frac-sub flip-- flip-+ div-inv
Counts
2 → 59
Calls
2 calls:
5.0ms
(/ x (+ x 1.0))
28.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series9.0ms

Counts
2 → 6
Calls
2 calls:
2.0ms
(/ x (+ x 1.0))
7.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify117.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0266459
1872434
23573429
35001429

prune98.0ms

Filtered
65 candidates to 44 candidates (32.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New62365
Fresh000
Picked101
Done000
Total63366

Merged error: 0.0b

Counts
66 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(/ (/ x (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))
0.1b
(/ x (sqrt (+ x 1.0)))
9.1b
(- (/ (/ x (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

rewrite241.0ms

Algorithm
rewrite-expression-head
Rules
413×times-frac
325×*-un-lft-identity
245×add-sqr-sqrt
238×sqrt-prod
189×add-cube-cbrt
59×distribute-lft-out
30×associate-/l*
22×sqrt-div
20×associate-/r/
14×associate-/r* difference-of-squares
11×add-exp-log flip3-+ add-cbrt-cube flip-+
10×div-inv
7×distribute-lft-out--
6×add-log-exp
5×pow1
4×cbrt-undiv div-exp
2×frac-2neg clear-num
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log frac-sub flip-- associate-/l/
Counts
4 → 333
Calls
4 calls:
3.0ms
(sqrt (+ x 1.0))
18.0ms
(/ (/ x (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))
6.0ms
(/ x (sqrt (+ x 1.0)))
195.0ms
(- (/ (/ x (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

series21.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(sqrt (+ x 1.0))
3.0ms
(/ (/ x (sqrt (+ x 1.0))) (sqrt (+ x 1.0)))
7.0ms
(/ x (sqrt (+ x 1.0)))
7.0ms
(- (/ (/ x (sqrt (+ x 1.0))) (sqrt (+ x 1.0))) (/ (+ x 1.0) (- x 1.0)))

simplify100.0ms

Algorithm
egg-herbie
Counts
345 → 345
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
09344355
134513838
250013815

prune406.0ms

Filtered
345 candidates to 154 candidates (55.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New3432345
Fresh022
Picked101
Done000
Total3444348

Merged error: 0.0b

Counts
348 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (+ x 1.0)) (- x 1.0))
0.1b
(/ x (sqrt (+ x 1.0)))
2.5b
(/ (- (* (/ x (sqrt (+ x 1.0))) (- x 1.0)) (* (sqrt (+ x 1.0)) (+ x 1.0))) (* (sqrt (+ x 1.0)) (- x 1.0)))
11.0b
(- (* (/ x (sqrt (+ x 1.0))) (- x 1.0)) (* (sqrt (+ x 1.0)) (+ x 1.0)))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
80×frac-times frac-sub
74×sqrt-div
67×flip3-+ flip-+
56×associate-*r/
42×associate-/l/
40×flip3-- associate-*l/ flip--
37×*-un-lft-identity
31×add-sqr-sqrt
25×add-cube-cbrt
24×times-frac
21×sqrt-prod
13×add-exp-log add-cbrt-cube
10×associate-/r/
8×associate-/r*
7×associate-*l*
6×pow1 associate-/l* add-log-exp
5×distribute-rgt-in sub-neg distribute-lft-in associate-*r* distribute-lft-out
4×associate--l+
3×cbrt-undiv div-exp
2×frac-2neg prod-exp clear-num cbrt-unprod div-inv associate--r+ unswap-sqr
1×diff-log div-sub pow-prod-down *-commutative distribute-lft-out-- difference-of-squares
Counts
4 → 212
Calls
4 calls:
19.0ms
(* (sqrt (+ x 1.0)) (- x 1.0))
10.0ms
(/ x (sqrt (+ x 1.0)))
39.0ms
(/ (- (* (/ x (sqrt (+ x 1.0))) (- x 1.0)) (* (sqrt (+ x 1.0)) (+ x 1.0))) (* (sqrt (+ x 1.0)) (- x 1.0)))
14.0ms
(- (* (/ x (sqrt (+ x 1.0))) (- x 1.0)) (* (sqrt (+ x 1.0)) (+ x 1.0)))

series94.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(* (sqrt (+ x 1.0)) (- x 1.0))
7.0ms
(/ x (sqrt (+ x 1.0)))
57.0ms
(/ (- (* (/ x (sqrt (+ x 1.0))) (- x 1.0)) (* (sqrt (+ x 1.0)) (+ x 1.0))) (* (sqrt (+ x 1.0)) (- x 1.0)))
23.0ms
(- (* (/ x (sqrt (+ x 1.0))) (- x 1.0)) (* (sqrt (+ x 1.0)) (+ x 1.0)))

simplify74.0ms

Algorithm
egg-herbie
Counts
224 → 224
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
019063772
150013669

prune966.0ms

Filtered
224 candidates to 192 candidates (14.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New2222224
Fresh123
Picked101
Done000
Total2244228

Merged error: 0.0b

Counts
228 → 4

localize35.0ms

Local error

Found 4 expressions with local error:

6.4b
(sqrt (+ (pow x 3) (pow 1.0 3)))
13.7b
(- (* (* x (- (* x x) (* 1.0 1.0))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))) (* (* (sqrt (+ x 1.0)) (+ x 1.0)) (* (sqrt (+ (pow x 3) (pow 1.0 3))) (+ x 1.0))))
13.8b
(sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))
13.8b
(sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
1408×frac-times
1350×sqrt-div
1107×flip3-+ flip-+
992×associate-*r/
640×frac-sub
512×associate-*l/
241×flip3-- flip--
17×*-un-lft-identity
15×sqrt-prod
10×add-sqr-sqrt
7×pow1 add-cube-cbrt
6×add-log-exp
5×distribute-lft-out
4×add-exp-log distribute-rgt-in unpow-prod-down distribute-lft-in cube-prod add-cbrt-cube associate--r+
3×rem-sqrt-square sqrt-pow1 pow1/2
1×sub-neg diff-log sum-cubes
Counts
4 → 707
Calls
4 calls:
10.0ms
(sqrt (+ (pow x 3) (pow 1.0 3)))
53.0ms
(- (* (* x (- (* x x) (* 1.0 1.0))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))) (* (* (sqrt (+ x 1.0)) (+ x 1.0)) (* (sqrt (+ (pow x 3) (pow 1.0 3))) (+ x 1.0))))
5.0ms
(sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))
5.0ms
(sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

series25.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(sqrt (+ (pow x 3) (pow 1.0 3)))
14.0ms
(- (* (* x (- (* x x) (* 1.0 1.0))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))) (* (* (sqrt (+ x 1.0)) (+ x 1.0)) (* (sqrt (+ (pow x 3) (pow 1.0 3))) (+ x 1.0))))
3.0ms
(sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))
4.0ms
(sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

simplify558.0ms

Algorithm
egg-herbie
Counts
719 → 719
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
0500161569

prune32.6s

Filtered
719 candidates to 706 candidates (1.8%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New7181719
Fresh033
Picked101
Done000
Total7194723

Merged error: 0.0b

Counts
723 → 4

regimes53.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 31.6b

bsearch33.0ms

Steps
ItersRangePoint
9
4429.475794956495
43212209514.887886
13089.408634996185
9
-481781.8837170955
-0.012224266776747678
-1.0063966518300564

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06054
16054

end0.0ms

sample740.0ms

Algorithm
intervals
Results
254.0ms1692×body1280valid
152.0ms1268×body640valid
126.0ms4080×body80valid
56.0ms649×body320valid
19.0ms311×body160valid

Profiling

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