Details

sample48.0ms

Algorithm

intervals

Results

13.0ms	463×	body	80	nan
12.0ms	248×	body	160	nan
7.0ms	256×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	5
1	12	5
2	12	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize8.0ms

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))))
28.9b	(sqrt (- (* x x) 1.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `log-prod` `sqrt-prod`
3×	`expm1-log1p-u` `fma-def` `add-cbrt-cube` `log1p-expm1-u`
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 → 52

Calls

3 calls:

7.0ms	(+ x (sqrt (- (* x x) 1.0)))
6.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
5.0ms	(sqrt (- (* x x) 1.0))

series328.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(+ x (sqrt (- (* x x) 1.0)))
200.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
57.0ms	(sqrt (- (* x x) 1.0))

simplify35.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	339	436
1	1140	401
2	5001	389

prune164.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log x) (/ (/ 0.25 x) x))
0.2b	(/ (/ 0.25 x) x)
0.2b	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
0.3b	(/ 0.09375 (pow x 4))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

870×	`times-frac`
804×	`add-sqr-sqrt`
668×	`*-un-lft-identity`
570×	`add-cube-cbrt`
544×	`prod-diff`
379×	`associate-+r+`
183×	`associate--l+`
124×	`pow1`
120×	`log-pow`
84×	`unpow-prod-down`
78×	`difference-of-squares`
62×	`distribute-lft-out--`
46×	`div-inv`
28×	`sqr-pow`
16×	`associate-/l*`
14×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`associate-/r*` `add-log-exp`
9×	`log-prod`
8×	`distribute-lft-out`
6×	`div-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `fma-def` `fma-neg` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `associate-+l+` `sum-log`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `flip3--` `flip3-+` `pow-exp` `flip--` `flip-+` `associate-/l/`

Counts

4 → 727

Calls

4 calls:

25.0ms	(- (log x) (/ (/ 0.25 x) x))
6.0ms	(/ (/ 0.25 x) x)
77.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
5.0ms	(/ 0.09375 (pow x 4))

series476.0ms

Counts

4 → 12

Calls

4 calls:

312.0ms	(- (log x) (/ (/ 0.25 x) x))
23.0ms	(/ (/ 0.25 x) x)
105.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
36.0ms	(/ 0.09375 (pow x 4))

simplify359.0ms

Algorithm

egg-herbie

Counts

739 → 739

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	2647	14534
1	5002	11801

prune2.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

47×	`*-un-lft-identity`
37×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`times-frac`
12×	`unpow-prod-down` `cube-prod` `associate-/r*`
11×	`associate-+r+`
10×	`add-exp-log`
9×	`prod-diff` `add-log-exp`
6×	`add-cbrt-cube`
5×	`pow1` `log-prod`
4×	`expm1-log1p-u` `cube-mult` `unpow3` `log1p-expm1-u` `distribute-lft-out` `sqr-pow`
3×	`fma-def` `div-exp` `associate-/l*`
2×	`log-div` `flip3-+` `sum-log` `flip-+` `distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `associate-+r-` `sub-neg` `frac-2neg` `diff-log` `rem-log-exp` `pow-exp` `clear-num` `log-pow` `fma-udef` `div-inv`

Counts

4 → 126

Calls

4 calls:

7.0ms	(+ x (- x (fma 0.5 (/ 1 x) (/ 0.125 (pow x 3)))))
1.0ms	(fma 0.5 (/ 1 x) (/ 0.125 (pow x 3)))
5.0ms	(log (+ x (- x (fma 0.5 (/ 1 x) (/ 0.125 (pow x 3))))))
9.0ms	(/ 0.125 (pow x 3))

series344.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ x (- x (fma 0.5 (/ 1 x) (/ 0.125 (pow x 3)))))
87.0ms	(fma 0.5 (/ 1 x) (/ 0.125 (pow x 3)))
168.0ms	(log (+ x (- x (fma 0.5 (/ 1 x) (/ 0.125 (pow x 3))))))
36.0ms	(/ 0.125 (pow x 3))

simplify62.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	447	911
1	2048	786
2	5001	786

prune293.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes12.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	9
1	15	9

end0.0ms

sample1.3s

Algorithm

intervals

Results

350.0ms	7606×	body	160	nan
340.0ms	16200×	body	80	nan
234.0ms	8000×	body	80	valid