Details

Time bar (total: 3.7s)

sample14.0ms

Algorithm
intervals
Results
5.0ms255×body80valid
2.0ms81×body80nan
0.0ms1×body1280valid

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))))

rewrite29.0ms

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:
8.0ms
(+ 1.0 (sqrt (+ x 1.0)))
19.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series183.0ms

Counts
2 → 6
Calls
2 calls:
45.0ms
(+ 1.0 (sqrt (+ x 1.0)))
138.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify36.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0290412
11095368
25001361

prune121.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt x) (cbrt x))
0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
8.0ms
(* (cbrt x) (cbrt x))
0.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series742.0ms

Counts
4 → 12
Calls
4 calls:
206.0ms
(* (cbrt x) (cbrt x))
180.0ms
(cbrt x)
180.0ms
(cbrt x)
176.0ms
(cbrt x)

simplify91.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 3 (86.0ms)

IterNodesCost
0119308
1477281
22972258
35001255

prune203.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.1b
(pow (sqrt (+ x 1.0)) 3)
4.9b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.6b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite104.0ms

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)))
5.0ms
(pow (sqrt (+ x 1.0)) 3)
16.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
53.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series345.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
70.0ms
(pow (sqrt (+ x 1.0)) 3)
60.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
198.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify146.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 2 (119.0ms)

IterNodesCost
08251791
141261518
250011510

prune445.0ms

Pruning

5 alts after pruning (2 fresh and 3 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))))
0.2b
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

rewrite79.0ms

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:
8.0ms
(+ 1.0 (sqrt (+ x 1.0)))
17.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
48.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series471.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(+ 1.0 (sqrt (+ x 1.0)))
296.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
134.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify70.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05111228
121961085
250011054

prune237.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes49.0ms

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

sample321.0ms

Algorithm
intervals
Results
159.0ms7996×body80valid
43.0ms2823×body80nan
0.0ms4×body1280valid