Details

Time bar (total: 4.7s)

sample25.0ms

Algorithm
intervals
Results
5.0ms288×body80nan
5.0ms57×body1280valid
2.0ms133×body80valid
2.0ms31×body640valid
1.0ms22×body320valid
0.0ms13×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.1b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite37.0ms

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:
4.0ms
(sqrt (+ x 1.0))
28.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series110.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(sqrt (+ x 1.0))
73.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify42.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
02991161
1921822
25001744

prune139.0ms

Filtered
95 candidates to 44 candidates (46.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
33×distribute-lft-out
32×sqrt-prod
24×times-frac
21×add-sqr-sqrt
18×add-cube-cbrt
7×fma-def
6×associate-/r*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 flip3-+ flip-+ associate-/l*
3×expm1-log1p-u log1p-expm1-u
2×sqrt-div associate-/r/ associate-/l/
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 → 94
Calls
3 calls:
4.0ms
(sqrt (+ x 1.0))
20.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
34.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series248.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(sqrt (+ x 1.0))
70.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
149.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify51.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0409789
11675716
25001675

prune223.0ms

Filtered
103 candidates to 68 candidates (66.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ x 1.0))
0.3b
(cbrt (+ x 1.0))
0.3b
(cbrt (+ x 1.0))
0.3b
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
35×*-un-lft-identity
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 swap-sqr flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 103
Calls
4 calls:
2.0ms
(cbrt (+ x 1.0))
2.0ms
(cbrt (+ x 1.0))
2.0ms
(cbrt (+ x 1.0))
25.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

series381.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(cbrt (+ x 1.0))
93.0ms
(cbrt (+ x 1.0))
88.0ms
(cbrt (+ x 1.0))
108.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

simplify161.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 3 (151.0ms)

IterNodesCost
0321818
11071769
24756694
35001692

prune389.0ms

Filtered
115 candidates to 83 candidates (72.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite276.0ms

Algorithm
rewrite-expression-head
Rules
597×*-un-lft-identity
420×sqrt-prod
256×distribute-lft-out
247×times-frac
130×add-sqr-sqrt
99×add-cube-cbrt
71×swap-sqr
33×associate-*r* associate-*l*
20×pow1
14×associate-/r/
12×associate-/r*
10×add-exp-log add-cbrt-cube
9×sqrt-pow1 flip3-+ pow1/2 flip-+ unswap-sqr
8×associate-/l*
7×div-inv
5×sqrt-div pow-prod-up
4×expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp
3×pow-prod-down pow-sqr
2×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ associate-*l/ prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 324
Calls
4 calls:
33.0ms
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
30.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
33.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
154.0ms
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

series836.0ms

Counts
4 → 12
Calls
4 calls:
364.0ms
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
143.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
151.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
179.0ms
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify130.0ms

Algorithm
egg-herbie
Counts
336 → 336
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
07233900
137333364
250023360

prune798.0ms

Filtered
336 candidates to 155 candidates (46.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes33.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01413
11813
21813

end0.0ms

sample681.0ms

Algorithm
intervals
Results
152.0ms1766×body1280valid
143.0ms8031×body80nan
86.0ms1219×body640valid
82.0ms4090×body80valid
31.0ms623×body320valid
10.0ms302×body160valid