Details

sample65.0ms

Algorithm

intervals

Results

31.0ms	66×	body	1280	valid
11.0ms	47×	body	640	valid
8.0ms	30×	body	2560	valid
3.0ms	24×	body	320	valid
3.0ms	76×	body	80	valid
1.0ms	13×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	5
1	10	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.3b	(+ x (sqrt (+ (* x x) 1.0)))
2.6b	(log (+ x (sqrt (+ (* x x) 1.0))))
17.7b	(sqrt (+ (* x x) 1.0))

rewrite17.0ms

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`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow` `hypot-def`

Counts

3 → 52

Calls

3 calls:

6.0ms	(+ x (sqrt (+ (* x x) 1.0)))
6.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))

series259.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(+ x (sqrt (+ (* x x) 1.0)))
162.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
41.0ms	(sqrt (+ (* x x) 1.0))

simplify35.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	331	422
1	1127	385
2	5002	366

prune182.0ms

Filtered

61 candidates to 55 candidates (90.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.1b	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
220×	`associate-r`
184×	`add-sqr-sqrt`
140×	`unpow-prod-down` `cube-prod`
126×	`*-un-lft-identity`
120×	`add-cube-cbrt`
80×	`sqrt-prod`
40×	`sqr-pow`
30×	`cube-mult` `unpow3`
25×	`add-exp-log` `unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
7×	`add-cbrt-cube`
6×	`pow1` `pow-to-exp` `pow-exp` `add-log-exp`
5×	`fma-neg` `prod-diff`
4×	`distribute-lft-out`
3×	`associate-r/` `associate-l*`
2×	`expm1-log1p-u` `diff-log` `log-pow` `frac-sub` `cbrt-unprod` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `flip3--` `flip3-+` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `flip--` `flip-+` `div-inv`

Counts

2 → 300

Calls

2 calls:

14.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
55.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series288.0ms

Counts

2 → 6

Calls

2 calls:

154.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
134.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify119.0ms

Algorithm

egg-herbie

Counts

306 → 306

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	888	2345
1	4813	1909
2	5001	1888

prune438.0ms

Filtered

306 candidates to 121 candidates (39.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.3b	(+ x (hypot x (sqrt 1.0)))
2.6b	(log (+ x (hypot x (sqrt 1.0))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity`
4×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod` `add-log-exp`
3×	`pow1` `add-exp-log` `fma-def`
2×	`expm1-log1p-u` `log-div` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `rem-log-exp` `sum-log` `log-pow`

Counts

2 → 34

Calls

2 calls:

3.0ms	(+ x (hypot x (sqrt 1.0)))
3.0ms	(log (+ x (hypot x (sqrt 1.0))))

series404.0ms

Counts

2 → 6

Calls

2 calls:

123.0ms	(+ x (hypot x (sqrt 1.0)))
281.0ms	(log (+ x (hypot x (sqrt 1.0))))

simplify77.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	238	284
1	786	255
2	3259	247
3	5001	245

prune105.0ms

Filtered

40 candidates to 33 candidates (82.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ x (hypot x (sqrt 1.0)))
0.3b	(+ x (hypot x (sqrt 1.0)))
2.6b	(log (sqrt (+ x (hypot x (sqrt 1.0)))))
2.6b	(log (sqrt (+ x (hypot x (sqrt 1.0)))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
14×	`log-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`pow1` `sqrt-prod` `add-log-exp`
6×	`add-exp-log` `fma-def` `log-pow`
4×	`expm1-log1p-u` `log-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`+-commutative` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log`

Counts

4 → 78

Calls

4 calls:

3.0ms	(+ x (hypot x (sqrt 1.0)))
3.0ms	(+ x (hypot x (sqrt 1.0)))
4.0ms	(log (sqrt (+ x (hypot x (sqrt 1.0)))))
4.0ms	(log (sqrt (+ x (hypot x (sqrt 1.0)))))

series836.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(+ x (hypot x (sqrt 1.0)))
124.0ms	(+ x (hypot x (sqrt 1.0)))
292.0ms	(log (sqrt (+ x (hypot x (sqrt 1.0)))))
289.0ms	(log (sqrt (+ x (hypot x (sqrt 1.0)))))

simplify107.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	285	724
1	883	658
2	3992	630
3	5001	624

prune270.0ms

Filtered

90 candidates to 76 candidates (84.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes41.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 32.1b

bsearch78.0ms

Steps

Iters	Range		Point
9	2.7581197155588776e-09	0.007472435306926121	0.0010210458391825244
8	-2693.2368339428763	-0.10280128843953673	-0.9985994311848064

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	35
1	54	35
2	57	35
3	57	35

end0.0ms

sample2.0s

Algorithm

intervals

Results

974.0ms	2265×	body	1280	valid
398.0ms	1595×	body	640	valid
224.0ms	796×	body	2560	valid
110.0ms	755×	body	320	valid
80.0ms	2186×	body	80	valid
35.0ms	403×	body	160	valid