Details

sample467.0ms

Algorithm

intervals

Results

262.0ms	66×	body	2560	valid
79.0ms	75×	body	1280	valid
33.0ms	60×	body	640	valid
13.0ms	34×	body	320	valid
4.0ms	15×	body	160	valid
1.0ms	6×	body	80	valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 32.6b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
2.3b	(- x (tan x))
2.3b	(- x (sin x))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 110

Calls

3 calls:

48.0ms	(/ (- x (sin x)) (- x (tan x)))
13.0ms	(- x (tan x))
60.0ms	(- x (sin x))

series300.0ms

Counts

3 → 9

Calls

3 calls:

145.0ms	(/ (- x (sin x)) (- x (tan x)))
79.0ms	(- x (tan x))
75.0ms	(- x (sin x))

simplify1.7s

Counts

119 → 119

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	209	1823
1	501	1569
2	2266	1386
done	5002	1362

prune326.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 9/40 (pow x 2))
0.2b	(fma 27/2800 (pow x 4) 1/2)
15.3b	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
8×	`add-exp-log` `associate-r`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow-prod-down` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `associate-l` `prod-diff` `prod-exp` `log1p-expm1-u`
2×	`fma-udef` `unpow2` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `fma-neg` `diff-log` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `associate--r+`

Counts

3 → 58

Calls

3 calls:

24.0ms	(* 9/40 (pow x 2))
1.0ms	(fma 27/2800 (pow x 4) 1/2)
13.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

series239.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(* 9/40 (pow x 2))
135.0ms	(fma 27/2800 (pow x 4) 1/2)
52.0ms	(- (* 9/40 (pow x 2)) (fma 27/2800 (pow x 4) 1/2))

simplify1.6s

Counts

67 → 67

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	106	845
1	250	714
2	1254	624
done	5001	581

prune256.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (sqrt 9/40))
0.2b	(* (* x (sqrt 9/40)) (* x (sqrt 9/40)))
0.2b	(fma 27/2800 (pow x 4) 1/2)
15.3b	(- (* (* x (sqrt 9/40)) (* x (sqrt 9/40))) (fma 27/2800 (pow x 4) 1/2))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

45×	`pow1`
18×	`add-exp-log` `pow-prod-down` `add-cbrt-cube`
13×	`add-sqr-sqrt`
9×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-l` `sqrt-prod` `pow-sqr` `pow-prod-up` `log1p-expm1-u`
3×	`prod-diff`
2×	`pow-plus` `*-commutative` `fma-udef` `unswap-sqr`
1×	`pow2` `sub-neg` `flip3--` `fma-neg` `diff-log` `swap-sqr` `flip--` `associate--r+` `difference-of-squares`

Counts

4 → 90

Calls

4 calls:

20.0ms	(* x (sqrt 9/40))
74.0ms	(* (* x (sqrt 9/40)) (* x (sqrt 9/40)))
1.0ms	(fma 27/2800 (pow x 4) 1/2)
81.0ms	(- (* (* x (sqrt 9/40)) (* x (sqrt 9/40))) (fma 27/2800 (pow x 4) 1/2))

series404.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* x (sqrt 9/40))
132.0ms	(* (* x (sqrt 9/40)) (* x (sqrt 9/40)))
125.0ms	(fma 27/2800 (pow x 4) 1/2)
90.0ms	(- (* (* x (sqrt 9/40)) (* x (sqrt 9/40))) (fma 27/2800 (pow x 4) 1/2))

simplify2.2s

Counts

102 → 102

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	120	1293
1	296	906
2	1536	807
done	5001	729

prune386.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (cbrt (fma 27/2800 (pow x 4) 1/2)) (* 2 3))
16.3b	(cbrt (fma 27/2800 (pow x 4) 1/2))
24.3b	(fma (pow x 4) 81/1600 (- (pow (cbrt (fma 27/2800 (pow x 4) 1/2)) (* 2 3))))
28.3b	(/ (fma (pow x 4) 81/1600 (- (pow (cbrt (fma 27/2800 (pow x 4) 1/2)) (* 2 3)))) (fma (pow x 2) 9/40 (fma (pow x 4) 27/2800 1/2)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-exp-log`
6×	`cbrt-prod` `unpow-prod-down` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow-pow` `pow1/3`
1×	`cbrt-undiv` `pow-to-exp` `pow-unpow` `frac-2neg` `div-exp` `pow-exp` `clear-num` `fma-udef` `div-inv` `sqr-pow`

Counts

4 → 73

Calls

4 calls:

8.0ms	(pow (cbrt (fma 27/2800 (pow x 4) 1/2)) (* 2 3))
2.0ms	(cbrt (fma 27/2800 (pow x 4) 1/2))
1.0ms	(fma (pow x 4) 81/1600 (- (pow (cbrt (fma 27/2800 (pow x 4) 1/2)) (* 2 3))))
11.0ms	(/ (fma (pow x 4) 81/1600 (- (pow (cbrt (fma 27/2800 (pow x 4) 1/2)) (* 2 3)))) (fma (pow x 2) 9/40 (fma (pow x 4) 27/2800 1/2)))

series2.6s

Counts

4 → 12

Calls

4 calls:

1.2s	(pow (cbrt (fma 27/2800 (pow x 4) 1/2)) (* 2 3))
985.0ms	(cbrt (fma 27/2800 (pow x 4) 1/2))
170.0ms	(fma (pow x 4) 81/1600 (- (pow (cbrt (fma 27/2800 (pow x 4) 1/2)) (* 2 3))))
194.0ms	(/ (fma (pow x 4) 81/1600 (- (pow (cbrt (fma 27/2800 (pow x 4) 1/2)) (* 2 3)))) (fma (pow x 2) 9/40 (fma (pow x 4) 27/2800 1/2)))

simplify809.0ms

Counts

85 → 85

Iterations

Useful iterations: done (806.0ms)

Iter	Nodes	Cost
0	184	2358
1	413	2119
2	1362	1948
done	5000	1880

prune577.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes97.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.6b

bsearch191.0ms

Steps

Iters	Range		Point
11	0.022891638200552334	5.118117448855024e+31	0.027540850594149503
10	-911936.9907706906	-4.3470241882695893e-07	-0.028532925378081175

simplify35.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	32	76
1	40	68
2	44	68
done	44	68

end0.0ms

sample13.5s

Algorithm

intervals

Results

5.8s	1664×	body	2560	valid
4.7s	2736×	body	1280	valid
1.8s	1835×	body	640	valid
709.0ms	949×	body	320	valid
143.0ms	482×	body	160	valid
55.0ms	334×	body	80	valid