Details

Time bar (total: 5.5s)

sample23.0ms

Algorithm
intervals
Results
12.0ms256×body80valid
4.0ms82×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

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.0b
(sqrt (+ x 1.0))
0.2b
(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite29.0ms

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
(+ 1.0 (sqrt (+ x 1.0)))
4.0ms
(sqrt (+ x 1.0))
16.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series218.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(+ 1.0 (sqrt (+ x 1.0)))
29.0ms
(sqrt (+ x 1.0))
142.0ms
(/ 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

prune131.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (* (cbrt (+ 1.0 (sqrt (+ x 1.0)))) (cbrt (+ 1.0 (sqrt (+ x 1.0))))))
0.8b
(cbrt (+ 1.0 (sqrt (+ x 1.0))))
0.8b
(cbrt (+ 1.0 (sqrt (+ x 1.0))))
0.8b
(cbrt (+ 1.0 (sqrt (+ x 1.0))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
15×add-exp-log *-un-lft-identity
12×pow1 cbrt-prod
9×add-sqr-sqrt add-cube-cbrt pow-flip flip3-+ pow1/3 flip-+
8×associate-/r/
7×add-cbrt-cube
4×frac-times div-exp add-log-exp
3×times-frac prod-exp distribute-lft-out associate-/l*
2×cbrt-undiv rec-exp 1-exp associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 frac-2neg pow-plus clear-num associate-/r* cbrt-unprod div-inv inv-pow
Counts
4 → 85
Calls
4 calls:
38.0ms
(/ 1 (* (cbrt (+ 1.0 (sqrt (+ x 1.0)))) (cbrt (+ 1.0 (sqrt (+ x 1.0))))))
8.0ms
(cbrt (+ 1.0 (sqrt (+ x 1.0))))
8.0ms
(cbrt (+ 1.0 (sqrt (+ x 1.0))))
11.0ms
(cbrt (+ 1.0 (sqrt (+ x 1.0))))

series1.9s

Counts
4 → 12
Calls
4 calls:
990.0ms
(/ 1 (* (cbrt (+ 1.0 (sqrt (+ x 1.0)))) (cbrt (+ 1.0 (sqrt (+ x 1.0))))))
232.0ms
(cbrt (+ 1.0 (sqrt (+ x 1.0))))
423.0ms
(cbrt (+ 1.0 (sqrt (+ x 1.0))))
239.0ms
(cbrt (+ 1.0 (sqrt (+ x 1.0))))

simplify68.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
05961220
123611083
250011031

prune247.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b
(pow (sqrt (+ x 1.0)) 3)
5.8b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
6.3b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite102.0ms

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:
20.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
5.0ms
(pow (sqrt (+ x 1.0)) 3)
15.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
53.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series343.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
69.0ms
(pow (sqrt (+ x 1.0)) 3)
67.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
191.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify129.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 2 (111.0ms)

IterNodesCost
07711703
138731474
250021459

prune389.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ x (+ 1.0 (/ (sqrt (+ (pow x 3) (pow 1.0 3))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))))
6.3b
(/ (sqrt (+ (pow x 3) (pow 1.0 3))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))
6.8b
(sqrt (+ (pow x 3) (pow 1.0 3)))
9.6b
(sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

rewrite247.0ms

Algorithm
rewrite-expression-head
Rules
143×*-un-lft-identity
114×sqrt-prod
84×times-frac
57×add-sqr-sqrt
55×add-cube-cbrt
44×distribute-lft-out
32×unpow-prod-down cube-prod
15×associate-/l*
10×associate-/r*
8×add-exp-log sqrt-div sum-cubes add-cbrt-cube
6×pow1
5×flip3-+ flip-+
4×associate-/r/ add-log-exp
2×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv associate-/l/
1×sqrt-undiv
Counts
4 → 176
Calls
4 calls:
151.0ms
(/ x (+ 1.0 (/ (sqrt (+ (pow x 3) (pow 1.0 3))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))))
52.0ms
(/ (sqrt (+ (pow x 3) (pow 1.0 3))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))
22.0ms
(sqrt (+ (pow x 3) (pow 1.0 3)))
12.0ms
(sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

series399.0ms

Counts
4 → 12
Calls
4 calls:
216.0ms
(/ x (+ 1.0 (/ (sqrt (+ (pow x 3) (pow 1.0 3))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))))
81.0ms
(/ (sqrt (+ (pow x 3) (pow 1.0 3))) (sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0)))))
50.0ms
(sqrt (+ (pow x 3) (pow 1.0 3)))
52.0ms
(sqrt (+ (* x x) (- (* 1.0 1.0) (* x 1.0))))

simplify79.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
05663175
123472942
250022931

prune400.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes25.0ms

Accuracy

99.4% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 1.9b

bsearch29.0ms

Steps
ItersRangePoint
6
3.9715340067303715
33.11368705657117
5.562868238198095

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02826
12826

end0.0ms

sample623.0ms

Algorithm
intervals
Results
397.0ms7997×body80valid
101.0ms2688×body80nan
1.0ms3×body1280valid