Details

sample357.0ms

Algorithm

intervals

Results

203.0ms	108×	body	1280	valid
61.0ms	63×	body	640	valid
23.0ms	30×	body	320	valid
23.0ms	256×	pre	80	true
9.0ms	42×	body	80	valid
6.0ms	13×	body	160	valid

simplify83.0ms

Calls

1 calls:

Slowest

83.0ms

(+ x (- (tan (+ y z)) (tan a)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize20.0ms

Local error

Found 3 expressions with local error:

3.0b	(tan (+ y z))
0.1b	(- (tan (+ y z)) (tan a))
0.1b	(+ x (- (tan (+ y z)) (tan a)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`tan-quot`
3×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
2×	`tan-sum` `associate-+r+` `sub-neg` `frac-sub`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--` `distribute-lft-out--` `difference-of-squares`

Calls

3 calls:

Slowest

6.0ms	(- (tan (+ y z)) (tan a))
3.0ms	(+ x (- (tan (+ y z)) (tan a)))
2.0ms	(tan (+ y z))

series277.0ms

Calls

3 calls:

Slowest

112.0ms	(+ x (- (tan (+ y z)) (tan a)))
108.0ms	(- (tan (+ y z)) (tan a))
58.0ms	(tan (+ y z))

simplify818.0ms

Calls

21 calls:

Slowest

341.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
97.0ms	(* (- 1 (* (tan y) (tan z))) (cos a))
60.0ms	(- (+ (/ (sin (+ z y)) (cos (+ z y))) x) (/ (sin a) (cos a)))
58.0ms	(- (+ (/ (sin (+ z y)) (cos (+ z y))) x) (/ (sin a) (cos a)))
52.0ms	(/ (exp (tan (+ y z))) (exp (tan a)))

prune547.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.1b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.1b	(+ (tan y) (tan z))
0.1b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`tan-quot`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`insert-posit16`
3×	`associate-r` `associate-l`
2×	`+-commutative` `associate-+r+` `sub-neg` `flip3-+` `flip-+` `difference-of-squares`
1×	`frac-times` `associate-+r-` `sum-log` `times-frac` `flip3--` `diff-log` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `flip--` `distribute-lft-out` `distribute-lft-out--`

Calls

4 calls:

Slowest

39.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
32.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
5.0ms	(* (tan y) (tan z))
4.0ms	(+ (tan y) (tan z))

series913.0ms

Calls

4 calls:

Slowest

386.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
337.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
96.0ms	(+ (tan y) (tan z))
95.0ms	(* (tan y) (tan z))

simplify2.4s

Calls

39 calls:

Slowest

391.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
289.0ms	(- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (+ (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) x)) (/ (sin a) (cos a)))
288.0ms	(- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (+ (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) x)) (/ (sin a) (cos a)))
276.0ms	(- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z))))))) (/ (sin a) (cos a)))
230.0ms	(+ (* 1/3 (* (pow z 3) y)) (+ (* 1/3 (* z (pow y 3))) (* z y)))

prune933.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

1.9b	(log (exp (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))
0.5b	(exp (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.2b	(* (tan y) (tan z))
0.1b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
12×	`exp-prod`
9×	`add-cube-cbrt` `add-log-exp`
7×	`pow1` `log-pow`
6×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
5×	`log-prod` `tan-quot`
4×	`exp-sum` `insert-posit16`
3×	`sub-neg` `times-frac` `associate-r` `associate-l` `distribute-lft-out--`
2×	`exp-diff` `diff-log` `rem-exp-log`
1×	`frac-times` `log-div` `flip3--` `rem-log-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `flip--`

Calls

4 calls:

Slowest

95.0ms	(log (exp (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))
78.0ms	(exp (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
39.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
10.0ms	(* (tan y) (tan z))

series1.3s

Calls

4 calls:

Slowest

445.0ms	(exp (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
430.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
367.0ms	(log (exp (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))
88.0ms	(* (tan y) (tan z))

simplify3.6s

Calls

56 calls:

Slowest

408.0ms	(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
285.0ms	(exp (- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z))))))) (/ (sin a) (cos a))))
274.0ms	(exp (- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z))))))) (/ (sin a) (cos a))))
255.0ms	(- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z))))))) (/ (sin a) (cos a)))
239.0ms	(- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z))))))) (/ (sin a) (cos a)))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (tan y))
0.6b	(cbrt (tan y))
0.6b	(cbrt (tan y))
0.5b	(* (cbrt (tan y)) (cbrt (tan y)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`pow1`
7×	`cbrt-div` `pow1/3` `tan-quot`
6×	`associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Calls

4 calls:

Slowest

7.0ms	(* (cbrt (tan y)) (cbrt (tan y)))
1.0ms	(cbrt (tan y))
1.0ms	(cbrt (tan y))
1.0ms	(cbrt (tan y))

series598.0ms

Calls

4 calls:

Slowest

169.0ms	(* (cbrt (tan y)) (cbrt (tan y)))
151.0ms	(cbrt (tan y))
139.0ms	(cbrt (tan y))
139.0ms	(cbrt (tan y))

simplify436.0ms

Calls

48 calls:

Slowest

59.0ms	(+ (* 1/9 (pow (pow y 7) 1/3)) (+ (pow y 1/3) (* 13/405 (pow (pow y 13) 1/3))))
42.0ms	(pow (/ (pow (sin y) 2) (pow (cos y) 2)) 1/3)
41.0ms	(+ (* 1/9 (pow (pow y 7) 1/3)) (+ (pow y 1/3) (* 13/405 (pow (pow y 13) 1/3))))
39.0ms	(+ (pow y 2/3) (+ (* 2/9 (pow (pow y 8) 1/3)) (* 31/405 (pow (pow y 14) 1/3))))
36.0ms	(+ (* 1/9 (pow (pow y 7) 1/3)) (+ (pow y 1/3) (* 13/405 (pow (pow y 13) 1/3))))

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes421.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch4.0ms

end0.0ms

sample13.3s

Algorithm

intervals

Results

8.2s	3918×	body	1280	valid
2.4s	1977×	body	640	valid
856.0ms	669×	body	320	valid
754.0ms	8000×	pre	80	true
663.0ms	1143×	body	80	valid
143.0ms	293×	body	160	valid