Details

Time bar (total: 3.2s)

sample14.0ms

Algorithm
intervals
Results
5.0ms256×body80valid
1.0ms101×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: 0.2b

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.0b
(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:
16.0ms
(+ 1.0 (sqrt (+ x 1.0)))
10.0ms
(sqrt (+ x 1.0))
31.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series197.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(+ 1.0 (sqrt (+ x 1.0)))
31.0ms
(sqrt (+ x 1.0))
129.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify35.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0317483
11159435
25001427

prune129.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (+ x 1.0)))
0.1b
(sqrt (sqrt (+ x 1.0)))
0.1b
(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
0.2b
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
106×sqrt-prod
62×add-sqr-sqrt
46×*-un-lft-identity
40×sqrt-pow1
32×sqrt-div
31×pow1
28×add-cube-cbrt
20×pow1/2
18×swap-sqr
10×associate-*r* associate-*l*
9×flip3-+ times-frac pow-prod-up flip-+ unswap-sqr
8×add-exp-log add-cbrt-cube distribute-lft-out
5×pow-prod-down pow-sqr
4×frac-times rem-sqrt-square add-log-exp
3×associate-/r* associate-/l*
2×associate-*r/ associate-*l/ associate-/r/
1×cbrt-undiv pow2 frac-2neg pow-plus sqrt-unprod div-exp prod-exp clear-num rem-square-sqrt *-commutative cbrt-unprod div-inv
Counts
4 → 161
Calls
4 calls:
8.0ms
(sqrt (sqrt (+ x 1.0)))
8.0ms
(sqrt (sqrt (+ x 1.0)))
9.0ms
(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
51.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series318.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(sqrt (sqrt (+ x 1.0)))
79.0ms
(sqrt (sqrt (+ x 1.0)))
126.0ms
(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
32.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify67.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05121295
123011129
250011105

prune283.0ms

Pruning

3 alts after pruning (2 fresh and 1 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)))
4.4b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
7.7b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite175.0ms

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:
11.0ms
(pow (sqrt (+ x 1.0)) 3)
39.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
29.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
86.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series307.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(pow (sqrt (+ x 1.0)) 3)
20.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
54.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
175.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify134.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 2 (111.0ms)

IterNodesCost
07711703
138701474
250021459

prune386.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
4.2b
(- (- (* 1.0 1.0) x) 1.0)
4.3b
(- 1.0 (sqrt (+ x 1.0)))

rewrite242.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
29×*-un-lft-identity
21×associate-*l*
16×times-frac
15×add-cube-cbrt
11×add-log-exp
9×add-exp-log add-cbrt-cube
8×difference-of-squares
7×pow1
6×associate-*r* sqrt-prod distribute-lft-out--
5×sub-neg flip3-- flip--
4×diff-log
2×distribute-rgt-in frac-times distribute-lft-in sqrt-div associate-*r/ prod-exp associate--l+ associate-/r/ cbrt-unprod unswap-sqr
1×cbrt-undiv associate--l- rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 div-exp pow-prod-down associate-*l/ *-commutative flip-+ div-inv distribute-lft-out
Counts
4 → 100
Calls
4 calls:
7.0ms
(sqrt (+ x 1.0))
165.0ms
(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
50.0ms
(- (- (* 1.0 1.0) x) 1.0)
16.0ms
(- 1.0 (sqrt (+ x 1.0)))

series155.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(sqrt (+ x 1.0))
69.0ms
(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
11.0ms
(- (- (* 1.0 1.0) x) 1.0)
48.0ms
(- 1.0 (sqrt (+ x 1.0)))

simplify49.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0425900
11822817
25001807

prune206.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes14.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0109
1109

end0.0ms

sample343.0ms

Algorithm
intervals
Results
154.0ms7998×body80valid
38.0ms2609×body80nan
0.0ms2×body1280valid