Details

sample36.0ms

Algorithm

intervals

Results

7.0ms	179×	body	80	valid
6.0ms	28×	body	1280	valid
3.0ms	23×	body	640	valid
3.0ms	104×	body	80	nan
2.0ms	14×	body	1280	nan
2.0ms	15×	body	640	nan
1.0ms	14×	body	320	valid
1.0ms	12×	body	160	valid
0.0ms	6×	body	160	nan
0.0ms	3×	body	320	nan

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	29	6
2	41	6
3	60	6
4	78	6
5	94	6
6	109	6
7	139	6
8	214	6
9	279	6
10	279	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.8b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (- 1.0 y))
0.0b	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
2.7b	(log (- 1.0 (/ (- x y) (- 1.0 y))))
3.1b	(- 1.0 (/ (- x y) (- 1.0 y)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
28×	`times-frac`
19×	`difference-of-squares`
18×	`add-cube-cbrt`
17×	`distribute-lft-out--`
12×	`log-prod`
7×	`add-exp-log` `add-log-exp`
6×	`pow1` `flip3--` `add-cbrt-cube` `flip--` `associate--r+`
5×	`associate-/r` `associate-/l`
4×	`log-div`
3×	`associate--r-`
2×	`sub-neg` `diff-log` `div-sub` `associate-/r/` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `div-inv`

Counts

4 → 108

Calls

4 calls:

10.0ms	(/ (- x y) (- 1.0 y))
23.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
22.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
20.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (- x y) (- 1.0 y))
95.0ms	(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
87.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))
55.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))

simplify50.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	488	942
1	1388	894
2	5001	876

prune289.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (log (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
0.1b	(* (- x y) (/ 1 (- 1.0 y)))
2.7b	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
6.2b	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
21×	`associate-r`
17×	`times-frac`
16×	`add-cube-cbrt`
14×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
7×	`flip3--` `flip--` `add-log-exp`
6×	`log-prod` `distribute-lft-out--`
5×	`associate-l` `difference-of-squares`
4×	`log-div` `prod-exp`
3×	`associate--r+` `unswap-sqr`
2×	`frac-times` `sub-neg` `diff-log` `div-exp` `associate-*l/` `associate-/r/` `log-pow` `cbrt-unprod` `associate--r-`
1×	`cbrt-undiv` `rec-exp` `1-exp` `associate-r/` `rem-log-exp` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 96

Calls

4 calls:

4.0ms	(- 1.0 (log (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
24.0ms	(* (- x y) (/ 1 (- 1.0 y)))
2.0ms	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
2.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

series282.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- 1.0 (log (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
43.0ms	(* (- x y) (/ 1 (- 1.0 y)))
88.0ms	(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
55.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

simplify59.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	516	863
1	2086	789
2	5003	762

prune250.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ (exp 1.0) (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
0.1b	(* (- x y) (/ 1 (- 1.0 y)))
0.2b	(/ (exp 1.0) (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
6.2b	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
35×	`times-frac`
29×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
15×	`log-prod`
11×	`add-cbrt-cube`
7×	`pow1`
6×	`flip3--` `associate-/r/` `flip--` `add-log-exp`
5×	`associate-l`
4×	`div-exp` `prod-exp` `distribute-lft-out--` `difference-of-squares`
3×	`associate-/r` `div-inv` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rem-log-exp` `associate-*l/` `cbrt-unprod`
1×	`sub-neg` `log-div` `rec-exp` `frac-2neg` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `clear-num` `log-pow` `un-div-inv` `-commutative`

Counts

4 → 117

Calls

4 calls:

3.0ms	(log (/ (exp 1.0) (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
24.0ms	(* (- x y) (/ 1 (- 1.0 y)))
5.0ms	(/ (exp 1.0) (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
5.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

series382.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(log (/ (exp 1.0) (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
42.0ms	(* (- x y) (/ 1 (- 1.0 y)))
128.0ms	(/ (exp 1.0) (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))
57.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

simplify72.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	611	1242
1	2587	1124
2	5001	1099

prune336.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (exp 1.0) (sqrt (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
2.7b	(log (/ 1 (sqrt (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))))
6.2b	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))
6.2b	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
32×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`log-prod`
21×	`sqrt-prod`
10×	`add-exp-log`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-/r*` `add-cbrt-cube`
5×	`log-pow`
4×	`flip3--` `sqrt-div` `rem-log-exp` `associate-/r/` `flip--`
3×	`pow-flip` `div-exp` `associate-/l*`
2×	`sub-neg` `diff-log` `div-inv`
1×	`cbrt-undiv` `log-div` `rec-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `log-rec` `clear-num` `inv-pow`

Counts

4 → 107

Calls

4 calls:

6.0ms	(/ (exp 1.0) (sqrt (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
4.0ms	(log (/ 1 (sqrt (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))))
2.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))
2.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

series474.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(/ (exp 1.0) (sqrt (- 1.0 (* (- x y) (/ 1 (- 1.0 y))))))
167.0ms	(log (/ 1 (sqrt (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))))
51.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))
56.0ms	(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))

simplify60.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	491	1544
1	1608	1427
2	5001	1325

prune536.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes58.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 18.1b

bsearch150.0ms

Steps

Iters	Range		Point
11	9.143643357499823e-08	2.0559595175552502e+22	24790650.313024804
8	-64880754058.88788	-1357526.7243520434	-119577009.99898484

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	28
1	41	28

end0.0ms

sample1.0s

Algorithm

intervals

Results

225.0ms	5665×	body	80	valid
166.0ms	845×	body	1280	valid
106.0ms	3700×	body	80	nan
106.0ms	771×	body	640	valid
57.0ms	360×	body	1280	nan
47.0ms	449×	body	320	valid
45.0ms	386×	body	640	nan
18.0ms	270×	body	160	valid
17.0ms	202×	body	320	nan
6.0ms	113×	body	160	nan