Details

Time bar (total: 3.6s)

sample14.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
1.0ms81×body80nan

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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

rewrite19.0ms

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:
3.0ms
(sqrt (+ x 1.0))
6.0ms
(+ 1.0 (sqrt (+ x 1.0)))
8.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series214.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(sqrt (+ x 1.0))
41.0ms
(+ 1.0 (sqrt (+ x 1.0)))
141.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify39.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0334508
11222457
25002445

prune159.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize6.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
108×times-frac
100×*-un-lft-identity
67×add-sqr-sqrt
64×add-cube-cbrt
19×associate-/r*
18×distribute-lft-out
17×add-exp-log
11×add-cbrt-cube
8×div-exp
7×associate-/l*
6×pow1 div-inv add-log-exp
4×cbrt-undiv expm1-log1p-u sqrt-prod log1p-expm1-u
3×fma-def flip3-+ flip-+
2×rec-exp frac-2neg sqrt-div 1-exp clear-num associate-/l/
1×+-commutative rem-sqrt-square pow-flip sqrt-pow1 pow1/2 sum-log associate-/r/ hypot-def inv-pow
Counts
4 → 161
Calls
4 calls:
3.0ms
(sqrt (+ x 1.0))
6.0ms
(+ 1.0 (sqrt (+ x 1.0)))
8.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) x)
11.0ms
(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

series300.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(sqrt (+ x 1.0))
45.0ms
(+ 1.0 (sqrt (+ x 1.0)))
84.0ms
(/ (+ 1.0 (sqrt (+ x 1.0))) x)
141.0ms
(/ 1 (/ (+ 1.0 (sqrt (+ x 1.0))) x))

simplify70.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
06151449
127081291
250011197

prune250.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.1b
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
0.3b
(/ (/ 1 (+ 1.0 (sqrt (+ x 1.0)))) (/ 1 x))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
585×times-frac
356×*-un-lft-identity
263×add-sqr-sqrt
260×add-cube-cbrt
48×add-exp-log distribute-lft-out
35×div-inv
34×div-exp
31×associate-/r/
21×associate-/l*
18×add-cbrt-cube
17×flip3-+ associate-/r* flip-+
9×cbrt-undiv rec-exp 1-exp
6×pow1 add-log-exp
4×expm1-log1p-u sqrt-prod log1p-expm1-u
3×fma-def
2×frac-2neg sqrt-div clear-num
1×+-commutative rem-sqrt-square pow-flip sqrt-pow1 pow1/2 sum-log hypot-def associate-/l/ inv-pow
Counts
4 → 374
Calls
4 calls:
7.0ms
(sqrt (+ x 1.0))
6.0ms
(+ 1.0 (sqrt (+ x 1.0)))
8.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
18.0ms
(/ (/ 1 (+ 1.0 (sqrt (+ x 1.0)))) (/ 1 x))

series327.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (+ x 1.0))
41.0ms
(+ 1.0 (sqrt (+ x 1.0)))
104.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
146.0ms
(/ (/ 1 (+ 1.0 (sqrt (+ x 1.0)))) (/ 1 x))

simplify76.0ms

Algorithm
egg-herbie
Counts
386 → 386
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
015984861
150014296

prune683.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.3b
(pow (sqrt (+ x 1.0)) 3)
5.1b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
7.0b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite62.0ms

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:
11.0ms
(* (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))))
19.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series337.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
67.0ms
(pow (sqrt (+ x 1.0)) 3)
64.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
189.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify137.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 2 (118.0ms)

IterNodesCost
08251791
141301518
250011510

prune430.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes15.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0125
1125

end0.0ms

sample332.0ms

Algorithm
intervals
Results
163.0ms7997×body80valid
46.0ms2693×body80nan
0.0ms3×body1280valid