Details

Time bar (total: 2.9s)

sample9.0ms

Algorithm
intervals
Results
4.0ms256×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
063
163

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.6b

localize4.0ms

Local error

Found 1 expressions with local error:

17.6b
(/ x (+ (* x x) 1.0))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
3×add-exp-log associate-/r* add-cbrt-cube associate-/l*
2×associate-/r/
1×pow1 cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ div-inv add-log-exp
Counts
1 → 29
Calls
1 calls:
6.0ms
(/ x (+ (* x x) 1.0))

series53.0ms

Counts
1 → 3
Calls
1 calls:
53.0ms
(/ x (+ (* x x) 1.0))

simplify53.0ms

Algorithm
egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0165210
1555195
21839192
35001192

prune64.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* x x) 1.0)))
0.0b
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
17.6b
(sqrt (+ (* x x) 1.0))
17.6b
(sqrt (+ (* x x) 1.0))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
28×add-exp-log
24×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×sqrt-div
9×div-exp
8×pow1 prod-exp
6×associate-/r* associate-/r/
5×cbrt-undiv flip3-+ flip-+
4×cbrt-unprod add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 158
Calls
4 calls:
7.0ms
(/ x (sqrt (+ (* x x) 1.0)))
46.0ms
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))
4.0ms
(sqrt (+ (* x x) 1.0))

series260.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(/ x (sqrt (+ (* x x) 1.0)))
57.0ms
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
45.0ms
(sqrt (+ (* x x) 1.0))
41.0ms
(sqrt (+ (* x x) 1.0))

simplify88.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
06151742
128851548
250011440

prune302.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (sqrt (+ (* x x) 1.0)))
0.0b
(* (/ x (sqrt (+ (* x x) 1.0))) (/ 1 (sqrt (+ (* x x) 1.0))))
17.6b
(sqrt (+ (* x x) 1.0))
17.6b
(sqrt (+ (* x x) 1.0))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
28×add-exp-log
24×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×sqrt-div
9×div-exp
8×pow1 prod-exp
6×associate-/r* associate-/r/
5×cbrt-undiv flip3-+ flip-+
4×cbrt-unprod add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative
Counts
4 → 159
Calls
4 calls:
7.0ms
(/ x (sqrt (+ (* x x) 1.0)))
47.0ms
(* (/ x (sqrt (+ (* x x) 1.0))) (/ 1 (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))
4.0ms
(sqrt (+ (* x x) 1.0))

series261.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(/ x (sqrt (+ (* x x) 1.0)))
57.0ms
(* (/ x (sqrt (+ (* x x) 1.0))) (/ 1 (sqrt (+ (* x x) 1.0))))
41.0ms
(sqrt (+ (* x x) 1.0))
45.0ms
(sqrt (+ (* x x) 1.0))

simplify82.0ms

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06381739
131711570
250011470

prune300.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

5.1b
(sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))
15.0b
(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
17.6b
(sqrt (+ (* x x) 1.0))
21.0b
(/ (sqrt (+ (pow (* x x) 3) (pow 1.0 3))) (sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
68×sqrt-prod
52×*-un-lft-identity
48×times-frac
40×add-sqr-sqrt
38×add-cube-cbrt
9×add-log-exp
8×sqrt-div associate-/l*
7×sum-cubes distribute-lft-out
6×pow1 add-exp-log associate-/r* add-cbrt-cube
5×flip3-+ flip-+
2×rem-sqrt-square associate-+r+ sqrt-pow1 pow1/2 sum-log associate-/r/ associate-/l/
1×cbrt-undiv +-commutative associate-+r- sub-neg sqrt-undiv frac-2neg diff-log div-exp clear-num div-inv
Counts
4 → 124
Calls
4 calls:
31.0ms
(sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))
17.0ms
(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
4.0ms
(sqrt (+ (* x x) 1.0))
61.0ms
(/ (sqrt (+ (pow (* x x) 3) (pow 1.0 3))) (sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))))

series283.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0))))
38.0ms
(+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))
45.0ms
(sqrt (+ (* x x) 1.0))
124.0ms
(/ (sqrt (+ (pow (* x x) 3) (pow 1.0 3))) (sqrt (+ (* (* x x) (* x x)) (- (* 1.0 1.0) (* (* x x) 1.0)))))

simplify64.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04242667
116552491
250012455

prune406.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes28.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.3b

bsearch88.0ms

Steps
ItersRangePoint
9
251.47950061764826
104248118811.33417
938.4209298049026
10
-2.7097114655346684e+19
-753118471.6501554
-6.071857942535248e+16

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04829
14829

end0.0ms

sample225.0ms

Algorithm
intervals
Results
134.0ms8000×body80valid