Details

sample77.0ms

Algorithm

intervals

Results

23.0ms	45×	body	1280	valid
15.0ms	50×	body	640	valid
14.0ms	159×	body	80	valid
6.0ms	29×	body	320	valid
5.0ms	97×	body	80	nan
2.0ms	11×	body	160	valid

simplify116.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (9.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x y))
0.1b	(* x (log (/ x (+ x y))))
9.4b	(log (/ x (+ x y)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
54×	`log-prod`
48×	`times-frac`
40×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
18×	`distribute-rgt-in` `distribute-lft-in`
13×	`distribute-lft-out`
10×	`add-exp-log`
8×	`associate-/r/`
7×	`pow1` `add-cbrt-cube`
4×	`flip3-+` `associate-r` `associate-/r*` `flip-+` `div-inv`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `associate-/l*` `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 → 123

Calls

3 calls:

5.0ms	(/ x (+ x y))
11.0ms	(* x (log (/ x (+ x y))))
4.0ms	(log (/ x (+ x y)))

series171.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ x (+ x y))
78.0ms	(* x (log (/ x (+ x y))))
53.0ms	(log (/ x (+ x y)))

simplify115.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	302	874
1	1266	813
2	4974	783
3	5001	783

prune276.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
1.5b	(log (/ (cbrt x) (cbrt (+ x y))))
1.5b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

98×	`cbrt-prod`
96×	`log-prod`
88×	`*-un-lft-identity`
84×	`times-frac`
60×	`add-sqr-sqrt` `add-cube-cbrt`
14×	`distribute-lft-out`
10×	`add-exp-log`
8×	`cbrt-div`
6×	`pow1`
4×	`expm1-log1p-u` `flip3-+` `rem-log-exp` `associate-/r/` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `pow1/3` `div-exp` `log-pow` `div-inv`

Counts

4 → 154

Calls

4 calls:

2.0ms	(cbrt (+ x y))
2.0ms	(cbrt (+ x y))
6.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
6.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series405.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(cbrt (+ x y))
127.0ms	(cbrt (+ x y))
72.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
74.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify137.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 3 (122.0ms)

Iter	Nodes	Cost
0	362	1602
1	963	1550
2	4023	1518
3	5002	1508

prune722.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.6b	(cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))
1.5b	(log (/ (cbrt x) (cbrt (+ x y))))
13.6b	(log (/ (cbrt x) (* (cbrt (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (cbrt (+ x y))))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

120×	`cbrt-div`
84×	`log-prod`
53×	`cbrt-prod`
49×	`*-un-lft-identity`
48×	`times-frac`
35×	`add-sqr-sqrt` `add-cube-cbrt` `flip3-+` `flip-+`
32×	`frac-times`
28×	`associate-/r/`
16×	`associate-*l/`
13×	`add-exp-log`
10×	`associate-*r/`
7×	`distribute-lft-out`
6×	`pow1`
5×	`rem-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`div-exp`
2×	`log-div` `pow1/3` `log-pow` `div-inv`
1×	`prod-exp`

Counts

4 → 146

Calls

4 calls:

2.0ms	(cbrt (+ x y))
7.0ms	(cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))
6.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
14.0ms	(log (/ (cbrt x) (* (cbrt (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (cbrt (+ x y))))))

series540.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(cbrt (+ x y))
262.0ms	(cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))
75.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
71.0ms	(log (/ (cbrt x) (* (cbrt (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (cbrt (+ x y))))))

simplify56.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	732	2199
1	1641	2099
2	5002	2080

prune837.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))
1.5b	(log (/ (cbrt x) (cbrt (+ x y))))
3.9b	(log (cbrt (/ (cbrt x) (* (cbrt (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (cbrt (+ x y)))))))
3.9b	(log (cbrt (/ (cbrt x) (* (cbrt (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (cbrt (+ x y)))))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

216×	`cbrt-div`
126×	`log-prod`
124×	`cbrt-prod`
61×	`flip3-+` `flip-+`
60×	`frac-times`
54×	`times-frac` `associate-/r/`
51×	`*-un-lft-identity`
39×	`add-sqr-sqrt` `add-cube-cbrt`
30×	`associate-*l/`
18×	`associate-*r/`
9×	`add-exp-log`
7×	`pow1`
6×	`distribute-lft-out`
5×	`log-pow`
4×	`expm1-log1p-u` `rem-log-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-div` `pow1/3` `div-inv`
1×	`div-exp`

Counts

4 → 184

Calls

4 calls:

7.0ms	(cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))
10.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
11.0ms	(log (cbrt (/ (cbrt x) (* (cbrt (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (cbrt (+ x y)))))))
11.0ms	(log (cbrt (/ (cbrt x) (* (cbrt (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (cbrt (+ x y)))))))

series487.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(cbrt (* (cbrt (+ x y)) (cbrt (+ x y))))
75.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
70.0ms	(log (cbrt (/ (cbrt x) (* (cbrt (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (cbrt (+ x y)))))))
78.0ms	(log (cbrt (/ (cbrt x) (* (cbrt (* (cbrt (+ x y)) (cbrt (+ x y)))) (cbrt (cbrt (+ x y)))))))

simplify175.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 3 (139.0ms)

Iter	Nodes	Cost
0	681	3640
1	1338	3519
2	4600	3502
3	5002	3497

prune1.3s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.5b

regimes69.0ms

Accuracy

34.3% (3.0b remaining)

Error of 4.1b against oracle of 1.1b and baseline of 5.7b

bsearch130.0ms

Steps

Iters	Range		Point
8	2.5709113650304338e+95	6.729939417616486e+99	9.990890679532267e+98
7	0.010591324377185865	0.817620533678417	0.8053557845630321

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	51
1	46	51

end0.0ms

sample2.2s

Algorithm

intervals

Results

752.0ms	1506×	body	1280	valid
449.0ms	1459×	body	640	valid
363.0ms	4978×	body	80	valid
179.0ms	844×	body	320	valid
163.0ms	3175×	body	80	nan
61.0ms	412×	body	160	valid