Details

sample697.0ms

Algorithm

intervals

Results

212.0ms	57×	body	2560	valid
195.0ms	94×	body	1280	valid
59.0ms	58×	body	640	valid
20.0ms	27×	body	320	valid
7.0ms	13×	body	160	valid
2.0ms	7×	body	80	valid

simplify32.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	19
3	19
2	17
1	13
0	6

prune55.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize38.0ms

Local error

Found 3 expressions with local error:

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

rewrite59.0ms

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×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 113

Calls

3 calls:

30.0ms	(/ (- x (sin x)) (- x (tan x)))
10.0ms	(- x (tan x))
16.0ms	(- x (sin x))

series265.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(/ (- x (sin x)) (- x (tan x)))
100.0ms	(- x (tan x))
79.0ms	(- x (sin x))

simplify1.9s

Counts

122 → 122

Iterations

Iter	Nodes
3	4455
2	1297
1	502
0	212

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 9/40 (* 27/2800 (* x x)))
0.1b	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
0.2b	(* 27/2800 (* x x))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-cbrt-cube` `add-exp-log`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `prod-diff` `add-cube-cbrt`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`distribute-rgt-in` `distribute-lft-in` `add-log-exp`
4×	`associate-r` `associate-l`
3×	`expm1-log1p-u` `sub-neg` `fma-neg` `insert-posit16` `log1p-expm1-u`
2×	`flip3--` `associate-r/` `-commutative` `flip--` `unswap-sqr`
1×	`diff-log`

Counts

3 → 77

Calls

3 calls:

11.0ms	(- 9/40 (* 27/2800 (* x x)))
26.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
19.0ms	(* 27/2800 (* x x))

series317.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(- 9/40 (* 27/2800 (* x x)))
181.0ms	(* (* x x) (- 9/40 (* 27/2800 (* x x))))
51.0ms	(* 27/2800 (* x x))

simplify2.7s

Counts

86 → 86

Iterations

Iter	Nodes
3	3373
2	1049
1	342
0	113

prune651.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin x) (sin x))
0.8b	(- (* x x) (* (sin x) (sin x)))
0.8b	(- x (tan x))
16.8b	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`prod-diff`
8×	`associate-/r/` `add-log-exp`
6×	`flip3--` `flip--`
4×	`expm1-log1p-u` `frac-times` `times-frac` `fma-neg` `insert-posit16` `log1p-expm1-u` `associate-/l*` `difference-of-squares`
3×	`flip3-+` `swap-sqr` `associate-r` `associate-l` `flip-+`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-l/` `prod-exp` `associate-r/` `cbrt-unprod` `sqr-sin` `associate-/l/`
1×	`pow2` `clear-num` `associate-/r` `frac-2neg` `pow-plus` `div-sub` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up` `div-inv` `sin-mult` `distribute-lft-out--` `associate--r-` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

14.0ms	(* (sin x) (sin x))
17.0ms	(- (* x x) (* (sin x) (sin x)))
10.0ms	(- x (tan x))
28.0ms	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

series437.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (sin x) (sin x))
96.0ms	(- (* x x) (* (sin x) (sin x)))
74.0ms	(- x (tan x))
232.0ms	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

simplify1.3s

Counts

127 → 127

Iterations

Iter	Nodes
2	3089
1	688
0	239

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize74.0ms

Local error

Found 4 expressions with local error:

7.1b	(/ (* (cbrt (- (* x x) (* (sin x) (sin x)))) (cbrt (- (* x x) (* (sin x) (sin x))))) (- x (tan x)))
16.6b	(cbrt (- (* x x) (* (sin x) (sin x))))
16.6b	(cbrt (- (* x x) (* (sin x) (sin x))))
16.6b	(cbrt (- (* x x) (* (sin x) (sin x))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
13×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`cbrt-prod`
10×	`flip3--` `flip--`
9×	`add-exp-log` `add-cube-cbrt`
8×	`associate-/l/`
7×	`add-cbrt-cube`
5×	`associate-/r*` `times-frac` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`cbrt-undiv` `div-exp` `associate-l/` `associate-r/` `associate-/r/` `distribute-lft-out--`
1×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 89

Calls

4 calls:

55.0ms	(/ (* (cbrt (- (* x x) (* (sin x) (sin x)))) (cbrt (- (* x x) (* (sin x) (sin x))))) (- x (tan x)))
10.0ms	(cbrt (- (* x x) (* (sin x) (sin x))))
11.0ms	(cbrt (- (* x x) (* (sin x) (sin x))))
11.0ms	(cbrt (- (* x x) (* (sin x) (sin x))))

series751.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(/ (* (cbrt (- (* x x) (* (sin x) (sin x)))) (cbrt (- (* x x) (* (sin x) (sin x))))) (- x (tan x)))
160.0ms	(cbrt (- (* x x) (* (sin x) (sin x))))
187.0ms	(cbrt (- (* x x) (* (sin x) (sin x))))
208.0ms	(cbrt (- (* x x) (* (sin x) (sin x))))

simplify2.7s

Counts

101 → 101

Iterations

Iter	Nodes
3	5435
2	1563
1	467
0	181

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes90.0ms

Accuracy

100% (0.0b remaining)

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

bsearch115.0ms

Steps

Iters	Range		Point
11	1.0334628320549359e-08	2.7368728718549235e+26	0.02472356942875851
8	-0.18430940072566707	-1.79411439440973e-05	-0.027300092888257143

simplify4.0ms

Iterations

Iter	Nodes
2	25
1	25
0	20

end0.0ms

sample16.8s

Algorithm

intervals

Results

7.5s	1597×	body	2560	valid
5.8s	2785×	body	1280	valid
2.1s	1900×	body	640	valid
798.0ms	924×	body	320	valid
235.0ms	456×	body	160	valid
111.0ms	338×	body	80	valid