Details

Time bar (total: 4.6s)

sample21.0ms

Algorithm
intervals
Results
12.0ms256×body80valid

simplify113.0ms

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

localize11.0ms

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))
0.0b
(* x (+ 0.99229 (* x 0.04481)))
17.2b
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite92.0ms

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:
71.0ms
(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
2.0ms
(+ 2.30753 (* x 0.27061))
7.0ms
(* x (+ 0.99229 (* x 0.04481)))
9.0ms
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series246.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
32.0ms
(+ 2.30753 (* x 0.27061))
63.0ms
(* x (+ 0.99229 (* x 0.04481)))
57.0ms
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify60.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0516893
12218827
25002827

prune225.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize14.0ms

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
(/ (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
17.1b
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
17.1b
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
164×add-sqr-sqrt
162×add-cube-cbrt *-un-lft-identity
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×flip3-+ associate-/r* flip-+
11×add-exp-log add-cbrt-cube
9×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
Counts
4 → 264
Calls
4 calls:
10.0ms
(/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
24.0ms
(/ (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (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)))))

series385.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
62.0ms
(/ (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
82.0ms
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
82.0ms
(sqrt (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify114.0ms

Algorithm
egg-herbie
Counts
276 → 276
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
09296227
135405694
250015608

prune616.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (+ 0.99229 (* x 0.04481)))
0.1b
(* (sqrt 0.70711) (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
0.2b
(* (sqrt 0.70711) (* (sqrt 0.70711) (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))
17.2b
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
21×*-un-lft-identity
19×add-cube-cbrt
15×add-exp-log associate-*l* add-cbrt-cube
13×pow1
11×distribute-rgt-in distribute-lft-in
10×times-frac associate-*r*
8×associate-*r/
7×sqrt-prod
6×sub-neg
5×pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×flip3-+ associate-/r* *-commutative flip-+ associate-/l* unswap-sqr
2×flip3-- associate-/r/ flip-- associate-/l/ difference-of-squares
1×cbrt-undiv frac-2neg div-exp clear-num div-inv distribute-lft-out--
Counts
4 → 115
Calls
4 calls:
7.0ms
(* x (+ 0.99229 (* x 0.04481)))
72.0ms
(* (sqrt 0.70711) (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
67.0ms
(* (sqrt 0.70711) (* (sqrt 0.70711) (- (/ (+ 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)))))

series414.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(* x (+ 0.99229 (* x 0.04481)))
133.0ms
(* (sqrt 0.70711) (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
153.0ms
(* (sqrt 0.70711) (* (sqrt 0.70711) (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))
61.0ms
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify79.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
06061382
127751233
250021233

prune313.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (cbrt (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)) (cbrt (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))
17.2b
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
17.2b
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
17.2b
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
50×*-un-lft-identity
36×add-cube-cbrt
32×cbrt-prod
31×times-frac
12×add-exp-log cbrt-div
11×pow1 swap-sqr
10×add-cbrt-cube
9×associate-*r* associate-*l* associate-/r* associate-/l*
8×difference-of-squares
6×flip3-- flip3-+ pow1/3 associate-/r/ flip-- flip-+ associate-/l/ distribute-lft-out--
4×frac-times add-log-exp unswap-sqr
3×cbrt-undiv frac-2neg div-exp clear-num div-inv
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 152
Calls
4 calls:
134.0ms
(* (cbrt (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)) (cbrt (- (/ (+ 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)))))

series400.0ms

Counts
4 → 12
Calls
4 calls:
220.0ms
(* (cbrt (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)) (cbrt (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))
62.0ms
(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
56.0ms
(/ (+ 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)))))

simplify68.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
04792688
117852564
250022409

prune555.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes48.0ms

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
02516
12516

end0.0ms

sample413.0ms

Algorithm
intervals
Results
316.0ms8000×body80valid