Details

sample50.0ms

Algorithm

intervals

Results

11.0ms	22×	body	1280	valid
10.0ms	213×	body	80	valid
7.0ms	27×	body	640	valid
4.0ms	20×	body	320	valid
3.0ms	82×	body	80	nan
1.0ms	10×	body	160	valid

simplify117.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 6 (30.0ms)

Iter	Nodes	Cost
0	18	7
1	27	7
2	54	7
3	111	7
4	314	7
5	801	7
6	4217	6
7	5001	6

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp (* y (log (/ y (+ z y))))) y)
0.0b	(/ y (+ z y))
0.1b	(* y (log (/ y (+ z y))))
9.4b	(log (/ y (+ z y)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

261×	`times-frac`
221×	`*-un-lft-identity`
198×	`log-prod`
149×	`add-sqr-sqrt`
147×	`add-cube-cbrt`
144×	`exp-sum`
90×	`distribute-rgt-in` `distribute-lft-in`
42×	`associate-/l*`
37×	`distribute-lft-out`
24×	`associate-/r/`
13×	`div-inv`
12×	`add-exp-log` `flip3-+` `flip-+`
10×	`add-cbrt-cube`
8×	`pow1`
7×	`associate-/r*`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`div-exp` `associate-l`
2×	`cbrt-undiv` `frac-2neg` `rem-log-exp` `clear-num` `log-pow`
1×	`log-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 296

Calls

4 calls:

33.0ms	(/ (exp (* y (log (/ y (+ z y))))) y)
5.0ms	(/ y (+ z y))
13.0ms	(* y (log (/ y (+ z y))))
4.0ms	(log (/ y (+ z y)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (exp (* y (log (/ y (+ z y))))) y)
40.0ms	(/ y (+ z y))
78.0ms	(* y (log (/ y (+ z y))))
55.0ms	(log (/ y (+ z y)))

simplify89.0ms

Algorithm

egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	836	3073
1	2886	2638
2	5002	2622

prune635.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
1.3b	(pow (/ (cbrt y) (cbrt (+ z y))) y)
5.0b	(log (/ (* (cbrt y) (cbrt y)) (* (cbrt (+ z y)) (cbrt (+ z y)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

0.0ms	(cbrt y)
0.0ms	(cbrt y)
12.0ms	(pow (/ (cbrt y) (cbrt (+ z y))) y)
11.0ms	(log (/ (* (cbrt y) (cbrt y)) (* (cbrt (+ z y)) (cbrt (+ z y)))))

series709.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt y)
180.0ms	(cbrt y)
260.0ms	(pow (/ (cbrt y) (cbrt (+ z y))) y)
83.0ms	(log (/ (* (cbrt y) (cbrt y)) (* (cbrt (+ z y)) (cbrt (+ z y)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	605	1262
1	1937	1200
2	5001	1144

prune540.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
1.3b	(pow (/ (cbrt y) (cbrt (+ z y))) y)
4.3b	(- (log (* (cbrt y) (cbrt y))) (log (* (cbrt (+ z y)) (cbrt (+ z y)))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

255×	`log-pow`
239×	`pow1`
164×	`pow1/3`
144×	`prod-diff`
77×	`*-un-lft-identity`
61×	`add-sqr-sqrt`
59×	`add-cube-cbrt`
58×	`pow-prod-down`
56×	`pow-prod-up`
54×	`pow-sqr`
51×	`cbrt-prod`
48×	`unpow-prod-down`
42×	`times-frac`
29×	`pow-plus`
27×	`pow2`
18×	`distribute-lft-out--`
14×	`cbrt-div`
12×	`fma-neg`
8×	`log-div` `associate--r-`
7×	`add-exp-log` `flip3-+` `flip-+`
6×	`distribute-lft-out`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`log-prod` `associate-r/` `associate-l/` `pow-exp` `associate-/r/`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `div-exp` `associate--l+` `flip--` `div-inv` `associate--r+` `difference-of-squares` `sqr-pow`

Counts

4 → 290

Calls

4 calls:

0.0ms	(cbrt y)
0.0ms	(cbrt y)
12.0ms	(pow (/ (cbrt y) (cbrt (+ z y))) y)
62.0ms	(- (log (* (cbrt y) (cbrt y))) (log (* (cbrt (+ z y)) (cbrt (+ z y)))))

series800.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(cbrt y)
182.0ms	(cbrt y)
266.0ms	(pow (/ (cbrt y) (cbrt (+ z y))) y)
157.0ms	(- (log (* (cbrt y) (cbrt y))) (log (* (cbrt (+ z y)) (cbrt (+ z y)))))

simplify97.0ms

Algorithm

egg-herbie

Counts

302 → 302

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	890	5317
1	2779	3310
2	5001	3264

prune701.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
1.3b	(pow (sqrt (/ (cbrt y) (cbrt (+ z y)))) y)
1.3b	(pow (sqrt (/ (cbrt y) (cbrt (+ z y)))) y)
4.3b	(- (log (* (cbrt y) (cbrt y))) (log (* (cbrt (+ z y)) (cbrt (+ z y)))))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

255×	`log-pow`
242×	`pow1`
163×	`pow1/3`
144×	`prod-diff`
118×	`*-un-lft-identity`
102×	`unpow-prod-down`
96×	`sqrt-prod`
93×	`cbrt-prod`
90×	`add-sqr-sqrt`
88×	`add-cube-cbrt`
84×	`times-frac`
58×	`pow-prod-down`
56×	`pow-prod-up`
54×	`pow-sqr`
29×	`pow-plus`
27×	`pow2`
18×	`distribute-lft-out--`
16×	`cbrt-div`
12×	`fma-neg` `distribute-lft-out`
8×	`log-div` `flip3-+` `flip-+` `associate--r-`
6×	`add-exp-log` `pow-unpow` `pow-pow`
4×	`expm1-log1p-u` `frac-times` `associate-/r/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `log-prod` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `pow-exp` `sqrt-pow2` `div-inv` `sqr-pow`
1×	`sub-neg` `flip3--` `diff-log` `associate--l+` `flip--` `associate--r+` `difference-of-squares`

Counts

4 → 352

Calls

4 calls:

1.0ms	(cbrt y)
16.0ms	(pow (sqrt (/ (cbrt y) (cbrt (+ z y)))) y)
16.0ms	(pow (sqrt (/ (cbrt y) (cbrt (+ z y)))) y)
62.0ms	(- (log (* (cbrt y) (cbrt y))) (log (* (cbrt (+ z y)) (cbrt (+ z y)))))

series897.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt y)
275.0ms	(pow (sqrt (/ (cbrt y) (cbrt (+ z y)))) y)
280.0ms	(pow (sqrt (/ (cbrt y) (cbrt (+ z y)))) y)
156.0ms	(- (log (* (cbrt y) (cbrt y))) (log (* (cbrt (+ z y)) (cbrt (+ z y)))))

simplify118.0ms

Algorithm

egg-herbie

Counts

364 → 364

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	966	6362
1	2894	4315
2	5003	4235

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes67.0ms

Accuracy

39.9% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 1.1b

bsearch77.0ms

Steps

Iters	Range		Point
8	-3.9037330911820875e+110	-1.70681033519655e+106	-9.228583832351033e+106

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	34
1	38	34

end0.0ms

sample1.5s

Algorithm

intervals

Results

348.0ms	756×	body	1280	valid
328.0ms	6536×	body	80	valid
254.0ms	935×	body	640	valid
105.0ms	589×	body	320	valid
98.0ms	2917×	body	80	nan
33.0ms	296×	body	160	valid