Details

Time bar (total: 10.0m)

sample42.0ms

Algorithm
intervals
Results
9.0ms60×body640valid
8.0ms243×body80nan
6.0ms36×body1280valid
4.0ms119×body80valid
3.0ms28×body320valid
1.0ms13×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0116
1146
2146

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: 21.5b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
3.9b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
1035×times-frac
875×*-un-lft-identity
742×add-sqr-sqrt
712×add-cube-cbrt
594×prod-diff
562×sqrt-prod
73×distribute-lft-out
54×div-inv
46×sqrt-div associate-/r/
23×flip3-+ flip-+
22×fma-neg
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
7×add-exp-log add-cbrt-cube
6×associate-/l*
5×add-log-exp
3×pow1 expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg flip3-- diff-log frac-sub flip--
Counts
3 → 739
Calls
3 calls:
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
4.0ms
(/ 1.0 (sqrt x))
48.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series255.0ms

Counts
3 → 9
Calls
3 calls:
77.0ms
(/ 1.0 (sqrt (+ x 1.0)))
37.0ms
(/ 1.0 (sqrt x))
141.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify261.0ms

Algorithm
egg-herbie
Counts
748 → 748
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
0151724924
1419718301
2500118266

prune1.3s

Filtered
748 candidates to 285 candidates (38.1%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New72820748
Fresh000
Picked101
Done000
Total72920749

Merged error: 20.8b

Counts
749 → 20

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt (sqrt x)))
0.3b
(/ (/ 1.0 (sqrt (sqrt x))) (sqrt (sqrt x)))
18.0b
(- (/ (/ 1.0 (sqrt (sqrt x))) (sqrt (sqrt x))) (/ 1.0 (sqrt (+ x 1.0))))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
21251×times-frac
18702×sqrt-prod
13431×*-un-lft-identity
11877×add-sqr-sqrt
11710×add-cube-cbrt
7641×prod-diff
854×distribute-lft-out
576×div-inv
568×sqrt-div associate-/r/
284×flip3-+ flip-+
283×fma-neg
39×difference-of-squares
37×associate-/l*
25×associate-/r*
13×add-exp-log add-cbrt-cube
6×add-log-exp
5×cbrt-undiv div-exp
4×pow1 expm1-log1p-u log1p-expm1-u distribute-lft-out--
3×frac-2neg clear-num
1×sub-neg flip3-- diff-log frac-sub flip-- associate-/l/
Counts
4 → 8418
Calls
4 calls:
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
5.0ms
(/ 1.0 (sqrt (sqrt x)))
16.0ms
(/ (/ 1.0 (sqrt (sqrt x))) (sqrt (sqrt x)))
477.0ms
(- (/ (/ 1.0 (sqrt (sqrt x))) (sqrt (sqrt x))) (/ 1.0 (sqrt (+ x 1.0))))

series415.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(/ 1.0 (sqrt (+ x 1.0)))
161.0ms
(/ 1.0 (sqrt (sqrt x)))
40.0ms
(/ (/ 1.0 (sqrt (sqrt x))) (sqrt (sqrt x)))
136.0ms
(- (/ (/ 1.0 (sqrt (sqrt x))) (sqrt (sqrt x))) (/ 1.0 (sqrt (+ x 1.0))))

simplify3.4s

Algorithm
egg-herbie
Counts
8430 → 8430
Iterations

Useful iterations: 0 (341.0ms)

IterNodesCost
05001396021

prune18.9s

Filtered
8430 candidates to 3926 candidates (46.6%)
Pruning

32 alts after pruning (32 fresh and 0 done)

PrunedKeptTotal
New8404268430
Fresh13619
Picked101
Done000
Total8418328450

Merged error: 20.7b

Counts
8450 → 32

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt x))
0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ (* 1.0 (pow (/ 1 x) 1/4)) (sqrt (sqrt x)))
15.9b
(- (/ (* 1.0 (pow (/ 1 x) 1/4)) (sqrt (sqrt x))) (/ 1.0 (sqrt (+ x 1.0))))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
557×times-frac
453×sqrt-prod
410×*-un-lft-identity
351×prod-diff
332×add-sqr-sqrt
322×add-cube-cbrt
43×div-inv distribute-lft-out
28×sqrt-div associate-/r/
26×add-exp-log
16×associate-/r*
14×flip3-+ flip-+
13×fma-neg
11×add-cbrt-cube
10×div-exp
6×pow1 prod-exp add-log-exp
4×expm1-log1p-u sqrt-pow1 pow-exp log1p-expm1-u associate-/l*
3×cbrt-undiv difference-of-squares
2×rem-sqrt-square frac-2neg pow1/2 clear-num
1×pow-to-exp sub-neg rec-exp flip3-- diff-log 1-exp frac-sub flip-- cbrt-unprod distribute-lft-out--
Counts
4 → 491
Calls
4 calls:
2.0ms
(sqrt (sqrt x))
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
12.0ms
(/ (* 1.0 (pow (/ 1 x) 1/4)) (sqrt (sqrt x)))
34.0ms
(- (/ (* 1.0 (pow (/ 1 x) 1/4)) (sqrt (sqrt x))) (/ 1.0 (sqrt (+ x 1.0))))

series432.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(sqrt (sqrt x))
70.0ms
(/ 1.0 (sqrt (+ x 1.0)))
73.0ms
(/ (* 1.0 (pow (/ 1 x) 1/4)) (sqrt (sqrt x)))
162.0ms
(- (/ (* 1.0 (pow (/ 1 x) 1/4)) (sqrt (sqrt x))) (/ 1.0 (sqrt (+ x 1.0))))

simplify197.0ms

Algorithm
egg-herbie
Counts
503 → 503
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
0142116481
1464712576
2500112562

prune883.0ms

Filtered
503 candidates to 208 candidates (41.4%)
Pruning

33 alts after pruning (32 fresh and 1 done)

PrunedKeptTotal
New4994503
Fresh32831
Picked011
Done000
Total50233535

Merged error: 20.7b

Counts
535 → 33

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (sqrt (+ x 1.0)))
0.3b
(cbrt (sqrt (+ x 1.0)))
0.3b
(cbrt (sqrt (+ x 1.0)))
21.6b
(- (/ 1.0 (sqrt x)) (/ (/ (/ 1.0 (cbrt (sqrt (+ x 1.0)))) (cbrt (sqrt (+ x 1.0)))) (cbrt (sqrt (+ x 1.0)))))

rewrite21.9s

Algorithm
rewrite-expression-head
Rules
292114×times-frac
184995×*-un-lft-identity
158229×cbrt-prod
140465×add-sqr-sqrt
139839×add-cube-cbrt
123445×sqrt-prod
80652×prod-diff
22575×distribute-lft-out
6109×div-inv
4890×cbrt-div sqrt-div
4884×associate-/r/
2445×flip3-+ flip-+
120×difference-of-squares
22×fma-neg
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×pow1/3
2×distribute-lft-out--
1×sub-neg flip3-- diff-log frac-sub flip--
Counts
4 → 80868
Calls
4 calls:
4.0ms
(cbrt (sqrt (+ x 1.0)))
4.0ms
(cbrt (sqrt (+ x 1.0)))
4.0ms
(cbrt (sqrt (+ x 1.0)))
4.4s
(- (/ 1.0 (sqrt x)) (/ (/ (/ 1.0 (cbrt (sqrt (+ x 1.0)))) (cbrt (sqrt (+ x 1.0)))) (cbrt (sqrt (+ x 1.0)))))

series355.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(cbrt (sqrt (+ x 1.0)))
78.0ms
(cbrt (sqrt (+ x 1.0)))
78.0ms
(cbrt (sqrt (+ x 1.0)))
121.0ms
(- (/ 1.0 (sqrt x)) (/ (/ (/ 1.0 (cbrt (sqrt (+ x 1.0)))) (cbrt (sqrt (+ x 1.0)))) (cbrt (sqrt (+ x 1.0)))))

simplify1.0m

Algorithm
egg-herbie
Counts
80880 → 80880
Iterations

Useful iterations: 0 (716.0ms)

IterNodesCost
0469758482677

prune4.0m

Filtered
80880 candidates to 34345 candidates (42.5%)
Pruning

56 alts after pruning (55 fresh and 1 done)

PrunedKeptTotal
New808374380880
Fresh191231
Picked101
Done011
Total808575680913

Merged error: 20.7b

Counts
80913 → 56

regimes1.0s

Accuracy

89.8% (0.5b remaining)

Error of 19.1b against oracle of 18.6b and baseline of 23.4b

bsearch71.0ms

Steps
ItersRangePoint
7
9.885888095165e+93
1.127880316639885e+96
4.3562617179563936e+94

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
050133
155133
257133
357133

end0.0ms

sample1.1s

Algorithm
intervals
Results
260.0ms8097×body80nan
246.0ms1838×body640valid
195.0ms1134×body1280valid
151.0ms4099×body80valid
62.0ms618×body320valid
20.0ms311×body160valid

end4.1m