Details

Time bar (total: 7.2s)

sample44.0ms

Algorithm
intervals
Results
11.0ms508×body80nan
10.0ms229×body160nan
7.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0115
1125
2125

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
0.2b
(log (+ x (sqrt (- (* x x) 1.0))))
28.5b
(sqrt (- (* x x) 1.0))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-sqr-sqrt
6×add-cube-cbrt
5×pow1 add-log-exp
4×add-exp-log log-prod sqrt-prod
3×expm1-log1p-u fma-def add-cbrt-cube log1p-expm1-u
2×log-div flip3-+ sqrt-div flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square flip3-- sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow flip-- difference-of-squares
Counts
3 → 52
Calls
3 calls:
9.0ms
(+ x (sqrt (- (* x x) 1.0)))
6.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
5.0ms
(sqrt (- (* x x) 1.0))

series309.0ms

Counts
3 → 9
Calls
3 calls:
63.0ms
(+ x (sqrt (- (* x x) 1.0)))
196.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
50.0ms
(sqrt (- (* x x) 1.0))

simplify36.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0339436
11140401
25001389

prune147.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (log x) (/ (/ 0.25 x) x))
0.1b
(/ 0.09375 (pow x 4))
0.2b
(/ (/ 0.25 x) x)
0.2b
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
870×times-frac
804×add-sqr-sqrt
668×*-un-lft-identity
570×add-cube-cbrt
544×prod-diff
379×associate-+r+
183×associate--l+
124×pow1
120×log-pow
84×unpow-prod-down
78×difference-of-squares
62×distribute-lft-out--
46×div-inv
28×sqr-pow
16×associate-/l*
14×add-exp-log
11×add-cbrt-cube
10×associate-/r* add-log-exp
9×log-prod
8×distribute-lft-out
6×div-exp
4×cbrt-undiv expm1-log1p-u fma-def fma-neg diff-log log1p-expm1-u
3×sub-neg associate-+l+ sum-log
2×frac-2neg clear-num
1×+-commutative pow-to-exp associate-+r- flip3-- flip3-+ pow-exp flip-- flip-+ associate-/l/
Counts
4 → 727
Calls
4 calls:
20.0ms
(- (log x) (/ (/ 0.25 x) x))
5.0ms
(/ 0.09375 (pow x 4))
6.0ms
(/ (/ 0.25 x) x)
72.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))

series491.0ms

Counts
4 → 12
Calls
4 calls:
327.0ms
(- (log x) (/ (/ 0.25 x) x))
35.0ms
(/ 0.09375 (pow x 4))
24.0ms
(/ (/ 0.25 x) x)
104.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))

simplify143.0ms

Algorithm
egg-herbie
Counts
739 → 739
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0264714534
1500211801

prune2.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- x (sqrt 1.0)))
0.0b
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.2b
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
22×sqrt-prod
17×*-un-lft-identity
14×sqrt-div
11×add-cube-cbrt
10×pow1
9×associate-*r*
7×add-exp-log associate-*l*
6×add-cbrt-cube add-log-exp
5×flip3-+ flip-+
4×expm1-log1p-u frac-times flip3-- flip-- log1p-expm1-u difference-of-squares unswap-sqr
3×log-prod fma-def sqrt-pow1 pow1/2 pow-prod-down
2×log-div associate-*r/ associate-*l/ distribute-lft-out--
1×+-commutative rem-sqrt-square sqrt-unprod rem-log-exp prod-exp sum-log log-pow *-commutative cbrt-unprod distribute-lft-out
Counts
4 → 96
Calls
4 calls:
6.0ms
(sqrt (- x (sqrt 1.0)))
3.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
2.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
13.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series904.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(sqrt (- x (sqrt 1.0)))
148.0ms
(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
476.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
208.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify54.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
05271181
118621066
250011049

prune314.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize20.0ms

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)

rewrite12.0ms

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)

series707.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(* (cbrt x) (cbrt x))
169.0ms
(cbrt x)
173.0ms
(cbrt x)
172.0ms
(cbrt x)

simplify87.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 3 (83.0ms)

IterNodesCost
0119308
1477281
22972258
35001255

prune319.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes13.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0139
1139

end0.0ms

sample1.3s

Algorithm
intervals
Results
364.0ms7614×body160nan
357.0ms15888×body80nan
232.0ms8000×body80valid