Details

Time bar (total: 3.4s)

sample14.0ms

Algorithm
intervals
Results
6.0ms256×body80valid
2.0ms84×body80nan

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
084
184

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
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
(sqrt (+ x 1.0))
0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite17.0ms

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:
3.0ms
(sqrt (+ x 1.0))
5.0ms
(+ 1.0 (sqrt (+ x 1.0)))
7.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series223.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(sqrt (+ x 1.0))
42.0ms
(+ 1.0 (sqrt (+ x 1.0)))
145.0ms
(/ 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

prune136.0ms

Filtered
70 candidates to 52 candidates (74.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

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:
3.0ms
(sqrt (+ x 1.0))
6.0ms
(+ 1.0 (sqrt (+ x 1.0)))
12.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
8.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

series332.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (+ x 1.0))
42.0ms
(+ 1.0 (sqrt (+ x 1.0)))
147.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))
105.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))

simplify54.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0452822
11960707
25001668

prune189.0ms

Filtered
118 candidates to 73 candidates (61.9%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.3b
(/ 1 (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))
3.2b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
9.3b
(* (/ 1 (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))

rewrite269.0ms

Algorithm
rewrite-expression-head
Rules
125×*-un-lft-identity
60×sqrt-div
59×add-sqr-sqrt
56×times-frac
41×distribute-lft-out
40×add-cube-cbrt associate-*l*
34×flip3-+ flip-+
30×associate-*r/
28×unpow-prod-down cube-prod
26×sqrt-prod
22×pow1
19×add-exp-log
16×frac-sub
14×frac-times
13×add-cbrt-cube
11×swap-sqr
10×associate-*r*
9×associate-*l/ associate-/r*
8×sqrt-pow1 pow1/2
7×sum-cubes unswap-sqr
6×add-log-exp
5×prod-exp pow-prod-up
4×div-exp pow-prod-down associate-/r/ sub-div
3×pow-sqr cbrt-unprod associate-/l*
2×cbrt-undiv rec-exp 1-exp *-commutative div-inv
1×pow2 distribute-rgt-in sub-neg flip3-- distribute-rgt-out-- pow-flip frac-2neg distribute-lft-in pow-plus sqrt-unprod diff-log clear-num rem-square-sqrt flip-- inv-pow
Counts
4 → 213
Calls
4 calls:
10.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
204.0ms
(/ 1 (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))
12.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
31.0ms
(* (/ 1 (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))

series515.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
143.0ms
(/ 1 (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))
60.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
295.0ms
(* (/ 1 (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3))) (+ (* 1.0 1.0) (- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))))

simplify60.0ms

Algorithm
egg-herbie
Counts
225 → 225
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011162857
150012438

prune466.0ms

Filtered
225 candidates to 114 candidates (50.7%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.2b
(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
0.2b
(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
9.7b
(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
70×cbrt-prod *-un-lft-identity
51×times-frac
44×add-sqr-sqrt add-cube-cbrt
24×unpow-prod-down cube-prod
17×associate-/r*
13×distribute-lft-out
7×add-exp-log
6×cube-div cube-mult unpow3 add-cbrt-cube add-log-exp sqr-pow
5×pow1
4×cbrt-div flip3-+ flip-+
3×pow-unpow associate-/l*
2×associate-/r/
1×cbrt-undiv +-commutative pow-to-exp pow-pow frac-2neg pow1/3 div-exp pow-exp clear-num sum-log rem-cbrt-cube div-inv rem-cube-cbrt
Counts
4 → 149
Calls
4 calls:
6.0ms
(+ 1.0 (sqrt (+ x 1.0)))
6.0ms
(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
10.0ms
(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
7.0ms
(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

series349.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(+ 1.0 (sqrt (+ x 1.0)))
114.0ms
(pow (+ 1.0 (sqrt (+ x 1.0))) 3)
143.0ms
(/ x (cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3)))
46.0ms
(cbrt (pow (+ 1.0 (sqrt (+ x 1.0))) 3))

simplify62.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
04981438
121741302
250031278

prune225.0ms

Filtered
161 candidates to 81 candidates (50.3%)
Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes21.0ms

Accuracy

99.7% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 7.2b

bsearch30.0ms

Steps
ItersRangePoint
7
0.24450492938876567
34.599243829922614
0.8825844651085238

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03426
13426

end0.0ms

sample329.0ms

Algorithm
intervals
Results
165.0ms7997×body80valid
47.0ms2578×body80nan
0.0ms3×body1280valid