Details

Time bar (total: 6.5s)

sample29.0ms

Algorithm
intervals
Results
6.0ms276×body80nan
4.0ms42×body640valid
4.0ms155×body80valid
3.0ms27×body1280valid
2.0ms21×body320valid
1.0ms11×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0116
1146
2146

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
3.1b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite152.0ms

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)))
3.0ms
(/ 1.0 (sqrt x))
67.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series265.0ms

Counts
3 → 9
Calls
3 calls:
81.0ms
(/ 1.0 (sqrt (+ x 1.0)))
45.0ms
(/ 1.0 (sqrt x))
139.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify244.0ms

Algorithm
egg-herbie
Counts
748 → 748
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
0151724924
1419718301
2500118266

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.9b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
3.0b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
68×sqrt-prod
58×*-un-lft-identity
51×add-sqr-sqrt
42×prod-diff
35×add-cube-cbrt
17×add-exp-log add-cbrt-cube
9×distribute-lft-out
7×pow1 fma-neg associate-*r*
6×associate-*r/ associate-*l*
5×prod-exp cbrt-unprod add-log-exp
4×cbrt-undiv sqrt-div div-exp difference-of-squares unswap-sqr
3×expm1-log1p-u pow-prod-down log1p-expm1-u distribute-lft-out--
2×flip3-- sqrt-pow1 flip3-+ pow1/2 associate-/r/ flip-- flip-+ associate-/l/
1×sub-neg frac-2neg times-frac sqrt-unprod diff-log clear-num associate-/r* *-commutative div-inv associate-/l*
Counts
3 → 132
Calls
3 calls:
55.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
13.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
27.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series428.0ms

Counts
3 → 9
Calls
3 calls:
286.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
64.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
78.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify85.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
06141715
128831280
250021185

prune307.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
1.9b
(+ x (- 1.0 x))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
112×*-un-lft-identity
41×distribute-lft-out
36×add-sqr-sqrt
35×sqrt-prod
31×times-frac
29×add-exp-log add-cbrt-cube
28×add-cube-cbrt
11×associate-+r+
9×cbrt-undiv div-exp prod-diff add-log-exp
8×pow1 prod-exp cbrt-unprod distribute-lft-out--
7×associate-*r* associate-/r*
6×associate-*l* associate-/l*
5×flip3-+ associate-*r/ flip-+
4×expm1-log1p-u sqrt-div associate-/r/ log1p-expm1-u unswap-sqr
3×fma-def pow-prod-down associate-/l/
2×associate-+r- frac-2neg sqrt-pow1 pow1/2 clear-num sum-log div-inv
1×+-commutative sub-neg sqrt-unprod diff-log div-sub *-commutative
Counts
4 → 156
Calls
4 calls:
47.0ms
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
29.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
17.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
9.0ms
(+ x (- 1.0 x))

series890.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
692.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
60.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms
(+ x (- 1.0 x))

simplify111.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
07991711
142361448
250011435

prune389.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
60×*-un-lft-identity
35×sqrt-prod
29×add-exp-log add-sqr-sqrt add-cbrt-cube
22×distribute-lft-out
21×add-cube-cbrt
19×times-frac
9×cbrt-undiv div-exp
8×pow1 prod-exp cbrt-unprod
7×fma-def associate-*r* associate-/r*
6×associate-*l* add-log-exp
5×associate-*r/
4×expm1-log1p-u flip3-+ sqrt-div associate-/r/ flip-+ log1p-expm1-u associate-/l* unswap-sqr
3×pow-prod-down
2×frac-2neg sqrt-pow1 pow1/2 clear-num div-inv
1×+-commutative sqrt-unprod sum-log *-commutative associate-/l/
Counts
4 → 131
Calls
4 calls:
19.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
26.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
35.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
14.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series763.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
144.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
495.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
62.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify90.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
07041320
136361120
250021050

prune304.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes50.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01619
11619

end0.0ms

sample845.0ms

Algorithm
intervals
Results
177.0ms1771×body640valid
172.0ms8072×body80nan
142.0ms1128×body1280valid
105.0ms4137×body80valid
50.0ms656×body320valid
15.0ms308×body160valid