Details

Time bar (total: 5.0s)

sample38.0ms

Algorithm
intervals
Results
26.0ms256×body80valid

simplify112.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0319
1519
2699
3869
4949
51059
61399
71779
82029
92469
104169
116159
129929
1319489
1422409
1531549
1650019

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
0.0b
(+ 2.30753 (* x 0.27061))
0.1b
(* x (+ 0.99229 (* x 0.04481)))
14.9b
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
18×*-un-lft-identity
16×add-cube-cbrt
10×add-exp-log times-frac add-cbrt-cube
9×associate-*r*
8×pow1
6×associate-*l* add-log-exp
4×flip3-+ associate-*r/ flip-+
3×distribute-rgt-in distribute-lft-in associate-/r* associate-/l*
2×sub-neg pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod associate-/l/ difference-of-squares unswap-sqr
1×cbrt-undiv +-commutative flip3-- frac-2neg div-exp clear-num sum-log flip-- div-inv distribute-lft-out--
Counts
4 → 91
Calls
4 calls:
72.0ms
(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
2.0ms
(+ 2.30753 (* x 0.27061))
11.0ms
(* x (+ 0.99229 (* x 0.04481)))
9.0ms
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series267.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
36.0ms
(+ 2.30753 (* x 0.27061))
72.0ms
(* x (+ 0.99229 (* x 0.04481)))
63.0ms
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify61.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0516893
12218827
25002827

prune221.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
0.2b
(* (/ 1 (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))))
14.8b
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
14.8b
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
28×add-exp-log
24×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×sqrt-div
9×div-exp
8×pow1 prod-exp
6×flip3-+ associate-/r* associate-/r/ flip-+
5×cbrt-undiv
4×cbrt-unprod add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-/l/
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 160
Calls
4 calls:
10.0ms
(/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
43.0ms
(* (/ 1 (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))))
3.0ms
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
3.0ms
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series384.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
56.0ms
(* (/ 1 (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))))
85.0ms
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
84.0ms
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify102.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
07822840
142632554
250012413

prune575.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 (cbrt (pow (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) 3))) (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))))
14.8b
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
14.8b
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
19.9b
(cbrt (pow (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) 3))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
201×add-sqr-sqrt
153×times-frac
108×cbrt-prod
85×*-un-lft-identity
69×associate-*l*
66×sqrt-prod
64×add-cube-cbrt
45×unswap-sqr
36×unpow-prod-down cube-prod
26×add-exp-log
24×associate-*r*
14×add-cbrt-cube
10×sqrt-div sqr-pow
8×pow1 div-exp prod-exp
5×flip3-+ flip-+
4×cbrt-undiv cube-div cube-mult cbrt-div unpow3 associate-/r/ cbrt-unprod add-log-exp
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp div-inv
1×frac-times pow1/3 associate-*r/ pow-prod-down associate-*l/ *-commutative rem-cbrt-cube
Counts
4 → 221
Calls
4 calls:
81.0ms
(* (/ 1 (cbrt (pow (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) 3))) (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))))
3.0ms
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
3.0ms
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
5.0ms
(cbrt (pow (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) 3))

series305.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (/ 1 (cbrt (pow (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) 3))) (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))))
80.0ms
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
80.0ms
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
83.0ms
(cbrt (pow (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) 3))

simplify59.0ms

Algorithm
egg-herbie
Counts
233 → 233
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08794325
150014023

prune627.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

14.8b
(/ (* 0.70711 (- (* (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (* x x))) (+ (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
14.9b
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
14.9b
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
14.9b
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
34×*-un-lft-identity
31×times-frac
30×add-sqr-sqrt add-cube-cbrt
15×add-exp-log add-cbrt-cube
13×associate-/r*
10×associate-/l*
8×associate-/r/ associate-/l/
7×flip3-+ flip-+
5×cbrt-undiv div-exp
4×pow1 frac-2neg clear-num div-inv add-log-exp
2×associate-*r/ distribute-lft-out
1×flip3-- prod-exp flip-- cbrt-unprod
Counts
4 → 120
Calls
4 calls:
52.0ms
(/ (* 0.70711 (- (* (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (* x x))) (+ (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
9.0ms
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
9.0ms
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
9.0ms
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series605.0ms

Counts
4 → 12
Calls
4 calls:
424.0ms
(/ (* 0.70711 (- (* (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (* x x))) (+ (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
58.0ms
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
62.0ms
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
61.0ms
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify69.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04722145
120901899
250011882

prune402.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes21.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03319
13319

end0.0ms

sample767.0ms

Algorithm
intervals
Results
668.0ms8000×body80valid