Details

Time bar (total: 10.5s)

sample48.0ms

Algorithm
intervals
Results
12.0ms266×body80nan
10.0ms54×body1280valid
7.0ms49×body640valid
6.0ms129×body80valid
1.0ms11×body320valid
1.0ms13×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: 30.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.2b
(- (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))
29.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series104.0ms

Counts
2 → 6
Calls
2 calls:
30.0ms
(sqrt (+ x 1.0))
74.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify41.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
02991161
1921822
25001744

prune138.0ms

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

rewrite61.0ms

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:
7.0ms
(sqrt (+ x 1.0))
20.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
31.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series239.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(sqrt (+ x 1.0))
69.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
141.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify55.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0409789
11675716
25001675

prune215.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.0b
(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))))
0.2b
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite228.0ms

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)))
26.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
90.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
32.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series816.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
168.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
147.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
335.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify167.0ms

Algorithm
egg-herbie
Counts
575 → 575
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
0110711444
145519783
250019783

prune637.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.0b
(expm1 (log1p (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
0.2b
(/ (expm1 (log1p (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
133×*-un-lft-identity
104×sqrt-prod
63×times-frac
52×add-sqr-sqrt
50×distribute-lft-out
43×add-cube-cbrt
18×associate-/r*
8×add-exp-log add-cbrt-cube
7×associate-/l*
6×sqrt-div
5×pow1
4×expm1-log1p-u flip3-+ associate-/r/ flip-+ hypot-def log1p-expm1-u add-log-exp
2×cbrt-undiv frac-2neg div-exp clear-num div-inv associate-/l/ expm1-udef
1×rem-sqrt-square expm1-log1p sqrt-pow1 pow1/2 div-sub
Counts
4 → 158
Calls
4 calls:
25.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.0ms
(expm1 (log1p (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
27.0ms
(/ (expm1 (log1p (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
35.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series5.5s

Counts
4 → 12
Calls
4 calls:
172.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
1.8s
(expm1 (log1p (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
3.1s
(/ (expm1 (log1p (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
344.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify67.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013093399
150022995

prune562.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes47.0ms

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 (1.0ms)

IterNodesCost
0126
1166
2166

end0.0ms

sample1.4s

Algorithm
intervals
Results
386.0ms8027×body80nan
318.0ms1695×body1280valid
220.0ms4166×body80valid
194.0ms1241×body640valid
71.0ms588×body320valid
26.0ms310×body160valid