Details

Time bar (total: 3.8s)

sample14.0ms

Algorithm
intervals
Results
5.0ms255×body80valid
2.0ms84×body80nan
0.0ms1×body1280valid

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

rewrite33.0ms

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:
4.0ms
(sqrt (+ x 1.0))
11.0ms
(+ 1.0 (sqrt (+ x 1.0)))
16.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series207.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(sqrt (+ x 1.0))
43.0ms
(+ 1.0 (sqrt (+ x 1.0)))
135.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify35.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0317484
11147435
25001427

prune142.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ 1.0 (pow (sqrt (+ x 1.0)) 1))
0.2b
(/ x (+ 1.0 (pow (sqrt (+ x 1.0)) 1)))

rewrite56.0ms

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:
4.0ms
(sqrt (+ x 1.0))
18.0ms
(+ 1.0 (pow (sqrt (+ x 1.0)) 1))
32.0ms
(/ x (+ 1.0 (pow (sqrt (+ x 1.0)) 1)))

series205.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(sqrt (+ x 1.0))
43.0ms
(+ 1.0 (pow (sqrt (+ x 1.0)) 1))
133.0ms
(/ x (+ 1.0 (pow (sqrt (+ x 1.0)) 1)))

simplify36.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0326547
11253480
25001465

prune159.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

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

rewrite121.0ms

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:
17.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
15.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
49.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
20.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series800.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
127.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
140.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
408.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify106.0ms

Algorithm
egg-herbie
Counts
329 → 329
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
08875646
135015039
250014956

prune483.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (pow (sqrt (+ x 1.0)) 1) (pow (sqrt (+ x 1.0)) 1))
0.2b
(pow (pow (sqrt (+ x 1.0)) 1) 3)
3.1b
(- (* (pow (sqrt (+ x 1.0)) 1) (pow (sqrt (+ x 1.0)) 1)) (* 1.0 (pow (sqrt (+ x 1.0)) 1)))
7.5b
(/ x (+ (pow 1.0 3) (pow (pow (sqrt (+ x 1.0)) 1) 3)))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
95×*-un-lft-identity
93×unpow-prod-down
65×add-sqr-sqrt
38×sqrt-prod
37×add-cube-cbrt
28×distribute-lft-out
27×times-frac cube-prod
20×add-exp-log
16×unswap-sqr
15×swap-sqr sqr-pow
11×associate-*r* associate-*l*
10×pow-exp
9×prod-exp associate-/r* add-cbrt-cube
8×pow-to-exp
6×add-log-exp
4×pow1 sum-cubes
3×pow-unpow associate-/l*
2×associate-/r/
1×cbrt-undiv pow2 cube-mult sub-neg flip3-- distribute-rgt-out-- pow-pow frac-2neg flip3-+ diff-log unpow3 div-exp pow-prod-down clear-num pow-sqr *-commutative pow-prod-up flip-- cbrt-unprod flip-+ div-inv rem-cube-cbrt
Counts
4 → 182
Calls
4 calls:
42.0ms
(* (pow (sqrt (+ x 1.0)) 1) (pow (sqrt (+ x 1.0)) 1))
10.0ms
(pow (pow (sqrt (+ x 1.0)) 1) 3)
14.0ms
(- (* (pow (sqrt (+ x 1.0)) 1) (pow (sqrt (+ x 1.0)) 1)) (* 1.0 (pow (sqrt (+ x 1.0)) 1)))
95.0ms
(/ x (+ (pow 1.0 3) (pow (pow (sqrt (+ x 1.0)) 1) 3)))

series342.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (pow (sqrt (+ x 1.0)) 1) (pow (sqrt (+ x 1.0)) 1))
69.0ms
(pow (pow (sqrt (+ x 1.0)) 1) 3)
66.0ms
(- (* (pow (sqrt (+ x 1.0)) 1) (pow (sqrt (+ x 1.0)) 1)) (* 1.0 (pow (sqrt (+ x 1.0)) 1)))
191.0ms
(/ x (+ (pow 1.0 3) (pow (pow (sqrt (+ x 1.0)) 1) 3)))

simplify118.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
06171500
132531122
250011110

prune394.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes18.0ms

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
0125
1125

end0.0ms

sample315.0ms

Algorithm
intervals
Results
161.0ms7998×body80valid
41.0ms2714×body80nan
0.0ms2×body1280valid