Details

Time bar (total: 6.6s)

sample30.0ms

Algorithm
intervals
Results
12.0ms75×body1280valid
4.0ms141×body80valid
3.0ms24×body640valid
1.0ms12×body320valid
0.0ms4×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: 14.3b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1.0 x)
0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b
(/ 1.0 (hypot 1.0 x))
1.9b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
23×add-sqr-sqrt
21×add-cube-cbrt
12×prod-diff
9×times-frac
8×add-log-exp
6×add-exp-log add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u
3×fma-def fma-neg associate-/r* sqrt-prod associate-/l*
1×cbrt-undiv +-commutative sub-neg hypot-udef flip3-- frac-2neg flip3-+ diff-log div-exp clear-num sum-log flip-- flip-+ div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 87
Calls
4 calls:
0.0ms
(hypot 1.0 x)
11.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
8.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series599.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(hypot 1.0 x)
100.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
99.0ms
(/ 1.0 (hypot 1.0 x))
341.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify56.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0539998
12059745
25001742

prune251.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 13.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
1.4b
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
21×add-sqr-sqrt add-cube-cbrt
18×times-frac
8×add-exp-log add-cbrt-cube
6×associate-/r* associate-/l* add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u
3×fma-def
2×cbrt-undiv frac-2neg div-exp clear-num div-inv
1×+-commutative flip3-+ sum-log flip-+ fma-udef distribute-lft-out
Counts
4 → 85
Calls
4 calls:
10.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
4.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
0.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

series444.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
99.0ms
(/ 1.0 (hypot 1.0 x))
98.0ms
(/ 1.0 (hypot 1.0 x))
149.0ms
(fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0))

simplify37.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0319561
11141522
25001520

prune339.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

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
(expm1 (log1p (/ 1.0 (hypot 1.0 x))))
1.4b
(fma (- 0.5) (+ 1.0 (expm1 (log1p (/ 1.0 (hypot 1.0 x))))) (* 1.0 1.0))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
8×add-exp-log add-cbrt-cube
6×associate-/r* associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×cbrt-undiv frac-2neg div-exp clear-num div-inv
1×expm1-log1p fma-udef expm1-udef
Counts
4 → 79
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
0.0ms
(expm1 (log1p (/ 1.0 (hypot 1.0 x))))
0.0ms
(fma (- 0.5) (+ 1.0 (expm1 (log1p (/ 1.0 (hypot 1.0 x))))) (* 1.0 1.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
102.0ms
(/ 1.0 (hypot 1.0 x))
101.0ms
(/ 1.0 (hypot 1.0 x))
517.0ms
(expm1 (log1p (/ 1.0 (hypot 1.0 x))))
367.0ms
(fma (- 0.5) (+ 1.0 (expm1 (log1p (/ 1.0 (hypot 1.0 x))))) (* 1.0 1.0))

simplify154.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 3 (147.0ms)

IterNodesCost
0254564
1869511
24493504
35001497

prune353.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(expm1 (log1p (/ 1.0 (hypot 1.0 x))))
0.1b
(exp (log (fma (- 0.5) (+ 1.0 (expm1 (log1p (/ 1.0 (hypot 1.0 x))))) (* 1.0 1.0))))
1.4b
(fma (- 0.5) (+ 1.0 (expm1 (log1p (/ 1.0 (hypot 1.0 x))))) (* 1.0 1.0))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u exp-prod log1p-expm1-u add-log-exp
3×log-prod exp-sum associate-/r* associate-/l*
1×cbrt-undiv expm1-log1p frac-2neg div-exp clear-num log-pow fma-udef div-inv rem-exp-log expm1-udef
Counts
4 → 67
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
0.0ms
(expm1 (log1p (/ 1.0 (hypot 1.0 x))))
3.0ms
(exp (log (fma (- 0.5) (+ 1.0 (expm1 (log1p (/ 1.0 (hypot 1.0 x))))) (* 1.0 1.0))))
0.0ms
(fma (- 0.5) (+ 1.0 (expm1 (log1p (/ 1.0 (hypot 1.0 x))))) (* 1.0 1.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
105.0ms
(/ 1.0 (hypot 1.0 x))
528.0ms
(expm1 (log1p (/ 1.0 (hypot 1.0 x))))
374.0ms
(exp (log (fma (- 0.5) (+ 1.0 (expm1 (log1p (/ 1.0 (hypot 1.0 x))))) (* 1.0 1.0))))
376.0ms
(fma (- 0.5) (+ 1.0 (expm1 (log1p (/ 1.0 (hypot 1.0 x))))) (* 1.0 1.0))

simplify154.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 3 (147.0ms)

IterNodesCost
0285614
1927549
24573522
35001516

prune339.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

regimes286.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.5b

bsearch101.0ms

Steps
ItersRangePoint
5
0.001242113813128165
0.002806896206153352
0.0013665712745287832
7
-0.002950799818357885
-5.931762247777049e-05
-0.002313696967980117

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06259
16259

end0.0ms

sample840.0ms

Algorithm
intervals
Results
457.0ms2927×body1280valid
119.0ms4043×body80valid
77.0ms601×body640valid
26.0ms278×body320valid
8.0ms151×body160valid