Details

Time bar (total: 3.6s)

sample19.0ms

Algorithm
intervals
Results
10.0ms255×body80valid
2.0ms77×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: 0.2b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
15×add-sqr-sqrt
12×add-cube-cbrt times-frac
5×distribute-lft-out
4×add-exp-log associate-/r* sqrt-prod add-cbrt-cube
3×pow1 associate-/l*
2×expm1-log1p-u flip3-+ sqrt-div associate-/r/ flip-+ log1p-expm1-u add-log-exp
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num hypot-def div-inv
Counts
2 → 54
Calls
2 calls:
4.0ms
(sqrt (+ x 1.0))
16.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series171.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(sqrt (+ x 1.0))
141.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify40.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0304400
11151366
25002357

prune118.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ (+ 1.0 (sqrt (+ x 1.0))) x)
0.2b
(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
108×times-frac
96×*-un-lft-identity
65×add-sqr-sqrt
62×add-cube-cbrt
19×associate-/r*
17×distribute-lft-out
16×add-exp-log
10×add-cbrt-cube
8×div-exp
7×associate-/l*
6×div-inv
5×pow1
4×cbrt-undiv sqrt-prod
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×rec-exp frac-2neg flip3-+ sqrt-div 1-exp clear-num flip-+ associate-/l/
1×rem-sqrt-square pow-flip sqrt-pow1 pow1/2 associate-/r/ hypot-def inv-pow
Counts
3 → 144
Calls
3 calls:
4.0ms
(sqrt (+ x 1.0))
24.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) x)
20.0ms
(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

series261.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(sqrt (+ x 1.0))
86.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) x)
140.0ms
(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

simplify65.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05891342
126421200
250021107

prune217.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize16.0ms

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)
3.5b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.8b
(/ 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)
14.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
56.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series520.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
63.0ms
(pow (sqrt (+ x 1.0)) 3)
246.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
191.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify132.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 2 (113.0ms)

IterNodesCost
08251791
141301518
250011510

prune435.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
360×times-frac
284×*-un-lft-identity
190×sqrt-prod
187×add-sqr-sqrt
184×add-cube-cbrt
50×distribute-lft-out
34×associate-/r*
10×add-exp-log add-cbrt-cube associate-/l*
9×div-inv
4×pow1 cbrt-undiv div-exp
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg flip3-+ sqrt-div clear-num flip-+ associate-/l/
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ hypot-def
Counts
3 → 288
Calls
3 calls:
4.0ms
(sqrt (+ x 1.0))
24.0ms
(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))
25.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))

series310.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(sqrt (+ x 1.0))
129.0ms
(/ (sqrt x) (/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x)))
147.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) (sqrt x))

simplify112.0ms

Algorithm
egg-herbie
Counts
297 → 297
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
08723979
142713565
250013546

prune395.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes36.0ms

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

sample503.0ms

Algorithm
intervals
Results
311.0ms7996×body80valid
74.0ms2563×body80nan
1.0ms4×body1280valid