Details

sample396.0ms

Algorithm

intervals

Results

154.0ms	61×	body	640	valid
121.0ms	63×	body	1280	valid
64.0ms	204×	body	80	valid
25.0ms	24×	body	320	valid
9.0ms	14×	body	160	valid

simplify102.0ms

Calls

1 calls:

Slowest

102.0ms

(/ 2 (* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize53.0ms

Local error

Found 4 expressions with local error:

14.7b	(* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
14.3b	(/ (pow t 3) (* l l))
3.4b	(* (* (/ (pow t 3) (* l l)) (sin k)) (tan k))
2.6b	(* (/ (pow t 3) (* l l)) (sin k))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-exp-log`
34×	`add-cbrt-cube`
22×	`prod-exp`
20×	`pow1`
16×	`cbrt-unprod`
16×	`associate-*l/`
11×	`add-cube-cbrt`
11×	`associate-l`
11×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`pow-prod-down`
10×	`times-frac`
10×	`frac-times`
9×	`associate-r`
8×	`tan-quot`
8×	`div-exp`
6×	`associate-*r/`
5×	`associate-/l*`
4×	`add-log-exp`
4×	`flip-+`
4×	`flip3-+`
4×	`cbrt-undiv`
4×	`pow-to-exp`
3×	`*-commutative`
3×	`unpow3`
3×	`cube-mult`
2×	`div-inv`
1×	`distribute-lft-in`
1×	`frac-2neg`
1×	`associate-/r*`
1×	`clear-num`
1×	`distribute-rgt-in`

Calls

4 calls:

Slowest

65.0ms	(* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
22.0ms	(* (* (/ (pow t 3) (* l l)) (sin k)) (tan k))
9.0ms	(* (/ (pow t 3) (* l l)) (sin k))
7.0ms	(/ (pow t 3) (* l l))

series591.0ms

Calls

4 calls:

Slowest

306.0ms	(* (* (* (/ (pow t 3) (* l l)) (sin k)) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
171.0ms	(* (* (/ (pow t 3) (* l l)) (sin k)) (tan k))
89.0ms	(* (/ (pow t 3) (* l l)) (sin k))
24.0ms	(/ (pow t 3) (* l l))

simplify14.7s

Calls

98 calls:

Slowest

655.0ms	(* (* (* (* (* (/ (pow t 3) (* l l)) (sin k)) (* (/ (pow t 3) (* l l)) (sin k))) (* (/ (pow t 3) (* l l)) (sin k))) (* (* (tan k) (tan k)) (tan k))) (* (* (+ (+ 1 (pow (/ k t) 2)) 1) (+ (+ 1 (pow (/ k t) 2)) 1)) (+ (+ 1 (pow (/ k t) 2)) 1)))
618.0ms	(* (* l l) (- (+ 1 (pow (/ k t) 2)) 1))
618.0ms	(* (* l l) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))
614.0ms	(- (+ 1 (pow (/ k t) 2)) 1)
596.0ms	(* (cos k) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))

prune2.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.4b

localize38.0ms

Local error

Found 4 expressions with local error:

14.7b	(* (* (* (/ (* t t) l) (* (/ t l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
7.3b	(/ (* t t) l)
3.4b	(* (* (/ (* t t) l) (* (/ t l) (sin k))) (tan k))
3.3b	(* (/ t l) (sin k))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

44×	`associate-*l/`
34×	`frac-times`
29×	`add-exp-log`
29×	`add-cbrt-cube`
29×	`pow1`
17×	`cbrt-unprod`
17×	`prod-exp`
17×	`pow-prod-down`
16×	`tan-quot`
14×	`associate-*r/`
9×	`associate-r`
8×	`flip-+`
8×	`add-cube-cbrt`
8×	`flip3-+`
8×	`*-un-lft-identity`
8×	`add-sqr-sqrt`
6×	`associate-l`
4×	`add-log-exp`
3×	`*-commutative`
2×	`div-inv`
1×	`associate-/l*`
1×	`distribute-lft-in`
1×	`frac-2neg`
1×	`clear-num`
1×	`distribute-rgt-in`

Calls

4 calls:

Slowest

88.0ms	(* (* (* (/ (* t t) l) (* (/ t l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
47.0ms	(* (* (/ (* t t) l) (* (/ t l) (sin k))) (tan k))
7.0ms	(* (/ t l) (sin k))
4.0ms	(/ (* t t) l)

series665.0ms

Calls

4 calls:

Slowest

350.0ms	(* (* (* (/ (* t t) l) (* (/ t l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
208.0ms	(* (* (/ (* t t) l) (* (/ t l) (sin k))) (tan k))
89.0ms	(* (/ t l) (sin k))
17.0ms	(/ (* t t) l)

simplify19.0s

Calls

99 calls:

Slowest

1.0s	(* (* l (cos k)) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))
606.0ms	(* (* l (cos k)) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))
605.0ms	(* (* l l) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))
589.0ms	(* (* l l) (- (+ 1 (pow (/ k t) 2)) 1))
563.0ms	(* (cos k) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.1b

localize32.0ms

Local error

Found 4 expressions with local error:

14.7b	(* (* (* (/ t (/ l t)) (* (/ t l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
3.4b	(* (* (/ t (/ l t)) (* (/ t l) (sin k))) (tan k))
3.3b	(* (/ t l) (sin k))
0.7b	(/ 2 (* (* (* (/ t (/ l t)) (* (/ t l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

78×	`associate-*l/`
63×	`frac-times`
29×	`add-exp-log`
29×	`add-cbrt-cube`
29×	`pow1`
28×	`tan-quot`
25×	`associate-*r/`
23×	`associate-/r/`
17×	`cbrt-unprod`
17×	`prod-exp`
17×	`pow-prod-down`
16×	`flip-+`
16×	`flip3-+`
9×	`associate-r`
8×	`add-cube-cbrt`
8×	`*-un-lft-identity`
8×	`add-sqr-sqrt`
6×	`associate-l`
4×	`add-log-exp`
3×	`*-commutative`
2×	`div-inv`
1×	`distribute-lft-in`
1×	`frac-2neg`
1×	`associate-/r*`
1×	`clear-num`
1×	`distribute-rgt-in`

Calls

4 calls:

Slowest

114.0ms	(* (* (* (/ t (/ l t)) (* (/ t l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
36.0ms	(* (* (/ t (/ l t)) (* (/ t l) (sin k))) (tan k))
15.0ms	(/ 2 (* (* (* (/ t (/ l t)) (* (/ t l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))
4.0ms	(* (/ t l) (sin k))

series728.0ms

Calls

4 calls:

Slowest

337.0ms	(* (* (* (/ t (/ l t)) (* (/ t l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
184.0ms	(/ 2 (* (* (* (/ t (/ l t)) (* (/ t l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1)))
148.0ms	(* (* (/ t (/ l t)) (* (/ t l) (sin k))) (tan k))
59.0ms	(* (/ t l) (sin k))

simplify25.1s

Calls

122 calls:

Slowest

997.0ms	(* (cos k) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))
762.0ms	(* (* (* t (* t (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
688.0ms	(* (/ l t) (- (+ 1 (pow (/ k t) 2)) 1))
646.0ms	(* (* (* t (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1))
634.0ms	(* (* l (cos k)) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))

prune1.8s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.5b

localize14.0ms

Local error

Found 4 expressions with local error:

11.2b	(* (* (* t (* (/ t l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
8.2b	(* (/ 2 (* (* (* t (* (/ t l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))) (/ l t))
3.3b	(* (/ t l) (sin k))
2.3b	(* (* t (* (/ t l) (sin k))) (tan k))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

29×	`associate-*l/`
26×	`associate-*r/`
21×	`associate-l`
20×	`frac-times`
15×	`add-exp-log`
15×	`add-cbrt-cube`
15×	`pow1`
14×	`tan-quot`
13×	`associate-r`
11×	`associate-/r/`
10×	`add-cube-cbrt`
10×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
8×	`flip-+`
8×	`flip3-+`
6×	`cbrt-unprod`
6×	`prod-exp`
6×	`pow-prod-down`
4×	`add-log-exp`
4×	`*-commutative`
3×	`div-inv`
1×	`distribute-lft-in`
1×	`distribute-rgt-in`

Calls

4 calls:

Slowest

34.0ms	(* (/ 2 (* (* (* t (* (/ t l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))) (/ l t))
29.0ms	(* (* (* t (* (/ t l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
16.0ms	(* (* t (* (/ t l) (sin k))) (tan k))
6.0ms	(* (/ t l) (sin k))

series715.0ms

Calls

4 calls:

Slowest

344.0ms	(* (* (* t (* (/ t l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
185.0ms	(* (/ 2 (* (* (* t (* (/ t l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))) (/ l t))
130.0ms	(* (* t (* (/ t l) (sin k))) (tan k))
56.0ms	(* (/ t l) (sin k))

simplify12.6s

Calls

83 calls:

Slowest

634.0ms	(* (* (* t (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1))
607.0ms	(* (* (* t (* t (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
553.0ms	(/ 2 (* (* (* t (* t (sin k))) (sin k)) (+ (+ 1 (pow (/ k t) 2)) 1)))
524.0ms	(* (* l (cos k)) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))
521.0ms	(+ (+ (log (* t (* (/ t l) (sin k)))) (log (tan k))) (log (+ (+ 1 (pow (/ k t) 2)) 1)))

prune1.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.8b

regimes377.0ms

Accuracy

69.3% (2.3b remaining)

Error of 8.7b against oracle of 6.4b and baseline of 13.9b

bsearch774.0ms

end0.0ms

sample14.8s

Algorithm

intervals

Results

6.8s	2061×	body	1280	valid
3.3s	1735×	body	640	valid
2.9s	6013×	body	80	valid
1.1s	881×	body	320	valid
482.0ms	435×	body	160	valid