Details

Time bar (total: 5.6s)

sample16.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
2.0ms81×body80nan

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
084
184

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.2b

Counts
2 → 1

localize5.0ms

Local error

Found 3 expressions with local error:

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

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
17×add-sqr-sqrt
14×add-cube-cbrt
12×times-frac
6×distribute-lft-out
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 associate-/r* sqrt-prod
3×expm1-log1p-u fma-def flip3-+ flip-+ log1p-expm1-u associate-/l*
2×sqrt-div associate-/r/
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 → 71
Calls
3 calls:
3.0ms
(sqrt (+ x 1.0))
6.0ms
(+ 1.0 (sqrt (+ x 1.0)))
7.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series216.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(sqrt (+ x 1.0))
41.0ms
(+ 1.0 (sqrt (+ x 1.0)))
142.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify40.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0334508
11222457
25002445

prune141.0ms

Filtered
80 candidates to 62 candidates (77.5%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New75580
Fresh000
Picked011
Done000
Total75681

Merged error: 0b

Counts
81 → 6

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.0b
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.4b
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.4b
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
378×times-frac
306×*-un-lft-identity
234×sqrt-prod
200×add-sqr-sqrt
190×add-cube-cbrt
58×distribute-lft-out
30×associate-/l*
24×sqrt-div
20×associate-/r/
14×associate-/r*
12×flip3-+ flip-+
11×add-exp-log add-cbrt-cube
10×div-inv
6×pow1
4×cbrt-undiv expm1-log1p-u div-exp hypot-def log1p-expm1-u add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 329
Calls
4 calls:
6.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
6.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
23.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
8.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
125.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
130.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
336.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
438.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify116.0ms

Algorithm
egg-herbie
Counts
341 → 341
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
09065694
135745078
250015045

prune425.0ms

Filtered
341 candidates to 152 candidates (44.6%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New3410341
Fresh044
Picked011
Done011
Total3416347

Merged error: 0b

Counts
347 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 1 (* (cbrt (+ 1.0 (sqrt (+ x 1.0)))) (cbrt (+ 1.0 (sqrt (+ x 1.0))))))
0.9b
(cbrt (+ 1.0 (sqrt (+ x 1.0))))
0.9b
(cbrt (+ 1.0 (sqrt (+ x 1.0))))
0.9b
(cbrt (+ 1.0 (sqrt (+ x 1.0))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
15×add-exp-log *-un-lft-identity
12×pow1 cbrt-prod
9×add-sqr-sqrt add-cube-cbrt pow-flip flip3-+ pow1/3 flip-+
8×associate-/r/
7×add-cbrt-cube
4×expm1-log1p-u frac-times div-exp log1p-expm1-u add-log-exp
3×times-frac prod-exp distribute-lft-out associate-/l*
2×cbrt-undiv rec-exp 1-exp associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 frac-2neg pow-plus clear-num associate-/r* cbrt-unprod div-inv inv-pow
Counts
4 → 93
Calls
4 calls:
16.0ms
(/ 1 (* (cbrt (+ 1.0 (sqrt (+ x 1.0)))) (cbrt (+ 1.0 (sqrt (+ x 1.0))))))
5.0ms
(cbrt (+ 1.0 (sqrt (+ x 1.0))))
6.0ms
(cbrt (+ 1.0 (sqrt (+ x 1.0))))
6.0ms
(cbrt (+ 1.0 (sqrt (+ x 1.0))))

series1.8s

Counts
4 → 12
Calls
4 calls:
1.0s
(/ 1 (* (cbrt (+ 1.0 (sqrt (+ x 1.0)))) (cbrt (+ 1.0 (sqrt (+ x 1.0))))))
249.0ms
(cbrt (+ 1.0 (sqrt (+ x 1.0))))
255.0ms
(cbrt (+ 1.0 (sqrt (+ x 1.0))))
244.0ms
(cbrt (+ 1.0 (sqrt (+ x 1.0))))

simplify79.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06221256
125091130
250021092

prune241.0ms

Filtered
105 candidates to 72 candidates (68.6%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1050105
Fresh033
Picked011
Done022
Total1056111

Merged error: 0b

Counts
111 → 6

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
70×*-un-lft-identity
59×add-sqr-sqrt
52×times-frac
40×add-cube-cbrt
39×sqrt-prod
30×associate-*r*
15×distribute-lft-out
11×add-exp-log add-cbrt-cube
7×pow1
6×associate-*l* associate-/l* add-log-exp unswap-sqr
4×expm1-log1p-u flip3-+ associate-/r* associate-/r/ flip-+ log1p-expm1-u
3×fma-def
2×cbrt-undiv sqrt-div div-exp prod-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num sum-log *-commutative hypot-def
Counts
4 → 144
Calls
4 calls:
3.0ms
(sqrt (+ x 1.0))
10.0ms
(+ 1.0 (sqrt (+ x 1.0)))
8.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
17.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series515.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (+ x 1.0))
41.0ms
(+ 1.0 (sqrt (+ x 1.0)))
301.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
136.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify67.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05541324
123241174
250011140

prune244.0ms

Filtered
156 candidates to 102 candidates (65.4%)
Pruning

6 alts after pruning (2 fresh and 4 done)

PrunedKeptTotal
New1560156
Fresh022
Picked011
Done033
Total1566162

Merged error: 0b

Counts
162 → 6

regimes44.0ms

Accuracy

0% (0.2b 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
084
184

end0.0ms

sample400.0ms

Algorithm
intervals
Results
214.0ms7998×body80valid
65.0ms2746×body80nan
0.0ms2×body1280valid

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