Details

Time bar (total: 4.4s)

sample19.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
2.0ms77×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: 0.2b

localize5.0ms

Local error

Found 3 expressions with local error:

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
17×add-sqr-sqrt
14×add-cube-cbrt
12×times-frac
6×distribute-lft-out
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 associate-/r* sqrt-prod
3×expm1-log1p-u fma-def flip3-+ flip-+ log1p-expm1-u associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log hypot-def div-inv
Counts
3 → 71
Calls
3 calls:
11.0ms
(+ 1.0 (sqrt (+ x 1.0)))
4.0ms
(sqrt (+ x 1.0))
17.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series208.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(+ 1.0 (sqrt (+ x 1.0)))
33.0ms
(sqrt (+ x 1.0))
135.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify37.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0334508
11222457
25002445

prune152.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.1b
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.3b
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.4b
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
378×times-frac
306×*-un-lft-identity
234×sqrt-prod
200×add-sqr-sqrt
190×add-cube-cbrt
58×distribute-lft-out
30×associate-/l*
24×sqrt-div
20×associate-/r/
14×associate-/r*
12×flip3-+ flip-+
11×add-exp-log add-cbrt-cube
10×div-inv
6×pow1
4×cbrt-undiv expm1-log1p-u div-exp hypot-def log1p-expm1-u add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 329
Calls
4 calls:
17.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
20.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
18.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
53.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series783.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
123.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
401.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
138.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify107.0ms

Algorithm
egg-herbie
Counts
341 → 341
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
09065694
135745078
250015052

prune442.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b
(pow (sqrt (+ x 1.0)) 3)
4.0b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.1b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite107.0ms

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:
20.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
6.0ms
(pow (sqrt (+ x 1.0)) 3)
13.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
57.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series323.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
61.0ms
(pow (sqrt (+ x 1.0)) 3)
62.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
180.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify131.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 2 (113.0ms)

IterNodesCost
08251791
141301518
250011510

prune423.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
70×*-un-lft-identity
59×add-sqr-sqrt
52×times-frac
40×add-cube-cbrt
39×sqrt-prod
30×associate-*r*
15×distribute-lft-out
11×add-exp-log add-cbrt-cube
7×pow1
6×associate-*l* associate-/l* add-log-exp unswap-sqr
4×expm1-log1p-u flip3-+ associate-/r* associate-/r/ flip-+ log1p-expm1-u
3×fma-def
2×cbrt-undiv sqrt-div div-exp prod-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num sum-log *-commutative hypot-def
Counts
4 → 144
Calls
4 calls:
4.0ms
(sqrt (+ x 1.0))
8.0ms
(+ 1.0 (sqrt (+ x 1.0)))
20.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
44.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series499.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(sqrt (+ x 1.0))
46.0ms
(+ 1.0 (sqrt (+ x 1.0)))
294.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
129.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify65.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05541324
123241174
250011140

prune287.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes39.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
084
184

end0.0ms

sample518.0ms

Algorithm
intervals
Results
313.0ms7997×body80valid
75.0ms2707×body80nan
1.0ms3×body1280valid