Details

Time bar (total: 5.8s)

sample32.0ms

Algorithm
intervals
Results
6.0ms288×body80nan
5.0ms42×body1280valid
4.0ms46×body640valid
3.0ms133×body80valid
2.0ms22×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

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
3.1b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
73×add-sqr-sqrt
69×times-frac
50×sqrt-prod
42×add-cube-cbrt
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/l* add-log-exp
5×pow1
4×sqrt-div div-inv
2×cbrt-undiv frac-2neg flip3-+ div-exp clear-num associate-/r/ flip-+
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log frac-sub flip--
Counts
4 → 133
Calls
4 calls:
4.0ms
(sqrt (+ x 1.0))
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
3.0ms
(/ 1.0 (sqrt x))
43.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series280.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(sqrt (+ x 1.0))
76.0ms
(/ 1.0 (sqrt (+ x 1.0)))
41.0ms
(/ 1.0 (sqrt x))
132.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify47.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
04431097
114341038
25001992

prune327.0ms

Filtered
145 candidates to 98 candidates (67.6%)
Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 18.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
0.3b
(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
0.5b
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
3.0b
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
362×times-frac
331×*-un-lft-identity
258×add-sqr-sqrt
180×sqrt-prod
174×add-cube-cbrt
88×distribute-lft-out
67×swap-sqr
49×associate-*r* associate-*l*
30×add-exp-log add-cbrt-cube
19×div-inv
18×pow1 frac-sub unswap-sqr
16×difference-of-squares
14×frac-times associate-*r/ associate-*l/ associate-/r*
11×associate-/r/ associate-/l/
9×cbrt-undiv div-exp
8×sqrt-div prod-exp cbrt-unprod
6×add-log-exp
5×flip3-+ flip-+
4×associate-/l*
2×pow2 flip3-- pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up flip--
1×sub-neg frac-2neg diff-log div-sub frac-add clear-num
Counts
4 → 354
Calls
4 calls:
101.0ms
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
41.0ms
(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
25.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
9.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

series482.0ms

Counts
4 → 12
Calls
4 calls:
359.0ms
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
29.0ms
(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
27.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
67.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

simplify88.0ms

Algorithm
egg-herbie
Counts
366 → 366
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
015935895
150025420

prune711.0ms

Filtered
366 candidates to 203 candidates (55.5%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
0.3b
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
1.5b
(- (+ x 1.0) x)

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
303×*-un-lft-identity
296×times-frac
124×sqrt-prod
117×distribute-lft-out
108×add-sqr-sqrt
106×add-cube-cbrt
37×add-exp-log add-cbrt-cube
35×associate-/r/
34×div-inv
30×associate-*l/
27×associate-/r*
17×flip3-+ flip-+
15×cbrt-undiv div-exp
13×associate-/l*
9×prod-exp cbrt-unprod add-log-exp
4×pow1
3×frac-2neg clear-num
2×sqrt-div diff-log distribute-lft-out--
1×sub-neg flip3-- frac-add associate--l+ sum-log flip-- associate-/l/ difference-of-squares
Counts
4 → 248
Calls
4 calls:
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
3.0ms
(/ 1.0 (sqrt x))
102.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
17.0ms
(- (+ x 1.0) x)

series609.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ 1.0 (sqrt (+ x 1.0)))
44.0ms
(/ 1.0 (sqrt x))
488.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
1.0ms
(- (+ x 1.0) x)

simplify63.0ms

Algorithm
egg-herbie
Counts
260 → 260
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012493999
150013639

prune508.0ms

Filtered
260 candidates to 140 candidates (53.8%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
0.6b
(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
5.7b
(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
298×*-un-lft-identity
297×times-frac
124×sqrt-prod
116×distribute-lft-out
106×add-sqr-sqrt add-cube-cbrt
58×add-exp-log add-cbrt-cube
37×associate-/r/
35×div-inv
32×associate-*l/
28×associate-/r*
21×cbrt-undiv div-exp
18×flip3-+ prod-exp cbrt-unprod flip-+
14×associate-/l*
4×pow1 frac-2neg clear-num add-log-exp
2×sqrt-div
1×frac-add associate-/l/
Counts
4 → 258
Calls
4 calls:
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
3.0ms
(/ 1.0 (sqrt x))
12.0ms
(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
91.0ms
(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

series639.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ 1.0 (sqrt (+ x 1.0)))
37.0ms
(/ 1.0 (sqrt x))
35.0ms
(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
491.0ms
(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

simplify65.0ms

Algorithm
egg-herbie
Counts
270 → 270
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012033694
150023295

prune535.0ms

Filtered
270 candidates to 146 candidates (54.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes36.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01512
11512

end0.0ms

sample834.0ms

Algorithm
intervals
Results
182.0ms1845×body640valid
171.0ms8031×body80nan
142.0ms1143×body1280valid
103.0ms4083×body80valid
44.0ms621×body320valid
15.0ms308×body160valid