Details

sample63.0ms

Algorithm

intervals

Results

24.0ms	53×	body	1280	valid
13.0ms	52×	body	640	valid
6.0ms	132×	body	80	valid
5.0ms	35×	body	320	valid
3.0ms	89×	body	80	nan
2.0ms	15×	body	160	valid

simplify113.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (8.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	108	6
4	310	4
5	792	4
6	4192	4
7	5002	4

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (exp (* x (log (/ x (+ x y))))) x)
0.1b	(* x (log (/ x (+ x y))))
7.1b	(log (/ x (+ x y)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

249×	`times-frac`
203×	`*-un-lft-identity`
198×	`log-prod`
144×	`exp-sum`
139×	`add-sqr-sqrt`
137×	`add-cube-cbrt`
90×	`distribute-rgt-in` `distribute-lft-in`
39×	`associate-/l*`
33×	`distribute-lft-out`
22×	`associate-/r/`
12×	`div-inv`
11×	`flip3-+` `flip-+`
9×	`add-exp-log`
7×	`pow1` `add-cbrt-cube`
4×	`associate-r`
3×	`expm1-log1p-u` `associate-l` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`div-exp` `rem-log-exp` `log-pow`
1×	`cbrt-undiv` `log-div` `frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 261

Calls

3 calls:

34.0ms	(/ (exp (* x (log (/ x (+ x y))))) x)
11.0ms	(* x (log (/ x (+ x y))))
4.0ms	(log (/ x (+ x y)))

series271.0ms

Counts

3 → 9

Calls

3 calls:

138.0ms	(/ (exp (* x (log (/ x (+ x y))))) x)
84.0ms	(* x (log (/ x (+ x y))))
50.0ms	(log (/ x (+ x y)))

simplify77.0ms

Algorithm

egg-herbie

Counts

270 → 270

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	795	2914
1	2455	2488
2	5002	2475

prune516.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
2.4b	(log (/ (cbrt x) (cbrt (+ x y))))
2.6b	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

61×	`log-prod`
51×	`cbrt-prod`
46×	`*-un-lft-identity`
43×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-exp-log`
14×	`cbrt-div`
10×	`associate-/r/`
7×	`flip3-+` `rem-log-exp` `flip-+`
6×	`pow1` `distribute-lft-out`
5×	`div-exp`
4×	`expm1-log1p-u` `frac-times` `prod-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `pow1/3` `associate-r/` `associate-l/` `log-pow` `div-inv`

Counts

4 → 116

Calls

4 calls:

0.0ms	(cbrt x)
1.0ms	(cbrt x)
6.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
12.0ms	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

series533.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt x)
192.0ms	(cbrt x)
70.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
89.0ms	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

simplify90.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 3 (79.0ms)

Iter	Nodes	Cost
0	449	1200
1	1120	1128
2	3610	1084
3	5002	1070

prune716.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(/ (exp (* -1 y)) x)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`associate-/r` `add-cbrt-cube` `associate-/l`
2×	`add-exp-log`
1×	`pow1` `cbrt-undiv` `exp-neg` `expm1-log1p-u` `frac-2neg` `mul-1-neg` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`

Counts

1 → 30

Calls

1 calls:

3.0ms

(/ (exp (* -1 y)) x)

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

(/ (exp (* -1 y)) x)

simplify55.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	118	194
1	313	179
2	1512	177
3	5001	177

prune64.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (* x (exp y)))
0.0b	(* x (exp y))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`pow1`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`div-exp` `prod-exp`
3×	`times-frac` `associate-r` `associate-l` `associate-/l*`
2×	`cbrt-undiv` `expm1-log1p-u` `rec-exp` `pow-flip` `1-exp` `pow-prod-down` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
1×	`frac-2neg` `clear-num` `associate-/r` `-commutative` `div-inv` `inv-pow` `unswap-sqr`

Counts

2 → 50

Calls

2 calls:

7.0ms	(/ 1 (* x (exp y)))
5.0ms	(* x (exp y))

series46.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(/ 1 (* x (exp y)))
22.0ms	(* x (exp y))

simplify96.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	179	216
1	804	181
2	4323	175
3	5002	175

prune78.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes58.0ms

Accuracy

93.8% (0.4b remaining)

Error of 1.4b against oracle of 1.0b and baseline of 7.1b

bsearch98.0ms

Steps

Iters	Range		Point
8	5.632723023752881e-15	8.639792360287736e-11	8.481780906699795e-11
8	-3.0637062240839107e+58	-2.510041587470139e+55	-3.0471893695682866e+55

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	26
1	39	26

end0.0ms

sample1.7s

Algorithm

intervals

Results

657.0ms	1506×	body	1280	valid
371.0ms	1481×	body	640	valid
199.0ms	4776×	body	80	valid
149.0ms	895×	body	320	valid
89.0ms	3025×	body	80	nan
44.0ms	443×	body	160	valid