Details

Time bar (total: 4.4s)

sample24.0ms

Algorithm
intervals
Results
4.0ms51×body1280valid
4.0ms237×body80nan
2.0ms130×body80valid
2.0ms35×body640valid
1.0ms25×body320valid
0.0ms15×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.8b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
61×sqrt-prod
54×*-un-lft-identity
42×add-sqr-sqrt prod-diff
31×add-cube-cbrt
9×distribute-lft-out
7×fma-neg
4×add-log-exp difference-of-squares
3×pow1 distribute-lft-out--
2×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 diff-log flip-- flip-+ hypot-def
Counts
2 → 89
Calls
2 calls:
7.0ms
(sqrt (+ x 1.0))
49.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series100.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(sqrt (+ x 1.0))
71.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify40.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
02991161
1921822
25001744

prune133.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
66×*-un-lft-identity
28×distribute-lft-out
24×times-frac sqrt-prod
18×add-sqr-sqrt
15×add-cube-cbrt
6×associate-/r*
4×add-exp-log add-cbrt-cube associate-/l*
3×pow1 flip3-+ flip-+
2×expm1-log1p-u sqrt-div associate-/r/ log1p-expm1-u associate-/l/ 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 → 71
Calls
2 calls:
7.0ms
(sqrt (+ x 1.0))
54.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series167.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(sqrt (+ x 1.0))
138.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify48.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0371654
11550602
25002560

prune155.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.0b
(expm1 (log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.1b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
68×*-un-lft-identity
28×distribute-lft-out
24×times-frac sqrt-prod
20×add-sqr-sqrt
17×add-cube-cbrt
6×add-exp-log associate-/r* add-cbrt-cube
5×pow1 expm1-log1p-u
4×log1p-expm1-u associate-/l* add-log-exp
3×flip3-+ flip-+
2×sqrt-div associate-/r/ associate-/l/
1×cbrt-undiv rem-sqrt-square log1p-udef expm1-log1p frac-2neg sqrt-pow1 pow1/2 log1p-expm1 div-exp clear-num hypot-def div-inv expm1-udef
Counts
4 → 93
Calls
4 calls:
7.0ms
(sqrt (+ x 1.0))
0.0ms
(log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.0ms
(expm1 (log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
55.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series1.4s

Counts
4 → 12
Calls
4 calls:
29.0ms
(sqrt (+ x 1.0))
440.0ms
(log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
774.0ms
(expm1 (log1p (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))
138.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify68.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
06371126
12696999
25001965

prune273.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (+ x 1.0)))
0.1b
(sqrt (sqrt (+ x 1.0)))
0.1b
(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
0.3b
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
106×sqrt-prod
63×add-sqr-sqrt
55×*-un-lft-identity
40×sqrt-pow1
32×sqrt-div
31×pow1
29×add-cube-cbrt
20×pow1/2
18×swap-sqr
12×times-frac distribute-lft-out
10×flip3-+ associate-*r* associate-*l* flip-+
9×pow-prod-up unswap-sqr
8×add-exp-log add-cbrt-cube
5×pow-prod-down pow-sqr
4×expm1-log1p-u frac-times rem-sqrt-square log1p-expm1-u associate-/l* add-log-exp
3×associate-/r*
2×associate-*r/ associate-*l/ associate-/r/ associate-/l/
1×cbrt-undiv pow2 frac-2neg pow-plus sqrt-unprod div-exp prod-exp clear-num rem-square-sqrt *-commutative cbrt-unprod div-inv
Counts
4 → 175
Calls
4 calls:
8.0ms
(sqrt (sqrt (+ x 1.0)))
9.0ms
(sqrt (sqrt (+ x 1.0)))
57.0ms
(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
47.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series340.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(sqrt (sqrt (+ x 1.0)))
87.0ms
(sqrt (sqrt (+ x 1.0)))
134.0ms
(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
31.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify89.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
05941528
128001345
250011318

prune436.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes36.0ms

Accuracy

0% (0.1b 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
0148
1188
2188

end0.0ms

sample722.0ms

Algorithm
intervals
Results
148.0ms8191×body80nan
146.0ms1727×body1280valid
85.0ms1282×body640valid
76.0ms4038×body80valid
33.0ms649×body320valid
10.0ms304×body160valid