Details

Time bar (total: 5.5s)

sample15.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
1.0ms100×body80nan

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
084
184

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
12×add-sqr-sqrt add-cube-cbrt times-frac
5×distribute-lft-out
4×add-exp-log associate-/r* add-cbrt-cube add-log-exp
3×fma-def associate-/l*
2×pow1 expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 52
Calls
2 calls:
16.0ms
(+ 1.0 (sqrt (+ x 1.0)))
34.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series172.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(+ 1.0 (sqrt (+ x 1.0)))
131.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify36.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0290412
11095368
25001361

prune112.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b
(pow (sqrt (+ x 1.0)) 3)
3.7b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
5.1b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
89×*-un-lft-identity
62×sqrt-div
43×add-sqr-sqrt
34×sqrt-prod
32×flip3-+ flip-+
31×add-cube-cbrt
28×associate-*r/ distribute-lft-out
27×times-frac
23×unpow-prod-down cube-prod
21×pow1
16×frac-sub
12×frac-times
11×swap-sqr
9×add-exp-log sqrt-pow1 pow1/2 associate-/r* add-cbrt-cube
8×associate-*l/
7×associate-*r* associate-*l*
6×add-log-exp
5×pow-prod-up
4×expm1-log1p-u sum-cubes log1p-expm1-u sub-div unswap-sqr
3×pow-unpow pow-pow pow-prod-down pow-sqr associate-/l*
2×cube-div associate-/r/
1×cbrt-undiv pow2 cube-mult pow-to-exp sub-neg flip3-- distribute-rgt-out-- frac-2neg pow-plus fma-neg sqrt-unprod diff-log unpow3 div-exp prod-diff pow-exp prod-exp clear-num rem-square-sqrt *-commutative sqrt-pow2 flip-- cbrt-unprod div-inv rem-cube-cbrt sqr-pow
Counts
4 → 194
Calls
4 calls:
38.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
10.0ms
(pow (sqrt (+ x 1.0)) 3)
28.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
87.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series311.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
61.0ms
(pow (sqrt (+ x 1.0)) 3)
59.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
175.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify136.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 2 (116.0ms)

IterNodesCost
08251791
141301518
250011510

prune431.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0))))
0.1b
(* (/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
0.1b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
3.7b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
132×times-frac
127×*-un-lft-identity
96×sqrt-div
76×add-sqr-sqrt
70×flip3-+ flip-+
66×associate-*r/
65×associate-*l*
63×associate-*l/
59×add-cube-cbrt
58×associate-/r/
52×frac-sub
36×add-exp-log
33×distribute-lft-out
29×add-cbrt-cube
26×sqrt-prod
21×pow1
14×frac-times div-exp
13×associate-/l*
11×swap-sqr div-inv
10×cbrt-undiv flip3-- associate-*r* prod-exp flip--
8×sqrt-pow1 pow1/2
7×cbrt-unprod
6×add-log-exp unswap-sqr
5×pow-prod-up
4×expm1-log1p-u pow-prod-down associate-/r* log1p-expm1-u sub-div
3×pow-sqr
2×1-exp *-commutative
1×pow2 distribute-rgt-in sub-neg distribute-rgt-out-- frac-2neg distribute-lft-in pow-plus fma-neg sqrt-unprod diff-log prod-diff clear-num rem-square-sqrt associate-/l/
Counts
4 → 282
Calls
4 calls:
286.0ms
(/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0))))
715.0ms
(* (/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
40.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
28.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

series777.0ms

Counts
4 → 12
Calls
4 calls:
423.0ms
(/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0))))
275.0ms
(* (/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
16.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
63.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

simplify95.0ms

Algorithm
egg-herbie
Counts
294 → 294
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
018605818
150015319

prune807.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
66×*-un-lft-identity
54×add-sqr-sqrt
52×times-frac
38×add-cube-cbrt
35×sqrt-prod
30×associate-*r*
14×distribute-lft-out
10×add-exp-log add-cbrt-cube
6×associate-*l* associate-/l* unswap-sqr
5×pow1 add-log-exp
4×associate-/r* associate-/r/
3×expm1-log1p-u fma-def flip3-+ flip-+ log1p-expm1-u
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×+-commutative frac-2neg associate-*r/ pow-prod-down clear-num sum-log *-commutative
Counts
3 → 125
Calls
3 calls:
16.0ms
(+ 1.0 (sqrt (+ x 1.0)))
31.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
77.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series464.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(+ 1.0 (sqrt (+ x 1.0)))
298.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
127.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify66.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05111228
121961085
250011054

prune240.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes18.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02625
12825
22825

end0.0ms

sample356.0ms

Algorithm
intervals
Results
155.0ms7996×body80valid
48.0ms2740×body80nan
0.0ms4×body1280valid