Details

Time bar (total: 4.1s)

sample22.0ms

Algorithm
intervals
Results
6.0ms50×body1280valid
4.0ms139×body80valid
3.0ms35×body640valid
2.0ms25×body320valid
0.0ms7×body160valid

simplify21.0ms

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

prune2.0ms

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: 27.4b

Counts
2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
2.2b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
981×*-un-lft-identity
736×times-frac
585×add-sqr-sqrt
468×prod-diff
419×add-cube-cbrt
189×distribute-lft-out
94×associate-/r/
90×distribute-lft-out--
81×difference-of-squares
47×div-inv
29×flip3-+ flip-+
20×flip3-- flip--
18×fma-neg
9×associate-/r*
7×add-exp-log add-cbrt-cube associate-/l*
5×add-log-exp
3×pow1 expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 596
Calls
3 calls:
5.0ms
(/ x (+ x 1.0))
8.0ms
(/ (+ x 1.0) (- x 1.0))
44.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series199.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(/ x (+ x 1.0))
39.0ms
(/ (+ x 1.0) (- x 1.0))
127.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify212.0ms

Algorithm
egg-herbie
Counts
605 → 605
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
0120818366
1368713388
2500113292

prune659.0ms

Filtered
605 candidates to 217 candidates (35.9%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New6014605
Fresh000
Picked101
Done000
Total6024606

Merged error: 0.2b

Counts
606 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

14.1b
(/ x (- (* x x) (* 1.0 1.0)))
14.1b
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
14.1b
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
27.8b
(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity
44×times-frac
33×add-sqr-sqrt add-cube-cbrt
14×difference-of-squares
12×associate-/r*
11×associate-/l*
10×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/r/
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp
3×cbrt-undiv flip3-- frac-2neg div-exp clear-num flip-- div-inv
2×flip3-+ flip-+
1×fma-udef
Counts
4 → 129
Calls
4 calls:
6.0ms
(/ x (- (* x x) (* 1.0 1.0)))
8.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
7.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
1.0ms
(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

series330.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(/ x (- (* x x) (* 1.0 1.0)))
42.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
37.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
187.0ms
(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

simplify59.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03931262
116001156
250011097

prune349.0ms

Filtered
141 candidates to 114 candidates (80.9%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1410141
Fresh033
Picked011
Done000
Total1414145

Merged error: 0.2b

Counts
145 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)
27.4b
(fma (/ (* (cbrt x) (cbrt x)) 1) (/ (cbrt x) (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(fma (/ (* (cbrt x) (cbrt x)) 1) (/ (cbrt x) (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

series867.0ms

Counts
4 → 12
Calls
4 calls:
368.0ms
(cbrt x)
178.0ms
(cbrt x)
188.0ms
(cbrt x)
133.0ms
(fma (/ (* (cbrt x) (cbrt x)) 1) (/ (cbrt x) (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

simplify60.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
0123312
1340272
21569258
35002253

prune142.0ms

Filtered
61 candidates to 54 candidates (88.5%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New60161
Fresh022
Picked011
Done011
Total60565

Merged error: 0.0b

Counts
65 → 5

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 1.0 (pow x 2) (fma 3.0 x 1.0))
0.1b
(fma 3.0 x 1.0)

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
2×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
2 → 20
Calls
2 calls:
1.0ms
(fma 1.0 (pow x 2) (fma 3.0 x 1.0))
1.0ms
(fma 3.0 x 1.0)

series52.0ms

Counts
2 → 6
Calls
2 calls:
21.0ms
(fma 1.0 (pow x 2) (fma 3.0 x 1.0))
31.0ms
(fma 3.0 x 1.0)

simplify121.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 4 (118.0ms)

IterNodesCost
04387
113777
262677
3388877
4500174

prune52.0ms

Filtered
26 candidates to 21 candidates (80.8%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New26026
Fresh022
Picked011
Done022
Total26531

Merged error: 0.0b

Counts
31 → 5

regimes33.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 29.0b

bsearch90.0ms

Steps
ItersRangePoint
11
1.2997713508729505
5.879238312391923e+20
49404672.01762006
9
-83730160.10765809
-5.855776674212404
-22594.137157907826

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04626
14926
24926

end0.0ms

sample614.0ms

Algorithm
intervals
Results
218.0ms1693×body1280valid
133.0ms1271×body640valid
112.0ms4128×body80valid
45.0ms604×body320valid
15.0ms304×body160valid