Details

sample65.0ms

Algorithm

intervals

Results

32.0ms	75×	body	1280	valid
11.0ms	47×	body	640	valid
9.0ms	32×	body	2560	valid
3.0ms	19×	body	320	valid
2.0ms	69×	body	80	valid
1.0ms	14×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.6b

localize6.0ms

Local error

Found 3 expressions with local error:

0.6b	(+ x (sqrt (+ (* x x) 1.0)))
4.0b	(log (+ x (sqrt (+ (* x x) 1.0))))
15.9b	(sqrt (+ (* x x) 1.0))

rewrite27.0ms

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:

12.0ms	(+ x (sqrt (+ (* x x) 1.0)))
9.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
5.0ms	(sqrt (+ (* x x) 1.0))

series438.0ms

Counts

3 → 9

Calls

3 calls:

227.0ms	(+ x (sqrt (+ (* x x) 1.0)))
169.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
41.0ms	(sqrt (+ (* x x) 1.0))

simplify32.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (27.0ms)

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

prune173.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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)))

rewrite236.0ms

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:

144.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
73.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series290.0ms

Counts

2 → 6

Calls

2 calls:

155.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
135.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify114.0ms

Algorithm

egg-herbie

Counts

306 → 306

Iterations

Useful iterations: 2 (91.0ms)

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

prune465.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot x (sqrt 1.0))
0.6b	(+ x (hypot x (sqrt 1.0)))
4.0b	(log (+ x (hypot x (sqrt 1.0))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 44

Calls

3 calls:

0.0ms	(hypot x (sqrt 1.0))
3.0ms	(+ x (hypot x (sqrt 1.0)))
3.0ms	(log (+ x (hypot x (sqrt 1.0))))

series512.0ms

Counts

3 → 9

Calls

3 calls:

103.0ms	(hypot x (sqrt 1.0))
126.0ms	(+ x (hypot x (sqrt 1.0)))
283.0ms	(log (+ x (hypot x (sqrt 1.0))))

simplify86.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	268	349
1	886	321
2	3696	305
3	5001	303

prune135.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ x (hypot x (sqrt 1.0)))
0.6b	(+ x (hypot x (sqrt 1.0)))
4.0b	(log (sqrt (+ x (hypot x (sqrt 1.0)))))
4.0b	(log (sqrt (+ x (hypot x (sqrt 1.0)))))

rewrite14.0ms

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

series862.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(+ x (hypot x (sqrt 1.0)))
126.0ms	(+ x (hypot x (sqrt 1.0)))
303.0ms	(log (sqrt (+ x (hypot x (sqrt 1.0)))))
299.0ms	(log (sqrt (+ x (hypot x (sqrt 1.0)))))

simplify106.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 3 (98.0ms)

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

prune271.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes30.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 32.9b

bsearch86.0ms

Steps

Iters	Range		Point
10	5.939545479408298e-16	0.006665254470786589	0.0011585336522522951
9	-14674.600957416102	-0.00012459925560949148	-1.0138774176732859

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	31
1	46	31

end0.0ms

sample1.9s

Algorithm

intervals

Results

933.0ms	2293×	body	1280	valid
380.0ms	1600×	body	640	valid
224.0ms	818×	body	2560	valid
103.0ms	758×	body	320	valid
67.0ms	2143×	body	80	valid
30.0ms	388×	body	160	valid