Details

sample435.0ms

Algorithm

intervals

Results

162.0ms	49×	body	2560	valid
142.0ms	91×	body	1280	valid
44.0ms	64×	body	640	valid
14.0ms	31×	body	320	valid
3.0ms	11×	body	160	valid
2.0ms	10×	body	80	valid

simplify28.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.7b	(- x (tan x))
0.7b	(- x (sin x))

rewrite116.0ms

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

Counts

3 → 80

Calls

3 calls:

94.0ms	(/ (- x (sin x)) (- x (tan x)))
9.0ms	(- x (tan x))
9.0ms	(- x (sin x))

series290.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(/ (- x (sin x)) (- x (tan x)))
112.0ms	(- x (tan x))
49.0ms	(- x (sin x))

simplify1.5s

Counts: 89 → 89

prune305.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.0b	(log (exp (/ (- x (sin x)) (- x (tan x)))))
0.7b	(- x (tan x))
0.7b	(- x (sin x))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 124

Calls

4 calls:

35.0ms	(/ (- x (sin x)) (- x (tan x)))
86.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
12.0ms	(- x (tan x))
10.0ms	(- x (sin x))

series374.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (- x (sin x)) (- x (tan x)))
117.0ms	(log (exp (/ (- x (sin x)) (- x (tan x)))))
98.0ms	(- x (tan x))
53.0ms	(- x (sin x))

simplify1.6s

Counts: 136 → 136

prune495.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
0.0b	(pow (/ (- x (sin x)) (- x (tan x))) 3)
0.7b	(- x (tan x))
0.7b	(- x (sin x))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-sqr-sqrt` `*-un-lft-identity`
100×	`times-frac`
68×	`cbrt-prod`
62×	`unpow-prod-down` `cube-prod`
50×	`add-cube-cbrt`
42×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r/` `add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
6×	`flip3--` `flip--`
5×	`pow1`
4×	`div-inv`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `sub-neg` `diff-log` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `div-exp` `rem-cbrt-cube`

Counts

4 → 188

Calls

4 calls:

47.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
46.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
10.0ms	(- x (tan x))
18.0ms	(- x (sin x))

series488.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(cbrt (pow (/ (- x (sin x)) (- x (tan x))) 3))
189.0ms	(pow (/ (- x (sin x)) (- x (tan x))) 3)
106.0ms	(- x (tan x))
50.0ms	(- x (sin x))

simplify1.3s

Counts: 200 → 200

prune504.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
0.5b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
0.7b	(- x (tan x))
0.7b	(- x (tan x))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`add-exp-log` `flip3--` `associate-/r/` `add-cbrt-cube` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 94

Calls

4 calls:

27.0ms	(/ (sin x) (- x (tan x)))
118.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
11.0ms	(- x (tan x))
12.0ms	(- x (tan x))

series574.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (sin x) (- x (tan x)))
320.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
77.0ms	(- x (tan x))
78.0ms	(- x (tan x))

simplify1.6s

Counts: 106 → 106

prune394.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes148.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.4b

bsearch110.0ms

Steps

Iters	Range		Point
8	0.00022617661863457038	0.0815671925612537	0.029716746907535074
11	-31.62993370098301	-4.221128360075206e-33	-0.03460187503695809

simplify1.2s

end0.0ms

sample13.8s

Algorithm

intervals

Results

6.6s	1589×	body	2560	valid
4.7s	2803×	body	1280	valid
1.4s	1851×	body	640	valid
505.0ms	938×	body	320	valid
253.0ms	465×	body	160	valid
57.0ms	354×	body	80	valid