Details

sample122.0ms

Algorithm

intervals

Results

49.0ms	63×	body	1280	valid
21.0ms	44×	body	640	valid
12.0ms	148×	body	80	valid
7.0ms	24×	body	320	valid
6.0ms	91×	body	80	nan
2.0ms	12×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	8	11
1	15	11
2	24	9
3	51	9
4	148	9
5	485	9
6	1979	9
done	5000	9

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.0b

localize28.0ms

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))))
7.7b	(log (/ x (+ x y)))

rewrite535.0ms

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×	`associate-r` `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 → 288

Calls

4 calls:

458.0ms	(/ (exp (* x (log (/ x (+ x y))))) x)
17.0ms	(/ x (+ x y))
28.0ms	(* x (log (/ x (+ x y))))
9.0ms	(log (/ x (+ x y)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(/ (exp (* x (log (/ x (+ x y))))) x)
53.0ms	(/ x (+ x y))
124.0ms	(* x (log (/ x (+ x y))))
74.0ms	(log (/ x (+ x y)))

simplify2.2s

Counts

300 → 300

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	470	5564
1	893	5032
2	3190	4546
done	5002	4544

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
3.8b	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
17×	`add-exp-log`
14×	`*-un-lft-identity`
13×	`log-prod`
12×	`cbrt-prod`
9×	`flip3-+` `flip-+`
8×	`add-sqr-sqrt` `add-cube-cbrt` `associate-/r/`
5×	`pow1` `rem-log-exp`
4×	`frac-times` `div-exp` `prod-exp` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3` `distribute-lft-out`
2×	`associate-r/` `associate-l/`
1×	`log-div` `times-frac` `log-pow` `div-inv`

Counts

4 → 69

Calls

4 calls:

4.0ms	(cbrt (+ x y))
4.0ms	(cbrt (+ x y))
6.0ms	(cbrt (+ x y))
40.0ms	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

series647.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(cbrt (+ x y))
171.0ms	(cbrt (+ x y))
177.0ms	(cbrt (+ x y))
123.0ms	(log (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))))

simplify924.0ms

Counts

81 → 81

Iterations

Useful iterations: done (922.0ms)

Iter	Nodes	Cost
0	122	1119
1	271	1074
2	699	935
3	2109	866
done	5002	854

prune621.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x y))
0.5b	(cbrt (+ x y))
2.1b	(log (fabs (/ (cbrt x) (cbrt (+ x y)))))
2.1b	(log (fabs (/ (cbrt x) (cbrt (+ x y)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
8×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt`
6×	`pow1` `add-exp-log` `log-prod`
4×	`cbrt-div` `add-cbrt-cube` `add-log-exp`
2×	`flip3-+` `pow1/3` `rem-log-exp` `log-pow` `flip-+` `distribute-lft-out`

Counts

4 → 52

Calls

4 calls:

8.0ms	(cbrt (+ x y))
8.0ms	(cbrt (+ x y))
10.0ms	(log (fabs (/ (cbrt x) (cbrt (+ x y)))))
2.0ms	(log (fabs (/ (cbrt x) (cbrt (+ x y)))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(cbrt (+ x y))
183.0ms	(cbrt (+ x y))
27.0ms	(log (fabs (/ (cbrt x) (cbrt (+ x y)))))
41.0ms	(log (fabs (/ (cbrt x) (cbrt (+ x y)))))

simplify889.0ms

Counts

64 → 64

Iterations

Useful iterations: done (887.0ms)

Iter	Nodes	Cost
0	79	716
1	155	686
2	425	618
3	1506	612
done	5001	608

prune485.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 1 expressions with local error:

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

rewrite26.0ms

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` `frac-2neg` `exp-diff` `div-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

24.0ms

(/ (exp (- y)) x)

series35.0ms

Counts

1 → 3

Calls

1 calls:

35.0ms

(/ (exp (- y)) x)

simplify3.1s

Counts

32 → 32

Iterations

Useful iterations: 3 (703.0ms)

Iter	Nodes	Cost
0	64	299
1	125	289
2	488	271
3	3657	267
done	5001	267

prune91.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes115.0ms

Accuracy

93.4% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 5.4b

bsearch113.0ms

Steps

Iters	Range		Point
7	1.899433490407338e-14	3.541339979661634e-13	3.5038509428931215e-13
8	-9.93160793826635e+68	-5.0548110587350964e+64	-5.1279911066425243e+64

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	53
1	32	53
done	32	53

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.3s	1512×	body	1280	valid
660.0ms	3069×	body	80	nan
614.0ms	1414×	body	640	valid
384.0ms	4962×	body	80	valid
250.0ms	850×	body	320	valid
71.0ms	430×	body	160	valid