Details

sample94.0ms

Algorithm

intervals

Results

28.0ms	48×	body	1280	valid
17.0ms	46×	body	640	valid
13.0ms	91×	body	80	nan
9.0ms	142×	body	80	valid
7.0ms	29×	body	320	valid
3.0ms	19×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (pow (/ x (+ x y)) x) x)
0.0b	(/ x (+ x y))
6.8b	(pow (/ x (+ x y)) x)

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
118×	`*-un-lft-identity`
90×	`unpow-prod-down`
80×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`associate-/l*`
19×	`distribute-lft-out`
16×	`add-exp-log`
12×	`associate-/r/`
7×	`div-exp` `associate-/r*` `add-cbrt-cube` `div-inv`
6×	`flip3-+` `flip-+`
5×	`sqr-pow`
4×	`pow1` `pow-exp`
3×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `clear-num`
1×	`pow-pow`

Counts

3 → 178

Calls

3 calls:

58.0ms	(/ (pow (/ x (+ x y)) x) x)
11.0ms	(/ x (+ x y))
23.0ms	(pow (/ x (+ x y)) x)

series600.0ms

Counts

3 → 9

Calls

3 calls:

200.0ms	(/ (pow (/ x (+ x y)) x) x)
63.0ms	(/ x (+ x y))
336.0ms	(pow (/ x (+ x y)) x)

simplify1.5s

Counts

187 → 187

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	282	2929
1	545	2745
2	1552	2688
done	5000	2684

prune585.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite19.0ms

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:

18.0ms

(/ (exp (- y)) x)

series31.0ms

Counts

1 → 3

Calls

1 calls:

31.0ms

(/ (exp (- y)) x)

simplify3.0s

Counts

34 → 34

Iterations

Useful iterations: 3 (231.0ms)

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

prune153.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
23×	`sqrt-prod`
22×	`sqrt-pow1` `times-frac` `associate-r`
20×	`exp-prod`
8×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
7×	`pow1`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `associate-l` `unswap-sqr`
4×	`neg-sub0` `exp-neg` `exp-diff`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `neg-mul-1` `rem-sqrt-square` `pow1/2` `associate-*l/` `prod-exp` `cbrt-unprod`
1×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv`

Counts

3 → 108

Calls

3 calls:

7.0ms	(sqrt (exp (- y)))
7.0ms	(sqrt (exp (- y)))
83.0ms	(* (sqrt (exp (- y))) (/ (sqrt (exp (- y))) x))

series72.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(sqrt (exp (- y)))
20.0ms	(sqrt (exp (- y)))
24.0ms	(* (sqrt (exp (- y))) (/ (sqrt (exp (- y))) x))

simplify3.5s

Counts

117 → 117

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	132	1204
1	265	965
2	783	859
3	2464	830
done	5000	826

prune400.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (- y)))
0.0b	(* (sqrt (sqrt (exp (- y)))) (/ (pow (sqrt (sqrt (exp (- y)))) 3) x))
0.0b	(/ (pow (sqrt (sqrt (exp (- y)))) 3) x)
0.0b	(pow (sqrt (sqrt (exp (- y)))) 3)

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

201×	`sqrt-prod`
196×	`add-sqr-sqrt`
168×	`times-frac`
120×	`add-cube-cbrt` `*-un-lft-identity`
81×	`unpow-prod-down` `cube-prod`
76×	`associate-r`
35×	`sqrt-pow1`
27×	`unswap-sqr`
24×	`associate-/l*`
20×	`add-exp-log` `exp-prod`
18×	`sqrt-div`
15×	`pow-pow`
12×	`add-cbrt-cube`
11×	`sqr-pow`
10×	`pow1`
9×	`associate-l`
8×	`cube-mult` `unpow3`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `div-exp`
5×	`neg-sub0` `exp-neg` `exp-diff`
4×	`cube-div` `expm1-log1p-u` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `pow1/2` `pow-exp` `associate-/r*`
2×	`cbrt-undiv` `frac-times` `neg-mul-1` `associate-*l/` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `sqrt-pow2` `rem-cube-cbrt`

Counts

4 → 332

Calls

4 calls:

7.0ms	(sqrt (exp (- y)))
127.0ms	(* (sqrt (sqrt (exp (- y)))) (/ (pow (sqrt (sqrt (exp (- y)))) 3) x))
31.0ms	(/ (pow (sqrt (sqrt (exp (- y)))) 3) x)
22.0ms	(pow (sqrt (sqrt (exp (- y)))) 3)

series357.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(sqrt (exp (- y)))
49.0ms	(* (sqrt (sqrt (exp (- y)))) (/ (pow (sqrt (sqrt (exp (- y)))) 3) x))
115.0ms	(/ (pow (sqrt (sqrt (exp (- y)))) 3) x)
165.0ms	(pow (sqrt (sqrt (exp (- y)))) 3)

simplify1.9s

Counts

344 → 344

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	317	5920
1	659	4885
2	2587	4105
done	5001	4081

prune863.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes121.0ms

Accuracy

89.5% (1.3b remaining)

Error of 1.8b against oracle of 0.5b and baseline of 12.4b

bsearch123.0ms

Steps

Iters	Range		Point
8	0.021902447110590684	639.503948019383	8.11468630217045
10	-30895859.745759934	-1.20447477858732e-06	-16.170247270044992

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	28	54
1	33	52
done	33	52

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	1531×	body	1280	valid
676.0ms	1482×	body	640	valid
426.0ms	4793×	body	80	valid
227.0ms	3004×	body	80	nan
211.0ms	860×	body	320	valid
105.0ms	422×	body	160	valid