Details

sample148.0ms

Algorithm

intervals

Results

39.0ms	47×	body	1280	valid
29.0ms	29×	body	320	valid
24.0ms	43×	body	640	valid
17.0ms	176×	body	80	valid
9.0ms	118×	body	80	nan
3.0ms	15×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	8	11
1	15	11
2	24	9
3	49	9
4	107	9
5	245	9
6	580	9
7	1850	9
done	5000	9

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp (* x (log (/ x (+ x y))))) x)
0.0b	(/ x (+ x y))
0.1b	(* x (log (/ x (+ x y))))
8.7b	(log (/ x (+ x y)))

rewrite185.0ms

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:

84.0ms	(/ (exp (* x (log (/ x (+ x y))))) x)
23.0ms	(/ x (+ x y))
28.0ms	(* x (log (/ x (+ x y))))
7.0ms	(log (/ x (+ x y)))

series494.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(/ (exp (* x (log (/ x (+ x y))))) x)
74.0ms	(/ x (+ x y))
126.0ms	(* x (log (/ x (+ x y))))
78.0ms	(log (/ x (+ x y)))

simplify3.2s

Counts

308 → 308

Iterations

Useful iterations: 3 (2.0s)

Iter	Nodes	Cost
0	478	5632
1	835	4771
2	1686	4591
3	4961	4500
done	5000	4500

prune885.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
3.9b	(log (/ (cbrt x) (cbrt (+ x y))))
3.9b	(log (/ (cbrt x) (cbrt (+ x y))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
16.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
13.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

series738.0ms

Counts

4 → 12

Calls

4 calls:

238.0ms	(cbrt x)
304.0ms	(cbrt x)
84.0ms	(log (/ (cbrt x) (cbrt (+ x y))))
111.0ms	(log (/ (cbrt x) (cbrt (+ x y))))

simplify1.9s

Counts

160 → 160

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	177	2306
1	321	2146
2	578	2060
3	1115	1986
4	2482	1982
done	5000	1976

prune651.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x y))
0.0b	(/ x (+ x y))
5.2b	(pow (/ x (+ x y)) x)
5.2b	(pow (/ x (+ x y)) x)

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

68×	`*-un-lft-identity`
48×	`times-frac`
40×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`unpow-prod-down`
14×	`add-exp-log` `distribute-lft-out`
8×	`associate-/r*` `associate-/r/` `add-cbrt-cube`
6×	`pow1` `pow-unpow` `associate-/l*`
4×	`expm1-log1p-u` `flip3-+` `div-exp` `pow-exp` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

4 → 140

Calls

4 calls:

19.0ms	(/ x (+ x y))
24.0ms	(/ x (+ x y))
14.0ms	(pow (/ x (+ x y)) x)
18.0ms	(pow (/ x (+ x y)) x)

series789.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ x (+ x y))
58.0ms	(/ x (+ x y))
352.0ms	(pow (/ x (+ x y)) x)
333.0ms	(pow (/ x (+ x y)) x)

simplify1.7s

Counts

152 → 152

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	133	1728
1	316	1616
2	781	1560
3	2157	1558
done	5001	1550

prune596.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite17.0ms

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` `associate-/l/`
1×	`pow1` `cbrt-undiv` `neg-sub0` `exp-neg` `expm1-log1p-u` `frac-2neg` `exp-diff` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 31

Calls

1 calls:

16.0ms

(/ (exp (- y)) x)

series24.0ms

Counts

1 → 3

Calls

1 calls:

24.0ms

(/ (exp (- y)) x)

simplify3.0s

Counts

34 → 34

Iterations

Useful iterations: 3 (237.0ms)

Iter	Nodes	Cost
0	66	311
1	120	300
2	293	280
3	709	278
4	2815	278
done	5002	278

prune74.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes60.0ms

Accuracy

94.3% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 5.8b

bsearch145.0ms

Steps

Iters	Range		Point
6	1.6549904719812824e-10	1.1362596833603348e-09	1.1158984721914147e-09
8	-1.1610098128388504e+53	-3.2818405371306287e+50	-4.12015628866316e+50

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	25	48
1	35	41
done	35	41

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.0s	1484×	body	1280	valid
595.0ms	1464×	body	640	valid
436.0ms	4912×	body	80	valid
261.0ms	798×	body	320	valid
207.0ms	3128×	body	80	nan
76.0ms	507×	body	160	valid