Details

sample647.0ms

Algorithm

intervals

Results

172.0ms	46×	body	2560	valid
95.0ms	92×	body	1280	valid
44.0ms	11×	body	160	valid
40.0ms	63×	body	640	valid
13.0ms	29×	body	320	valid
2.0ms	15×	body	80	valid

simplify32.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	6	9
1	13	9
2	17	9
3	19	9
done	19	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.6b

localize62.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.7b	(- x (tan x))
0.7b	(- x (sin x))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

46.0ms	(/ (- x (sin x)) (- x (tan x)))
16.0ms	(- x (tan x))
105.0ms	(- x (sin x))

series269.0ms

Counts

3 → 9

Calls

3 calls:

134.0ms	(/ (- x (sin x)) (- x (tan x)))
63.0ms	(- x (tan x))
71.0ms	(- x (sin x))

simplify1.7s

Counts

89 → 89

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	157	1237
1	366	1200
2	915	1147
3	2339	1147
done	5000	1133

prune238.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (- x (tan x)))
0.4b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.7b	(- x (tan x))
0.7b	(- x (tan x))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 94

Calls

4 calls:

19.0ms	(/ (sin x) (- x (tan x)))
90.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
6.0ms	(- x (tan x))
6.0ms	(- x (tan x))

series468.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (sin x) (- x (tan x)))
260.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
67.0ms	(- x (tan x))
58.0ms	(- x (tan x))

simplify2.4s

Counts

106 → 106

Iterations

Useful iterations: 3 (871.0ms)

Iter	Nodes	Cost
0	177	1565
1	377	1511
2	938	1449
3	2824	1445
done	5001	1445

prune370.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (exp (/ (- x (sin x)) (- x (tan x)))))
0.0b	(/ (- x (sin x)) (- x (tan x)))
0.7b	(- x (tan x))
0.7b	(- x (sin x))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt` `*-un-lft-identity`
50×	`times-frac`
32×	`log-pow`
31×	`exp-prod`
28×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
3×	`log-prod`
2×	`sub-neg` `diff-log` `div-sub` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `log-div` `frac-2neg` `exp-diff` `div-exp` `rem-log-exp` `clear-num`

Counts

4 → 124

Calls

4 calls:

79.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
34.0ms	(/ (- x (sin x)) (- x (tan x)))
6.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series370.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
115.0ms	(/ (- x (sin x)) (- x (tan x)))
84.0ms	(- x (tan x))
60.0ms	(- x (sin x))

simplify2.0s

Counts

136 → 136

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	219	1941
1	432	1793
2	1001	1712
3	2470	1712
done	5001	1684

prune437.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
18.6b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

3 → 66

Calls

3 calls:

23.0ms	(* 27/2800 (pow x 4))
15.0ms	(* 9/40 (pow x 2))
21.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series150.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(* 27/2800 (pow x 4))
29.0ms	(* 9/40 (pow x 2))
70.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify2.6s

Counts

75 → 75

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	121	788
1	277	703
2	674	643
3	2581	637
done	5000	634

prune211.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes81.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.0b

bsearch129.0ms

Steps

Iters	Range		Point
9	0.0033303272193615503	311302.39110615524	0.028662423939317287
9	-7.35943201301068	-4.403108084983288e-07	-0.029638169034640425

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	46
1	31	46
done	31	46

end0.0ms

sample13.8s

Algorithm

intervals

Results

5.9s	1601×	body	2560	valid
4.6s	2779×	body	1280	valid
1.7s	1836×	body	640	valid
575.0ms	963×	body	320	valid
540.0ms	347×	body	80	valid
146.0ms	474×	body	160	valid