Details

sample529.0ms

Algorithm

intervals

Results

188.0ms	50×	body	2560	valid
128.0ms	92×	body	1280	valid
54.0ms	64×	body	640	valid
43.0ms	21×	body	160	valid
13.0ms	19×	body	320	valid
2.0ms	10×	body	80	valid

simplify51.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.5b

localize24.0ms

Local error

Found 3 expressions with local error:

1.4b	(- x (sin x))
1.4b	(- x (tan x))
0.0b	(/ (- x (sin x)) (- x (tan x)))

rewrite50.0ms

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

Counts

3 → 83

Calls

3 calls:

Slowest

33.0ms	(/ (- x (sin x)) (- x (tan x)))
7.0ms	(- x (sin x))
4.0ms	(- x (tan x))

series309.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

146.0ms	(/ (- x (sin x)) (- x (tan x)))
94.0ms	(- x (sin x))
68.0ms	(- x (tan x))

simplify1.2s

Counts: 92 → 92

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 3 expressions with local error:

1.4b	(- x (sin x))
1.4b	(- x (tan x))
0.0b	(/ (- x (sin x)) (- x (tan x)))

rewrite32.0ms

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

Counts

3 → 83

Calls

3 calls:

Slowest

18.0ms	(/ (- x (sin x)) (- x (tan x)))
8.0ms	(- x (sin x))
4.0ms	(- x (tan x))

series274.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

134.0ms	(/ (- x (sin x)) (- x (tan x)))
80.0ms	(- x (tan x))
60.0ms	(- x (sin x))

simplify1.1s

Counts: 92 → 92

prune918.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize80.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (/ (* (/ (sin x) x) (/ (sin x) x)) (cos x)) 1)
0.6b	(- (+ (/ (sin x) (* (cos x) x)) (* (/ (sin x) (* (cos x) x)) (/ (sin x) (* (cos x) x)))) (/ (sin x) x))
0.2b	(/ (sin x) (* (cos x) x))
0.2b	(/ (sin x) (* (cos x) x))

rewrite320.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
11×	`add-log-exp`
10×	`times-frac`
8×	`add-cube-cbrt`
6×	`associate-/l*` `difference-of-squares`
5×	`frac-sub`
4×	`pow1` `cbrt-undiv` `div-exp` `insert-posit16`
3×	`diff-log` `frac-add`
2×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `flip3--` `difference-of-sqr-1` `prod-exp` `cbrt-unprod` `div-inv` `flip--` `distribute-lft-out--`
1×	`frac-times` `sum-log` `flip3-+` `associate-l/` `associate--l+` `associate-r/` `flip-+`

Counts

4 → 87

Calls

4 calls:

Slowest

251.0ms	(- (+ (/ (sin x) (* (cos x) x)) (* (/ (sin x) (* (cos x) x)) (/ (sin x) (* (cos x) x)))) (/ (sin x) x))
25.0ms	(/ (sin x) (* (cos x) x))
23.0ms	(/ (sin x) (* (cos x) x))
19.0ms	(- (/ (* (/ (sin x) x) (/ (sin x) x)) (cos x)) 1)

series502.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

232.0ms	(- (+ (/ (sin x) (* (cos x) x)) (* (/ (sin x) (* (cos x) x)) (/ (sin x) (* (cos x) x)))) (/ (sin x) x))
131.0ms	(- (/ (* (/ (sin x) x) (/ (sin x) x)) (cos x)) 1)
73.0ms	(/ (sin x) (* (cos x) x))
66.0ms	(/ (sin x) (* (cos x) x))

simplify3.5s

Counts: 99 → 99

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

16.8b	(- (- (* (* x 9/40) x) 1/2) (* (pow x 4) 27/2800))
0.2b	(* x 9/40)
0.1b	(* (* x 9/40) x)
0.1b	(* (pow x 4) 27/2800)

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`pow1` `associate-l`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-r` `add-log-exp`
7×	`prod-exp`
5×	`cbrt-unprod`
4×	`unpow-prod-down` `pow-prod-down` `insert-posit16` `unswap-sqr`
3×	`diff-log` `*-commutative`
2×	`sub-neg` `associate--l+` `sqr-pow`
1×	`associate--l-` `pow-to-exp` `flip3--` `pow-exp` `flip--`

Counts

4 → 81

Calls

4 calls:

Slowest

169.0ms	(- (- (* (* x 9/40) x) 1/2) (* (pow x 4) 27/2800))
22.0ms	(* (* x 9/40) x)
17.0ms	(* (pow x 4) 27/2800)
5.0ms	(* x 9/40)

series248.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

88.0ms	(- (- (* (* x 9/40) x) 1/2) (* (pow x 4) 27/2800))
76.0ms	(* (pow x 4) 27/2800)
54.0ms	(* (* x 9/40) x)
30.0ms	(* x 9/40)

simplify1.1s

Counts: 93 → 93

prune1.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes96.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.7b

bsearch173.0ms

end0.0ms

sample15.9s

Algorithm

intervals

Results

6.7s	1645×	body	2560	valid
5.6s	2712×	body	1280	valid
2.1s	1884×	body	640	valid
617.0ms	910×	body	320	valid
594.0ms	475×	body	160	valid
132.0ms	374×	body	80	valid