Details

Time bar (total: 5.0s)

sample17.0ms

Algorithm
intervals
Results
6.0ms256×body80valid
2.0ms70×body80nan

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
084
184

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.2b

Counts
2 → 1

localize5.0ms

Local error

Found 3 expressions with local error:

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

rewrite21.0ms

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:
10.0ms
(+ 1.0 (sqrt (+ x 1.0)))
3.0ms
(sqrt (+ x 1.0))
7.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series25.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(+ 1.0 (sqrt (+ x 1.0)))
3.0ms
(sqrt (+ x 1.0))
17.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify46.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0460585
11938554
25002551

prune316.0ms

Filtered
70 candidates to 55 candidates (21.4%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New67370
Fresh000
Picked011
Done000
Total67471

Merged error: 0b

Counts
71 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.0b
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.4b
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.4b
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
378×times-frac
306×*-un-lft-identity
232×sqrt-prod
192×add-sqr-sqrt
190×add-cube-cbrt
58×distribute-lft-out
30×associate-/l*
24×sqrt-div
20×associate-/r/
14×associate-/r*
12×flip3-+ flip-+
11×add-exp-log add-cbrt-cube
10×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 317
Calls
4 calls:
5.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
5.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
8.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
23.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series73.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
11.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
34.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
17.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify128.0ms

Algorithm
egg-herbie
Counts
329 → 329
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
011265982
146615345
250025337

prune1.6s

Filtered
329 candidates to 148 candidates (55.0%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New3290329
Fresh022
Picked011
Done011
Total3294333

Merged error: 0b

Counts
333 → 4

localize14.0ms

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)
2.4b
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
7.3b
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite58.0ms

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
(* (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))))
18.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series32.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
9.0ms
(pow (sqrt (+ x 1.0)) 3)
5.0ms
(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
16.0ms
(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify49.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09651793
150011577

prune1.4s

Filtered
196 candidates to 102 candidates (48.0%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1960196
Fresh011
Picked011
Done022
Total1964200

Merged error: 0b

Counts
200 → 4

localize9.0ms

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))))
2.4b
(- (- (* 1.0 1.0) x) 1.0)
2.4b
(- 1.0 (sqrt (+ x 1.0)))

rewrite36.0ms

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:
3.0ms
(sqrt (+ x 1.0))
17.0ms
(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
7.0ms
(- (- (* 1.0 1.0) x) 1.0)
6.0ms
(- 1.0 (sqrt (+ x 1.0)))

series17.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(sqrt (+ x 1.0))
7.0ms
(* (/ x (- (- (* 1.0 1.0) x) 1.0)) (- 1.0 (sqrt (+ x 1.0))))
2.0ms
(- (- (* 1.0 1.0) x) 1.0)
5.0ms
(- 1.0 (sqrt (+ x 1.0)))

simplify56.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0503940
12155875
25001866

prune478.0ms

Filtered
112 candidates to 82 candidates (26.8%)
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New1120112
Fresh000
Picked011
Done033
Total1124116

Merged error: 0b

Counts
116 → 4

regimes72.0ms

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
084
184

end0.0ms

sample403.0ms

Algorithm
intervals
Results
192.0ms8000×body80valid
58.0ms2688×body80nan

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