Details

sample405.0ms

Algorithm

intervals

Results

140.0ms	51×	body	2560	valid
129.0ms	91×	body	1280	valid
34.0ms	61×	body	640	valid
14.0ms	32×	body	320	valid
3.0ms	12×	body	160	valid
1.0ms	9×	body	80	valid

simplify22.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.8b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.9b	(- x (tan x))
1.9b	(- x (sin x))

rewrite104.0ms

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:

84.0ms	(/ (- x (sin x)) (- x (tan x)))
6.0ms	(- x (tan x))
9.0ms	(- x (sin x))

series293.0ms

Counts

3 → 9

Calls

3 calls:

119.0ms	(/ (- x (sin x)) (- x (tan x)))
93.0ms	(- x (tan x))
80.0ms	(- x (sin x))

simplify1.6s

Counts: 89 → 89

prune301.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.8b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.9b	(- x (tan x))
1.9b	(- x (tan x))

rewrite166.0ms

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:

24.0ms	(/ (sin x) (- x (tan x)))
125.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
5.0ms	(- x (tan x))
6.0ms	(- x (tan x))

series646.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (sin x) (- x (tan x)))
340.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
106.0ms	(- x (tan x))
73.0ms	(- x (tan x))

simplify1.6s

Counts: 106 → 106

prune380.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 9/40 (pow x 2))
0.1b	(* 27/2800 (pow x 4))
20.6b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 66

Calls

3 calls:

13.0ms	(* 9/40 (pow x 2))
27.0ms	(* 27/2800 (pow x 4))
19.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series164.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(* 9/40 (pow x 2))
63.0ms	(* 27/2800 (pow x 4))
69.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify610.0ms

Counts: 75 → 75

prune248.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 9/40 (pow x 2))
0.1b	(* 27/2800 (pow x 4))
20.6b	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`add-log-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 64

Calls

3 calls:

25.0ms	(* 9/40 (pow x 2))
23.0ms	(* 27/2800 (pow x 4))
20.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

series275.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* 9/40 (pow x 2))
53.0ms	(* 27/2800 (pow x 4))
167.0ms	(- (* 9/40 (pow x 2)) (* 27/2800 (pow x 4)))

simplify654.0ms

Counts: 73 → 73

prune234.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes36.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.5b

bsearch145.0ms

Steps

Iters	Range		Point
8	0.0026080803058150265	15.61478477777618	0.03454704490516465
8	-0.06705623481545048	-1.7104155354788486e-05	-0.030141557185488794

simplify1.2s

end0.0ms

sample13.6s

Algorithm

intervals

Results

7.0s	1641×	body	2560	valid
3.7s	2745×	body	1280	valid
1.8s	1855×	body	640	valid
401.0ms	940×	body	320	valid
178.0ms	470×	body	160	valid
109.0ms	349×	body	80	valid