Details

Time bar (total: 12.0s)

sample29.0ms

Algorithm
intervals
Results
14.0ms90×body1280valid
4.0ms131×body80valid
2.0ms16×body640valid
1.0ms10×body320valid
1.0ms9×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0196
1266
2336
3356
4416
5446
6446

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(hypot 1.0 x)
2.5b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
20×add-cube-cbrt
12×prod-diff
9×times-frac
7×pow1
6×add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u sqrt-prod log1p-expm1-u
3×fma-neg associate-/r* associate-/l*
2×sqrt-pow1 sqrt-div associate-*r/
1×cbrt-undiv sub-neg hypot-udef flip3-- frac-2neg flip3-+ pow1/2 diff-log div-exp pow-prod-down clear-num flip-- flip-+ div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 85
Calls
4 calls:
7.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.0ms
(/ 1.0 (hypot 1.0 x))
0.0ms
(hypot 1.0 x)
3.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series814.0ms

Counts
4 → 12
Calls
4 calls:
270.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
106.0ms
(/ 1.0 (hypot 1.0 x))
62.0ms
(hypot 1.0 x)
376.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify59.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05331074
12023830
25002827

prune269.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.0b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
30×times-frac
29×add-sqr-sqrt add-cube-cbrt
10×add-exp-log associate-/r* add-cbrt-cube
9×associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u distribute-lft-out add-log-exp
3×cbrt-undiv frac-2neg div-exp clear-num div-inv
2×associate-/r/
1×flip3-+ flip-+ fma-udef
Counts
4 → 103
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series1.6s

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ 1.0 (hypot 1.0 x))
108.0ms
(/ 1.0 (hypot 1.0 x))
1.2s
(/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
160.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify92.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
07641571
135391461
250011448

prune458.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(* (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
2.0b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt *-un-lft-identity
32×times-frac
29×add-cube-cbrt
18×associate-*r*
17×add-exp-log
13×add-cbrt-cube
6×pow1 associate-/r* associate-/l*
4×expm1-log1p-u div-exp prod-exp log1p-expm1-u add-log-exp
3×cbrt-undiv associate-*l* div-inv distribute-lft-out unswap-sqr
2×frac-2neg clear-num associate-/r/ cbrt-unprod
1×rec-exp flip3-+ 1-exp associate-*r/ pow-prod-down un-div-inv *-commutative flip-+ fma-udef
Counts
4 → 111
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(/ 1.0 (hypot 1.0 x))
16.0ms
(* (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ 1.0 (hypot 1.0 x))
110.0ms
(/ 1.0 (hypot 1.0 x))
1.4s
(* (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
149.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify104.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
08601600
141581445
250011434

prune429.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.0b
(* (* (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (sqrt (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))) (sqrt (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
0.0b
(* (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (sqrt (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
2.0b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
57×sqrt-prod
51×*-un-lft-identity
44×add-sqr-sqrt
42×associate-*r*
40×times-frac
31×add-cube-cbrt
13×pow1
11×add-exp-log add-cbrt-cube
9×distribute-lft-out
6×sqrt-div associate-/r/
4×expm1-log1p-u associate-*r/ associate-*l* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
3×rem-sqrt-square sqrt-pow1 flip3-+ flip-+ div-inv
2×*-commutative
1×frac-times pow-flip pow1/2 associate-*l/ fma-udef inv-pow
Counts
4 → 128
Calls
4 calls:
7.0ms
(sqrt (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
43.0ms
(* (* (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (sqrt (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))) (sqrt (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
20.0ms
(* (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (sqrt (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
0.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series4.2s

Counts
4 → 12
Calls
4 calls:
1.1s
(sqrt (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
1.3s
(* (* (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (sqrt (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))) (sqrt (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
1.8s
(* (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (sqrt (/ 1 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
156.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify58.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012223355
150013076

prune587.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

regimes523.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.9b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04847
14847

end0.0ms

sample800.0ms

Algorithm
intervals
Results
444.0ms2741×body1280valid
123.0ms4105×body80valid
84.0ms665×body640valid
30.0ms318×body320valid
9.0ms171×body160valid