Details

Time bar (total: 5.5s)

sample15.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
2.0ms105×body80nan

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
084
184

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.1b
(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
14×add-sqr-sqrt
13×add-cube-cbrt
12×times-frac
6×distribute-lft-out
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 associate-/r* sqrt-prod
3×flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 61
Calls
3 calls:
8.0ms
(sqrt (+ x 1.0))
16.0ms
(+ 1.0 (sqrt (+ x 1.0)))
34.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series213.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(sqrt (+ x 1.0))
42.0ms
(+ 1.0 (sqrt (+ x 1.0)))
141.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify36.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0317483
11159435
25001427

prune139.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.1b
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
0.1b
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
31×add-sqr-sqrt
26×times-frac
23×add-cube-cbrt
18×associate-*r*
17×add-exp-log
11×add-cbrt-cube
9×distribute-lft-out
8×pow1
6×add-log-exp
4×flip3-+ div-exp prod-exp associate-/r* sqrt-prod associate-/r/ flip-+
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp sqrt-div 1-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num sum-log un-div-inv *-commutative inv-pow
Counts
4 → 106
Calls
4 calls:
7.0ms
(sqrt (+ x 1.0))
16.0ms
(+ 1.0 (sqrt (+ x 1.0)))
34.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
74.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

series321.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (+ x 1.0))
41.0ms
(+ 1.0 (sqrt (+ x 1.0)))
102.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
142.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

simplify54.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0452821
11973707
25002668

prune189.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (sqrt (+ x 1.0)) 3)
0.2b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
4.3b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
8.0b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
89×*-un-lft-identity
62×sqrt-div
43×add-sqr-sqrt
34×sqrt-prod
32×flip3-+ flip-+
31×add-cube-cbrt
28×associate-*r/ distribute-lft-out
27×times-frac
23×unpow-prod-down cube-prod
21×pow1
16×frac-sub
12×frac-times
11×swap-sqr
9×add-exp-log sqrt-pow1 pow1/2 associate-/r* add-cbrt-cube
8×associate-*l/
7×associate-*r* associate-*l*
6×add-log-exp
5×pow-prod-up
4×sum-cubes sub-div unswap-sqr
3×pow-unpow pow-pow pow-prod-down pow-sqr associate-/l*
2×cube-div associate-/r/
1×cbrt-undiv pow2 cube-mult pow-to-exp sub-neg flip3-- distribute-rgt-out-- frac-2neg pow-plus sqrt-unprod diff-log unpow3 div-exp pow-exp prod-exp clear-num rem-square-sqrt *-commutative sqrt-pow2 flip-- cbrt-unprod div-inv rem-cube-cbrt sqr-pow
Counts
4 → 184
Calls
4 calls:
10.0ms
(pow (sqrt (+ x 1.0)) 3)
40.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
29.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
89.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series342.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(pow (sqrt (+ x 1.0)) 3)
17.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
67.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
189.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify128.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 2 (112.0ms)

IterNodesCost
07711703
138701474
250021459

prune415.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0))))
0.1b
(* (/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
0.2b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
4.3b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
132×times-frac
127×*-un-lft-identity
96×sqrt-div
76×add-sqr-sqrt
70×flip3-+ flip-+
66×associate-*r/
65×associate-*l*
63×associate-*l/
59×add-cube-cbrt
58×associate-/r/
52×frac-sub
36×add-exp-log
33×distribute-lft-out
29×add-cbrt-cube
26×sqrt-prod
21×pow1
14×frac-times div-exp
13×associate-/l*
11×swap-sqr div-inv
10×cbrt-undiv flip3-- associate-*r* prod-exp flip--
8×sqrt-pow1 pow1/2
7×cbrt-unprod
6×add-log-exp unswap-sqr
5×pow-prod-up
4×pow-prod-down associate-/r* sub-div
3×pow-sqr
2×1-exp *-commutative
1×pow2 distribute-rgt-in sub-neg distribute-rgt-out-- frac-2neg distribute-lft-in pow-plus sqrt-unprod diff-log clear-num rem-square-sqrt associate-/l/
Counts
4 → 272
Calls
4 calls:
299.0ms
(/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0))))
740.0ms
(* (/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
39.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
32.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

series814.0ms

Counts
4 → 12
Calls
4 calls:
434.0ms
(/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0))))
293.0ms
(* (/ (/ x (* (- (+ (* 1.0 1.0) (+ x 1.0)) (* 1.0 (sqrt (+ x 1.0)))) 1)) (+ 1.0 (sqrt (+ x 1.0)))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))
25.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
61.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))

simplify83.0ms

Algorithm
egg-herbie
Counts
284 → 284
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
017875715
150035251

prune797.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes46.0ms

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
02625
12825
22825

end0.0ms

sample345.0ms

Algorithm
intervals
Results
156.0ms7996×body80valid
40.0ms2756×body80nan
0.0ms4×body1280valid