Details

Time bar (total: 7.3s)

sample31.0ms

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

localize11.0ms

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))))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
1035×times-frac
879×*-un-lft-identity
747×add-sqr-sqrt
714×add-cube-cbrt
594×prod-diff
566×sqrt-prod
74×distribute-lft-out
54×div-inv
48×sqrt-div
46×associate-/r/
24×flip3-+ flip-+
22×fma-neg
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-exp-log add-cbrt-cube
6×associate-/l* add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log frac-sub flip-- hypot-def
Counts
4 → 758
Calls
4 calls:
4.0ms
(sqrt (+ x 1.0))
7.0ms
(/ 1.0 (sqrt (+ x 1.0)))
3.0ms
(/ 1.0 (sqrt x))
69.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series282.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(sqrt (+ x 1.0))
76.0ms
(/ 1.0 (sqrt (+ x 1.0)))
38.0ms
(/ 1.0 (sqrt x))
139.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify243.0ms

Algorithm
egg-herbie
Counts
770 → 770
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
0153825021
1427818390
2500118355

prune1.2s

Filtered
770 candidates to 303 candidates (39.4%)
Pruning

19 alts after pruning (19 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)))))

rewrite221.0ms

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×expm1-log1p-u log1p-expm1-u associate-/l*
2×pow2 flip3-- pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up flip--
1×sub-neg frac-2neg fma-neg diff-log div-sub prod-diff frac-add clear-num
Counts
4 → 364
Calls
4 calls:
109.0ms
(/ (- (* (/ 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)))))
46.0ms
(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
24.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
13.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

series487.0ms

Counts
4 → 12
Calls
4 calls:
368.0ms
(/ (- (* (/ 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)))))
25.0ms
(* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))
34.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
60.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

simplify81.0ms

Algorithm
egg-herbie
Counts
376 → 376
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
016396037
150015555

prune771.0ms

Filtered
376 candidates to 213 candidates (56.6%)
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)

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
319×*-un-lft-identity
296×times-frac
124×sqrt-prod
121×distribute-lft-out
116×add-sqr-sqrt
114×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*
12×prod-diff
9×prod-exp cbrt-unprod add-log-exp
4×pow1 expm1-log1p-u fma-neg log1p-expm1-u
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 → 272
Calls
4 calls:
7.0ms
(/ 1.0 (sqrt (+ x 1.0)))
3.0ms
(/ 1.0 (sqrt x))
113.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
23.0ms
(- (+ x 1.0) x)

series614.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ 1.0 (sqrt (+ x 1.0)))
43.0ms
(/ 1.0 (sqrt x))
494.0ms
(/ (/ (* (* 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)

simplify67.0ms

Algorithm
egg-herbie
Counts
284 → 284
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
013274194
150013759

prune548.0ms

Filtered
284 candidates to 153 candidates (53.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.2b

localize17.0ms

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)))))

rewrite139.0ms

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 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×sqrt-div
1×frac-add associate-/l/
Counts
4 → 266
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))
99.0ms
(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

series649.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ 1.0 (sqrt (+ x 1.0)))
36.0ms
(/ 1.0 (sqrt x))
40.0ms
(/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x))
484.0ms
(/ (/ (* (* 1.0 1.0) 1.0) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

simplify73.0ms

Algorithm
egg-herbie
Counts
278 → 278
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012383739
150013341

prune587.0ms

Filtered
278 candidates to 154 candidates (55.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes37.0ms

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

sample861.0ms

Algorithm
intervals
Results
182.0ms1845×body640valid
174.0ms8031×body80nan
152.0ms1143×body1280valid
110.0ms4083×body80valid
45.0ms621×body320valid
16.0ms308×body160valid