Details

sample727.0ms

Algorithm

intervals

Results

239.0ms	55×	body	2560	valid
171.0ms	96×	body	1280	valid
82.0ms	56×	body	640	valid
12.0ms	22×	body	320	valid
6.0ms	15×	body	160	valid
3.0ms	12×	body	80	valid

simplify51.0ms

Counts: 1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize20.0ms

Local error

Found 3 expressions with local error:

1.4b	(- x (tan x))
1.2b	(- x (sin x))
0.0b	(/ (- x (sin x)) (- x (tan x)))

rewrite33.0ms

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

18.0ms	(/ (- x (sin x)) (- x (tan x)))
7.0ms	(- x (tan x))
6.0ms	(- x (sin x))

series250.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

122.0ms	(/ (- x (sin x)) (- x (tan x)))
77.0ms	(- x (tan x))
50.0ms	(- x (sin x))

simplify1.1s

Counts: 173 → 122

prune962.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

114×	`pow1`
36×	`pow-prod-up`
23×	`pow-prod-down`
22×	`pow-sqr`
18×	`pow-plus`
15×	`add-cbrt-cube` `add-exp-log`
13×	`pow2`
8×	`prod-exp` `cbrt-unprod`
3×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`swap-sqr` `associate-r` `associate-l` `*-commutative` `unswap-sqr`

Counts

3 → 88

Calls

3 calls:

Slowest

30.0ms	(* (* x x) (* x x))
1.0ms	(fma 9/40 (* x x) (- (fma 27/2800 (* (* x x) (* x x)) 1/2)))
0.0ms	(fma 27/2800 (* (* x x) (* x x)) 1/2)

series237.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

132.0ms	(fma 27/2800 (* (* x x) (* x x)) 1/2)
64.0ms	(fma 9/40 (* x x) (- (fma 27/2800 (* (* x x) (* x x)) 1/2)))
41.0ms	(* (* x x) (* x x))

simplify1.1s

Counts: 97 → 97

prune911.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

1.4b	(- x (tan x))
1.4b	(- x (tan x))
0.8b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.1b	(/ (sin x) (- x (tan x)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

713×	`*-un-lft-identity`
703×	`add-sqr-sqrt`
678×	`times-frac`
459×	`prod-diff`
417×	`add-cube-cbrt`
147×	`distribute-lft-out--`
141×	`difference-of-squares`
92×	`associate-/r/`
49×	`flip3--` `flip--`
46×	`div-inv`
27×	`fma-neg`
10×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub` `sub-div`

Counts

4 → 592

Calls

4 calls:

Slowest

84.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
24.0ms	(/ (sin x) (- x (tan x)))
10.0ms	(- x (tan x))
10.0ms	(- x (tan x))

series540.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

277.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
112.0ms	(/ (sin x) (- x (tan x)))
78.0ms	(- x (tan x))
73.0ms	(- x (tan x))

simplify1.3s

Counts: 1092 → 604

prune7.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

1.4b	(- x (tan x))
1.4b	(- x (tan x))
1.4b	(- x (tan x))
1.4b	(- x (tan x))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 116

Calls

4 calls:

Slowest

6.0ms	(- x (tan x))
5.0ms	(- x (tan x))
5.0ms	(- x (tan x))
5.0ms	(- x (tan x))

series289.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

78.0ms	(- x (tan x))
71.0ms	(- x (tan x))
71.0ms	(- x (tan x))
70.0ms	(- x (tan x))

simplify434.0ms

Counts: 176 → 128

prune1.5s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes43.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.2b

bsearch139.0ms

end0.0ms

sample16.9s

Algorithm

intervals

Results

8.1s	1619×	body	2560	valid
4.9s	2818×	body	1280	valid
2.2s	1814×	body	640	valid
1.2s	912×	body	320	valid
229.0ms	498×	body	160	valid
85.0ms	339×	body	80	valid