Details

sample679.0ms

Algorithm

intervals

Results

267.0ms	63×	body	2560	valid
215.0ms	75×	body	1280	valid
73.0ms	69×	body	640	valid
23.0ms	26×	body	320	valid
6.0ms	14×	body	160	valid
3.0ms	9×	body	80	valid

simplify485.0ms

Counts: 1 → 1

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize34.0ms

Local error

Found 3 expressions with local error:

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

rewrite68.0ms

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:

Slowest

37.0ms	(/ (- x (sin x)) (- x (tan x)))
15.0ms	(- x (sin x))
10.0ms	(- x (tan x))

series300.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

110.0ms	(/ (- x (sin x)) (- x (tan x)))
99.0ms	(- x (tan x))
91.0ms	(- x (sin x))

simplify1.6s

Counts: 122 → 122

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

15.3b	(- (* (* x x) 9/40) (fma 27/2800 (* (* x x) (* x x)) 1/2))
0.3b	(fma 27/2800 (* (* x x) (* x x)) 1/2)
0.1b	(* (* x x) 9/40)
0.1b	(* (* x x) (* x x))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

120×	`pow1`
36×	`pow-prod-up`
26×	`pow-prod-down`
22×	`pow-sqr`
21×	`add-cbrt-cube` `add-exp-log`
18×	`pow-plus`
13×	`pow2`
11×	`prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u`
3×	`prod-diff`
2×	`associate-l` `*-commutative` `fma-udef` `unswap-sqr`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `swap-sqr` `flip--` `associate--r+`

Counts

4 → 119

Calls

4 calls:

Slowest

37.0ms	(* (* x x) (* x x))
37.0ms	(- (* (* x x) 9/40) (fma 27/2800 (* (* x x) (* x x)) 1/2))
27.0ms	(* (* x x) 9/40)
0.0ms	(fma 27/2800 (* (* x x) (* x x)) 1/2)

series293.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

129.0ms	(fma 27/2800 (* (* x x) (* x x)) 1/2)
68.0ms	(- (* (* x x) 9/40) (fma 27/2800 (* (* x x) (* x x)) 1/2))
49.0ms	(* (* x x) 9/40)
47.0ms	(* (* x x) (* x x))

simplify1.3s

Counts: 131 → 131

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt` `*-un-lft-identity`
50×	`times-frac`
42×	`add-cube-cbrt`
32×	`log-pow`
31×	`exp-prod`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`add-log-exp`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u`
3×	`log-prod`
2×	`sub-neg` `diff-log` `div-sub` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `exp-diff` `div-exp` `rem-log-exp`

Counts

4 → 160

Calls

4 calls:

Slowest

35.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
31.0ms	(/ (- x (sin x)) (- x (tan x)))
7.0ms	(- x (sin x))
6.0ms	(- x (tan x))

series403.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

150.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
118.0ms	(/ (- x (sin x)) (- x (tan x)))
92.0ms	(- x (tan x))
42.0ms	(- x (sin x))

simplify1.8s

Counts: 172 → 172

prune1.8s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

37.6b	(/ (- (* x (* x x)) (* (tan x) (* (tan x) (tan x)))) (fma (tan x) (+ x (tan x)) (* x x)))
0.8b	(- x (sin x))
0.8b	(- (* x (* x x)) (* (tan x) (* (tan x) (tan x))))
0.2b	(* (tan x) (tan x))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt`
12×	`times-frac`
11×	`pow1`
10×	`cube-unmult` `prod-diff`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`difference-cubes`
4×	`expm1-log1p-u` `fma-neg` `tan-quot` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r` `flip3--` `swap-sqr` `associate-r` `associate-l*` `flip--`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`pow2` `frac-times` `cbrt-undiv` `clear-num` `frac-2neg` `pow-plus` `div-sub` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

Slowest

109.0ms	(/ (- (* x (* x x)) (* (tan x) (* (tan x) (tan x)))) (fma (tan x) (+ x (tan x)) (* x x)))
47.0ms	(- (* x (* x x)) (* (tan x) (* (tan x) (tan x))))
28.0ms	(* (tan x) (tan x))
13.0ms	(- x (sin x))

series658.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

378.0ms	(/ (- (* x (* x x)) (* (tan x) (* (tan x) (tan x)))) (fma (tan x) (+ x (tan x)) (* x x)))
179.0ms	(- (* x (* x x)) (* (tan x) (* (tan x) (tan x))))
59.0ms	(- x (sin x))
42.0ms	(* (tan x) (tan x))

simplify582.0ms

Counts: 127 → 127

prune1.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes93.0ms

Accuracy

100% (0.0b remaining)

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

bsearch185.0ms

end0.0ms

sample16.4s

Algorithm

intervals

Results

6.8s	1665×	body	2560	valid
5.4s	2706×	body	1280	valid
2.4s	1831×	body	640	valid
871.0ms	943×	body	320	valid
744.0ms	502×	body	160	valid
90.0ms	353×	body	80	valid