Details

Time bar (total: 6.7s)

sample43.0ms

Algorithm
intervals
Results
10.0ms263×body80nan
8.0ms48×body1280valid
7.0ms54×body640valid
6.0ms128×body80valid
2.0ms20×body320valid
0.0ms6×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: 19.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
2.7b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite158.0ms

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:
9.0ms
(/ 1.0 (sqrt (+ x 1.0)))
3.0ms
(/ 1.0 (sqrt x))
71.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series259.0ms

Counts
3 → 9
Calls
3 calls:
78.0ms
(/ 1.0 (sqrt (+ x 1.0)))
44.0ms
(/ 1.0 (sqrt x))
136.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify241.0ms

Algorithm
egg-herbie
Counts
748 → 748
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
0151724924
1419718301
2500118266

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 18.6b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
2.7b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite104.0ms

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:
56.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
14.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
28.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series418.0ms

Counts
3 → 9
Calls
3 calls:
283.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
59.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
76.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify84.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
06141715
128831280
250021185

prune293.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 18.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(/ (* 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)))
2.4b
(+ x (- 1.0 x))

rewrite113.0ms

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:
49.0ms
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
31.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
18.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
9.0ms
(+ x (- 1.0 x))

series718.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
516.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
58.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms
(+ x (- 1.0 x))

simplify113.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
07991711
142361448
250011435

prune407.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite90.0ms

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:
20.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
28.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
23.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
15.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series793.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
150.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
515.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
64.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify94.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
07041320
136361120
250021050

prune307.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes55.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0119
1119

end0.0ms

sample1.2s

Algorithm
intervals
Results
301.0ms7979×body80nan
241.0ms1855×body640valid
198.0ms4113×body80valid
183.0ms1164×body1280valid
60.0ms590×body320valid
20.0ms278×body160valid