Details

sample475.0ms

Algorithm

intervals

Results

132.0ms	57×	body	2560	valid
57.0ms	84×	body	1280	valid
23.0ms	72×	body	640	valid
5.0ms	23×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	7×	body	80	valid

simplify14.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.8b	(- x (sin x))
1.0b	(- x (tan x))

rewrite23.0ms

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:

11.0ms	(/ (- x (sin x)) (- x (tan x)))
3.0ms	(- x (sin x))
5.0ms	(- x (tan x))

series177.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(/ (- x (sin x)) (- x (tan x)))
37.0ms	(- x (sin x))
62.0ms	(- x (tan x))

simplify1.0s

Counts

89 → 89

Iterations

Useful iterations: done (998.0ms)

Iter	Nodes	Cost
0	157	1237
1	366	1200
2	959	1147
3	2670	1147
done	5000	1145

prune211.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.3b	(* 9/40 (pow x 2))
14.6b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite21.0ms

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:

5.0ms	(* 27/2800 (pow x 4))
6.0ms	(* 9/40 (pow x 2))
8.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series119.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(* 27/2800 (pow x 4))
25.0ms	(* 9/40 (pow x 2))
50.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify1.3s

Counts

75 → 75

Iterations

Useful iterations: 3 (418.0ms)

Iter	Nodes	Cost
0	121	788
1	279	703
2	796	643
3	2530	637
done	5000	637

prune148.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.0b	(log (exp (/ (- x (sin x)) (- x (tan x)))))
0.8b	(- x (sin x))
1.0b	(- x (tan x))

rewrite48.0ms

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:

12.0ms	(/ (- x (sin x)) (- x (tan x)))
25.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
3.0ms	(- x (sin x))
3.0ms	(- x (tan x))

series247.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (- x (sin x)) (- x (tan x)))
80.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
31.0ms	(- x (sin x))
55.0ms	(- x (tan x))

simplify1.1s

Counts

136 → 136

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	219	1941
1	433	1793
2	1046	1712
3	2845	1712
done	5001	1710

prune327.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes43.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.8b

bsearch92.0ms

Steps

Iters	Range		Point
10	5.968040026638966e-05	117627206.70733242	0.02844105962587155
10	-64880754058.88788	-2.651420353119469e-05	-0.02582917538591079

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	25	43
1	31	33
done	31	33

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.6s	1666×	body	2560	valid
1.8s	2753×	body	1280	valid
630.0ms	1842×	body	640	valid
207.0ms	918×	body	320	valid
72.0ms	462×	body	160	valid
41.0ms	359×	body	80	valid