Details

sample571.0ms

Algorithm

intervals

Results

212.0ms	53×	body	2560	valid
145.0ms	79×	body	1280	valid
45.0ms	65×	body	640	valid
14.0ms	27×	body	320	valid
6.0ms	20×	body	160	valid
2.0ms	12×	body	80	valid

simplify17.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.6b	(- x (tan x))
1.7b	(- x (sin x))

rewrite103.0ms

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:

32.0ms	(/ (- x (sin x)) (- x (tan x)))
14.0ms	(- x (tan x))
52.0ms	(- x (sin x))

series448.0ms

Counts

3 → 9

Calls

3 calls:

153.0ms	(/ (- x (sin x)) (- x (tan x)))
185.0ms	(- x (tan x))
110.0ms	(- x (sin x))

simplify1.5s

Counts

89 → 89

Iterations

Useful iterations: done (1.4s)

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

prune336.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.1b	(* 9/40 (pow x 2))
13.1b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite80.0ms

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:

13.0ms	(* 27/2800 (pow x 4))
33.0ms	(* 9/40 (pow x 2))
32.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series198.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(* 27/2800 (pow x 4))
55.0ms	(* 9/40 (pow x 2))
72.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify2.5s

Counts

75 → 75

Iterations

Useful iterations: done (2.5s)

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

prune200.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

1.6b	(- x (tan x))
1.6b	(- x (tan x))
1.7b	(- x (sin x))
1.7b	(- x (sin x))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

12.0ms	(- x (tan x))
11.0ms	(- x (tan x))
12.0ms	(- x (sin x))
8.0ms	(- x (sin x))

series268.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(- x (tan x))
66.0ms	(- x (tan x))
57.0ms	(- x (sin x))
52.0ms	(- x (sin x))

simplify1.8s

Counts

68 → 68

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	76	566
1	153	550
2	345	516
3	725	516
4	1670	516
done	5000	516

prune306.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin x) (sin x))
1.6b	(- x (tan x))
1.7b	(- (* x x) (* (sin x) (sin x)))
12.7b	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt`
8×	`associate-/r/` `add-log-exp`
6×	`flip3--` `flip--`
4×	`frac-times` `times-frac` `associate-/l*` `difference-of-squares`
3×	`flip3-+` `swap-sqr` `associate-r` `associate-l` `flip-+`
2×	`cbrt-undiv` `sub-neg` `diff-log` `associate-r/` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod` `sqr-sin` `associate-/l/`
1×	`pow2` `frac-2neg` `pow-plus` `div-sub` `pow-prod-down` `clear-num` `associate-/r` `pow-sqr` `-commutative` `pow-prod-up` `div-inv` `sin-mult` `distribute-lft-out--` `associate--r-` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

13.0ms	(* (sin x) (sin x))
6.0ms	(- x (tan x))
9.0ms	(- (* x x) (* (sin x) (sin x)))
65.0ms	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

series404.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (sin x) (sin x))
81.0ms	(- x (tan x))
73.0ms	(- (* x x) (* (sin x) (sin x)))
229.0ms	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

simplify1.9s

Counts

101 → 101

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	200	1607
1	554	1436
2	2307	1286
done	5000	1119

prune403.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes80.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.7b

bsearch150.0ms

Steps

Iters	Range		Point
9	0.0030847216915828425	5729.342694487068	1.5862025016764627
11	-30636816361710.875	-9.292394687435822e-10	-1.5618126542548791

simplify9.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	25	63
1	31	43
done	31	43

end0.0ms

sample13.9s

Algorithm

intervals

Results

5.7s	1582×	body	2560	valid
5.3s	2688×	body	1280	valid
1.9s	1934×	body	640	valid
451.0ms	944×	body	320	valid
143.0ms	480×	body	160	valid
66.0ms	372×	body	80	valid