Details

Time bar (total: 5.1s)

sample25.0ms

Algorithm
intervals
Results
5.0ms276×body80nan
5.0ms51×body1280valid
3.0ms139×body80valid
2.0ms29×body640valid
1.0ms26×body320valid
0.0ms11×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.1b

localize5.0ms

Local error

Found 1 expressions with local error:

3.2b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
57×sqrt-prod
50×*-un-lft-identity
42×prod-diff
37×add-sqr-sqrt
29×add-cube-cbrt
8×distribute-lft-out
7×fma-neg
4×difference-of-squares
3×distribute-lft-out-- add-log-exp
1×pow1 add-exp-log expm1-log1p-u sub-neg flip3-- diff-log add-cbrt-cube flip-- log1p-expm1-u
Counts
1 → 70
Calls
1 calls:
28.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series71.0ms

Counts
1 → 3
Calls
1 calls:
71.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify132.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 3 (123.0ms)

IterNodesCost
02521065
1759733
24363623
35001593

prune87.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
74×*-un-lft-identity
32×distribute-lft-out
28×sqrt-prod
24×times-frac
16×add-sqr-sqrt add-cube-cbrt
7×fma-def
6×associate-/r*
4×add-exp-log add-cbrt-cube associate-/l* add-log-exp
3×flip3-+ flip-+
2×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 75
Calls
2 calls:
22.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
31.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series205.0ms

Counts
2 → 6
Calls
2 calls:
68.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
136.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify44.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0356693
11446627
25001586

prune162.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite226.0ms

Algorithm
rewrite-expression-head
Rules
1122×*-un-lft-identity
908×sqrt-prod
774×times-frac
460×distribute-lft-out
310×add-sqr-sqrt
292×add-cube-cbrt
46×associate-/l*
28×sqrt-div
24×associate-/r/
18×associate-/r*
15×flip3-+ flip-+
12×div-inv
11×add-exp-log add-cbrt-cube
8×hypot-def
6×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
Counts
4 → 563
Calls
4 calls:
25.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
27.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
33.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
87.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series813.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
166.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
340.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
141.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify187.0ms

Algorithm
egg-herbie
Counts
575 → 575
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
0110711444
145519783
250019783

prune637.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.4b
(pow (sqrt x) 3/2)
0.5b
(* (sqrt x) (sqrt x))
2.9b
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
121×sqrt-prod
98×*-un-lft-identity
61×add-sqr-sqrt
54×times-frac
49×add-cube-cbrt
44×sqrt-div
28×distribute-lft-out
21×pow1
18×associate-/l/
16×frac-add
14×flip3-+ flip-+
9×add-exp-log flip3-- sqrt-pow1 pow1/2 associate-/r* flip--
8×frac-times swap-sqr add-cbrt-cube
6×unpow-prod-down associate-*r* associate-*l* associate-/l* add-log-exp
5×pow-prod-up
4×expm1-log1p-u associate-*r/ associate-*l/ log1p-expm1-u unswap-sqr
3×pow-unpow pow-pow pow-prod-down pow-sqr
2×associate-/r/
1×cbrt-undiv pow2 pow-to-exp sub-neg sqrt-undiv distribute-rgt-out-- frac-2neg pow-plus fma-neg sqrt-unprod diff-log div-exp prod-diff pow-exp prod-exp clear-num rem-square-sqrt *-commutative sqrt-pow2 cbrt-unprod div-inv sqr-pow
Counts
4 → 197
Calls
4 calls:
89.0ms
(/ (sqrt (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
2.0ms
(pow (sqrt x) 3/2)
7.0ms
(* (sqrt x) (sqrt x))
6.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))

series637.0ms

Counts
4 → 12
Calls
4 calls:
412.0ms
(/ (sqrt (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
117.0ms
(pow (sqrt x) 3/2)
15.0ms
(* (sqrt x) (sqrt x))
92.0ms
(- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))

simplify142.0ms

Algorithm
egg-herbie
Counts
209 → 209
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
09204239
143253877
250013875

prune725.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes30.0ms

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
0126
1166
2166

end0.0ms

sample693.0ms

Algorithm
intervals
Results
169.0ms1797×body1280valid
137.0ms7781×body80nan
92.0ms1283×body640valid
78.0ms3999×body80valid
35.0ms621×body320valid
11.0ms300×body160valid