Details

Time bar (total: 3.8s)

sample14.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
2.0ms103×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

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite19.0ms

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:
6.0ms
(+ 1.0 (sqrt (+ x 1.0)))
3.0ms
(sqrt (+ x 1.0))
8.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series211.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(+ 1.0 (sqrt (+ x 1.0)))
32.0ms
(sqrt (+ x 1.0))
136.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify38.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0334508
11222457
25002445

prune152.0ms

Filtered
80 candidates to 62 candidates (77.5%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New77380
Fresh000
Picked101
Done000
Total78381

Merged error: 0b

Counts
81 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt x) (cbrt x))
0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
6.0ms
(* (cbrt x) (cbrt x))
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series716.0ms

Counts
4 → 12
Calls
4 calls:
197.0ms
(* (cbrt x) (cbrt x))
174.0ms
(cbrt x)
175.0ms
(cbrt x)
170.0ms
(cbrt x)

simplify95.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0119308
1477281
22972258
35001255

prune201.0ms

Filtered
93 candidates to 72 candidates (77.4%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New93093
Fresh022
Picked011
Done000
Total93396

Merged error: 0b

Counts
96 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (expm1 (log1p (sqrt (+ x 1.0)))))
0.0b
(sqrt (+ x 1.0))
0.2b
(/ x (+ 1.0 (expm1 (log1p (sqrt (+ x 1.0))))))
1.6b
(expm1 (log1p (sqrt (+ x 1.0))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
18×add-sqr-sqrt
15×add-cube-cbrt
12×times-frac
6×add-exp-log add-cbrt-cube distribute-lft-out add-log-exp
5×pow1
4×expm1-log1p-u associate-/r* sqrt-prod log1p-expm1-u
3×fma-def flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/ expm1-udef
1×cbrt-undiv +-commutative associate-+r- rem-sqrt-square expm1-log1p frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log hypot-def div-inv
Counts
4 → 83
Calls
4 calls:
3.0ms
(+ 1.0 (expm1 (log1p (sqrt (+ x 1.0)))))
4.0ms
(sqrt (+ x 1.0))
6.0ms
(/ x (+ 1.0 (expm1 (log1p (sqrt (+ x 1.0))))))
1.0ms
(expm1 (log1p (sqrt (+ x 1.0))))

series772.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(+ 1.0 (expm1 (log1p (sqrt (+ x 1.0)))))
30.0ms
(sqrt (+ x 1.0))
381.0ms
(/ x (+ 1.0 (expm1 (log1p (sqrt (+ x 1.0))))))
173.0ms
(expm1 (log1p (sqrt (+ x 1.0))))

simplify39.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0348713
11238609
25001585

prune204.0ms

Filtered
95 candidates to 77 candidates (81.1%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New95095
Fresh011
Picked011
Done011
Total95398

Merged error: 0b

Counts
98 → 3

localize7.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

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:
6.0ms
(+ 1.0 (sqrt (+ x 1.0)))
3.0ms
(sqrt (+ x 1.0))
9.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
21.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series499.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(+ 1.0 (sqrt (+ x 1.0)))
34.0ms
(sqrt (+ x 1.0))
287.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
136.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify66.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05541324
123241174
250011140

prune287.0ms

Filtered
156 candidates to 104 candidates (66.7%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1560156
Fresh000
Picked011
Done022
Total1563159

Merged error: 0b

Counts
159 → 3

regimes18.0ms

Accuracy

99.4% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 1.4b

bsearch36.0ms

Steps
ItersRangePoint
9
0.06406876111163662
2027774.326345067
0.10511709333523044

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01913
11913

end0.0ms

sample315.0ms

Algorithm
intervals
Results
153.0ms7996×body80valid
47.0ms2702×body80nan
0.0ms4×body1280valid