Details

sample458.0ms

Algorithm

intervals

Results

197.0ms	61×	body	2560	valid
90.0ms	88×	body	1280	valid
76.0ms	30×	body	320	valid
32.0ms	59×	body	640	valid
3.0ms	10×	body	80	valid
3.0ms	8×	body	160	valid

simplify7.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.1b	(- x (tan x))
1.1b	(- x (sin x))

rewrite139.0ms

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:

100.0ms	(/ (- x (sin x)) (- x (tan x)))
12.0ms	(- x (tan x))
20.0ms	(- x (sin x))

series264.0ms

Counts

3 → 9

Calls

3 calls:

97.0ms	(/ (- x (sin x)) (- x (tan x)))
95.0ms	(- x (tan x))
73.0ms	(- x (sin x))

simplify69.0ms

Counts: 89 → 89

prune360.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 27/2800 (pow x 4)) 1/2)
0.1b	(* 9/40 (pow x 2))
0.3b	(* 27/2800 (pow x 4))
16.8b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
15×	`associate-r`
14×	`add-exp-log`
11×	`add-log-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `sqr-pow`
2×	`pow-to-exp` `diff-log` `pow-exp` `sum-log` `*-commutative` `cbrt-unprod` `unpow2`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `flip--` `flip-+` `associate--r+`

Counts

4 → 77

Calls

4 calls:

10.0ms	(+ (* 27/2800 (pow x 4)) 1/2)
21.0ms	(* 9/40 (pow x 2))
16.0ms	(* 27/2800 (pow x 4))
21.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series278.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(+ (* 27/2800 (pow x 4)) 1/2)
40.0ms	(* 9/40 (pow x 2))
64.0ms	(* 27/2800 (pow x 4))
57.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify169.0ms

Counts: 89 → 89

prune311.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.0b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.1b	(- x (tan x))
1.1b	(- x (tan x))

rewrite149.0ms

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:

20.0ms	(/ (sin x) (- x (tan x)))
103.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
16.0ms	(- x (tan x))
6.0ms	(- x (tan x))

series551.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (sin x) (- x (tan x)))
278.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
100.0ms	(- x (tan x))
75.0ms	(- x (tan x))

simplify121.0ms

Counts: 106 → 106

prune389.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

1.1b	(- x (tan x))
1.1b	(- x (tan x))
1.1b	(- x (sin x))
1.1b	(- x (sin x))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

7.0ms	(- x (tan x))
11.0ms	(- x (tan x))
13.0ms	(- x (sin x))
9.0ms	(- x (sin x))

series317.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- x (tan x))
114.0ms	(- x (tan x))
71.0ms	(- x (sin x))
42.0ms	(- x (sin x))

simplify63.0ms

Counts: 68 → 68

prune347.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes101.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.4b

bsearch198.0ms

Steps

Iters	Range		Point
9	8.845201659255268e-06	4.45864614599283	0.02932571162275987
10	-119.54622503529531	-1.822584514918214e-10	-0.032103680125466064

simplify85.0ms

end0.0ms

sample13.1s

Algorithm

intervals

Results

5.4s	1582×	body	2560	valid
4.8s	2738×	body	1280	valid
1.9s	1900×	body	640	valid
461.0ms	927×	body	320	valid
130.0ms	473×	body	160	valid
60.0ms	380×	body	80	valid