Details

Time bar (total: 3.5s)

sample28.0ms

Algorithm
intervals
Results
5.0ms304×body80nan
4.0ms53×body1280valid
3.0ms41×body640valid
2.0ms135×body80valid
1.0ms18×body320valid
0.0ms9×body160valid

simplify5.0ms

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: 28.9b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.3b
(- (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))

series104.0ms

Counts
2 → 6
Calls
2 calls:
33.0ms
(sqrt (+ x 1.0))
71.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify42.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
02991161
1921822
25001744

prune142.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

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)))

rewrite60.0ms

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))
19.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
33.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series232.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(sqrt (+ x 1.0))
62.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
138.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify49.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0409789
11675716
25001675

prune218.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.3b
(cbrt (+ x 1.0))
0.3b
(cbrt (+ x 1.0))
0.3b
(cbrt (+ x 1.0))

rewrite32.0ms

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:
22.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
2.0ms
(cbrt (+ x 1.0))
2.0ms
(cbrt (+ x 1.0))
2.0ms
(cbrt (+ x 1.0))

series354.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
84.0ms
(cbrt (+ x 1.0))
84.0ms
(cbrt (+ x 1.0))
85.0ms
(cbrt (+ x 1.0))

simplify148.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 3 (139.0ms)

IterNodesCost
0321818
11064769
24750694
35001688

prune403.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
22×cbrt-prod
18×*-un-lft-identity
10×add-sqr-sqrt add-cube-cbrt
8×cbrt-div sqrt-prod
4×pow1 add-exp-log expm1-log1p-u flip3-+ pow1/3 sqrt-div add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out add-log-exp
Counts
4 → 70
Calls
4 calls:
3.0ms
(cbrt (sqrt (+ x 1.0)))
3.0ms
(cbrt (sqrt (+ x 1.0)))
2.0ms
(cbrt (+ x 1.0))
2.0ms
(cbrt (+ x 1.0))

series355.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(cbrt (sqrt (+ x 1.0)))
90.0ms
(cbrt (sqrt (+ x 1.0)))
90.0ms
(cbrt (+ x 1.0))
88.0ms
(cbrt (+ x 1.0))

simplify96.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 3 (83.0ms)

IterNodesCost
0307600
1892564
23153524
35001510

prune391.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes67.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0126
1166
2166

end0.0ms

sample634.0ms

Algorithm
intervals
Results
144.0ms1695×body1280valid
133.0ms7960×body80nan
80.0ms1245×body640valid
76.0ms4137×body80valid
30.0ms616×body320valid
10.0ms307×body160valid