Details

sample62.0ms

Algorithm

intervals

Results

27.0ms	69×	body	1280	valid
12.0ms	50×	body	640	valid
6.0ms	21×	body	2560	valid
3.0ms	26×	body	320	valid
3.0ms	68×	body	80	valid
2.0ms	22×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	5
1	10	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.7b

localize10.0ms

Local error

Found 3 expressions with local error:

1.0b	(+ x (sqrt (+ (* x x) 1.0)))
4.3b	(log (+ x (sqrt (+ (* x x) 1.0))))
14.0b	(sqrt (+ (* x x) 1.0))

rewrite42.0ms

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:

16.0ms	(+ x (sqrt (+ (* x x) 1.0)))
16.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
9.0ms	(sqrt (+ (* x x) 1.0))

series265.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(+ x (sqrt (+ (* x x) 1.0)))
169.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
43.0ms	(sqrt (+ (* x x) 1.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (30.0ms)

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

prune259.0ms

Pruning

5 alts after pruning (5 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)))

rewrite287.0ms

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:

187.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
81.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series278.0ms

Counts

2 → 6

Calls

2 calls:

143.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
136.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify123.0ms

Algorithm

egg-herbie

Counts

306 → 306

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	888	2291
1	4768	1819
2	5001	1795

prune585.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot x (sqrt 1.0))
1.0b	(+ (hypot x (sqrt 1.0)) x)
4.3b	(log (* 1 (+ (hypot x (sqrt 1.0)) x)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-exp-log`
6×	`pow1` `*-un-lft-identity`
5×	`add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt`
3×	`expm1-log1p-u` `fma-def` `rem-log-exp` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `flip3-+` `associate-*r/` `prod-exp` `log-pow` `flip-+`
1×	`+-commutative` `log-prod` `hypot-udef` `1-exp` `pow-prod-down` `sum-log` `distribute-lft-out`

Counts

3 → 44

Calls

3 calls:

0.0ms	(hypot x (sqrt 1.0))
5.0ms	(+ (hypot x (sqrt 1.0)) x)
13.0ms	(log (* 1 (+ (hypot x (sqrt 1.0)) x)))

series485.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(hypot x (sqrt 1.0))
122.0ms	(+ (hypot x (sqrt 1.0)) x)
269.0ms	(log (* 1 (+ (hypot x (sqrt 1.0)) x)))

simplify38.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	288	336
1	1100	310
2	5002	294

prune187.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (hypot x (sqrt 1.0)) x)
4.3b	(log (* 1 (+ (hypot x (sqrt 1.0)) x)))
4.3b	(log (* 1 (+ (hypot x (sqrt 1.0)) x)))
4.3b	(log (* 1 (+ (hypot x (sqrt 1.0)) x)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log`
13×	`pow1`
9×	`rem-log-exp`
7×	`*-un-lft-identity`
6×	`log-div` `associate-*r/` `prod-exp` `log-pow` `add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
3×	`log-prod` `fma-def` `1-exp` `pow-prod-down`
1×	`+-commutative` `sum-log` `distribute-lft-out`

Counts

4 → 68

Calls

4 calls:

5.0ms	(+ (hypot x (sqrt 1.0)) x)
9.0ms	(log (* 1 (+ (hypot x (sqrt 1.0)) x)))
9.0ms	(log (* 1 (+ (hypot x (sqrt 1.0)) x)))
9.0ms	(log (* 1 (+ (hypot x (sqrt 1.0)) x)))

series941.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(+ (hypot x (sqrt 1.0)) x)
270.0ms	(log (* 1 (+ (hypot x (sqrt 1.0)) x)))
271.0ms	(log (* 1 (+ (hypot x (sqrt 1.0)) x)))
275.0ms	(log (* 1 (+ (hypot x (sqrt 1.0)) x)))

simplify128.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (122.0ms)

Iter	Nodes	Cost
0	258	585
1	1000	522
2	4895	507
3	5001	506

prune548.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes46.0ms

Accuracy

99.6% (0.1b remaining)

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

bsearch97.0ms

Steps

Iters	Range		Point
7	5.9790464235888496e-05	0.007285382865895221	0.00086075359748218
10	-569.2304264003914	-7.772245281701499e-10	-1.0022090002759816

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	32
1	63	32
2	66	32
3	66	32

end0.0ms

sample2.0s

Algorithm

intervals

Results

975.0ms	2287×	body	1280	valid
411.0ms	1619×	body	640	valid
253.0ms	842×	body	2560	valid
121.0ms	794×	body	320	valid
73.0ms	2098×	body	80	valid
34.0ms	360×	body	160	valid