Details

Time bar (total: 5.9s)

sample66.0ms

Algorithm
intervals
Results
21.0ms511×body80nan
17.0ms246×body160nan
13.0ms256×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1115
2115

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (sqrt (- (* x x) 1.0)))
0.2b
(log (+ x (sqrt (- (* x x) 1.0))))
30.1b
(sqrt (- (* x x) 1.0))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
7×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×add-exp-log log-prod sqrt-prod
3×add-cbrt-cube
2×log-div flip3-+ sqrt-div flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square flip3-- sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow flip-- difference-of-squares
Counts
3 → 43
Calls
3 calls:
8.0ms
(+ x (sqrt (- (* x x) 1.0)))
9.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
5.0ms
(sqrt (- (* x x) 1.0))

series324.0ms

Counts
3 → 9
Calls
3 calls:
71.0ms
(+ x (sqrt (- (* x x) 1.0)))
199.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
55.0ms
(sqrt (- (* x x) 1.0))

simplify135.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 3 (129.0ms)

IterNodesCost
0316408
11042379
24663366
35003365

prune132.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ 0.25 x) x)
0.2b
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
0.2b
(/ 0.09375 (pow x 4))

rewrite328.0ms

Algorithm
rewrite-expression-head
Rules
96×times-frac
83×*-un-lft-identity
63×add-sqr-sqrt add-cube-cbrt
16×associate-/l*
13×add-exp-log
12×unpow-prod-down
10×associate-/r* add-cbrt-cube distribute-lft-out--
9×pow1
8×associate--l+ distribute-lft-out add-log-exp
7×associate-+r+
6×log-prod div-exp log-pow div-inv
4×cbrt-undiv sqr-pow
3×associate-+l+ diff-log sum-log
2×sub-neg frac-2neg clear-num
1×+-commutative pow-to-exp associate-+r- flip3-+ pow-exp flip-+ associate-/l/
Counts
3 → 147
Calls
3 calls:
6.0ms
(/ (/ 0.25 x) x)
313.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
4.0ms
(/ 0.09375 (pow x 4))

series163.0ms

Counts
3 → 9
Calls
3 calls:
25.0ms
(/ (/ 0.25 x) x)
97.0ms
(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
40.0ms
(/ 0.09375 (pow x 4))

simplify60.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
06081049
12305939
25002934

prune377.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (- (- x (/ 0.125 (pow x 3))) (* 0.5 (/ 1 x))))
0.2b
(/ 0.125 (pow x 3))
0.2b
(log (+ x (- (- x (/ 0.125 (pow x 3))) (* 0.5 (/ 1 x)))))

rewrite427.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
33×*-un-lft-identity
29×add-sqr-sqrt add-cube-cbrt
12×unpow-prod-down cube-prod associate-/r* add-log-exp
9×add-exp-log
5×add-cbrt-cube
4×pow1 cube-mult associate-+r+ log-prod unpow3 sqr-pow
3×diff-log div-exp sum-log associate-/l*
2×sub-neg log-div flip3-+ associate--l+ flip-+ distribute-lft-out
1×cbrt-undiv +-commutative pow-to-exp associate-+r- frac-2neg rem-log-exp pow-exp clear-num log-pow div-inv
Counts
3 → 99
Calls
3 calls:
237.0ms
(+ x (- (- x (/ 0.125 (pow x 3))) (* 0.5 (/ 1 x))))
4.0ms
(/ 0.125 (pow x 3))
182.0ms
(log (+ x (- (- x (/ 0.125 (pow x 3))) (* 0.5 (/ 1 x)))))

series248.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(+ x (- (- x (/ 0.125 (pow x 3))) (* 0.5 (/ 1 x))))
41.0ms
(/ 0.125 (pow x 3))
163.0ms
(log (+ x (- (- x (/ 0.125 (pow x 3))) (* 0.5 (/ 1 x)))))

simplify50.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0381740
11765687
25001687

prune206.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (log 2) (log (sqrt x)))
0.1b
(/ (/ 0.25 x) x)
0.2b
(/ 0.09375 (pow x 4))
0.3b
(+ (+ (log 2) (log (sqrt x))) (- (- (log (sqrt x)) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))

rewrite406.0ms

Algorithm
rewrite-expression-head
Rules
131×*-un-lft-identity
96×times-frac
67×add-sqr-sqrt add-cube-cbrt
40×distribute-lft-out
29×pow1
25×log-pow distribute-lft-out--
17×add-log-exp
16×associate-+r+ associate-/l*
15×log-prod
14×add-exp-log associate--l+
12×unpow-prod-down
11×add-cbrt-cube
10×associate-/r* sum-log
8×frac-add
6×flip3-+ diff-log div-exp sqrt-prod flip-+ div-inv
4×cbrt-undiv associate-+l+ flip3-- frac-sub flip-- sqr-pow
2×+-commutative sub-neg frac-2neg clear-num
1×pow-to-exp associate-+r- pow-exp associate-/l/
Counts
4 → 195
Calls
4 calls:
5.0ms
(+ (log 2) (log (sqrt x)))
5.0ms
(/ (/ 0.25 x) x)
3.0ms
(/ 0.09375 (pow x 4))
381.0ms
(+ (+ (log 2) (log (sqrt x))) (- (- (log (sqrt x)) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))

series259.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(+ (log 2) (log (sqrt x)))
31.0ms
(/ (/ 0.25 x) x)
36.0ms
(/ 0.09375 (pow x 4))
106.0ms
(+ (+ (log 2) (log (sqrt x))) (- (- (log (sqrt x)) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))

simplify95.0ms

Algorithm
egg-herbie
Counts
207 → 207
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
09562157
138521946
250021931

prune569.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes12.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0178
1178

end0.0ms

sample1.9s

Algorithm
intervals
Results
596.0ms16347×body80nan
535.0ms7835×body160nan
405.0ms8000×body80valid