Details

Time bar (total: 42.7s)

sample347.0ms

Algorithm
intervals
Results
220.0ms131×body1280valid
55.0ms58×body640valid
21.0ms256×pre80true
13.0ms23×body320valid
8.0ms37×body80valid
3.0ms7×body160valid

simplify406.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
406.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize17.0ms

Local error

Found 3 expressions with local error:

2.0b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity add-log-exp
5×add-sqr-sqrt
4×tan-quot
3×pow1 add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
2×tan-sum associate-+r+ sum-log sub-neg diff-log frac-sub distribute-lft-out distribute-lft-out--
1×+-commutative associate-+r- flip3-+ flip3-- flip-+ flip-- difference-of-squares
Counts
3 → 45
Calls
3 calls:
Slowest
30.0ms
(- (tan (+ y z)) (tan a))
21.0ms
(+ x (- (tan (+ y z)) (tan a)))
5.0ms
(tan (+ y z))

series378.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
155.0ms
(- (tan (+ y z)) (tan a))
148.0ms
(+ x (- (tan (+ y z)) (tan a)))
75.0ms
(tan (+ y z))

simplify1.3s

Counts
25 → 54
Calls
25 calls:
Slowest
366.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
127.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
119.0ms
(* (exp x) (exp (- (tan (+ y z)) (tan a))))
104.0ms
(* (exp x) (/ (exp (tan (+ y z))) (exp (tan a))))
102.0ms
(+ (* 1/3 (pow y 3)) (+ z y))

prune624.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan y) (tan z))
0.2b
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.1b
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.1b
(+ (tan y) (tan z))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
13×add-sqr-sqrt add-log-exp
7×tan-quot
6×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
4×insert-posit16
3×sum-log associate-*r* associate-*l* distribute-lft-out
2×+-commutative associate-+r+ sub-neg flip3-+ diff-log flip-+ distribute-lft-out-- difference-of-squares
1×frac-times associate-+r- times-frac flip3-- pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod flip-- unswap-sqr
Counts
4 → 71
Calls
4 calls:
Slowest
79.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
53.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
13.0ms
(* (tan y) (tan z))
7.0ms
(+ (tan y) (tan z))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
514.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
447.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
131.0ms
(+ (tan y) (tan z))
110.0ms
(* (tan y) (tan z))

simplify3.1s

Counts
45 → 83
Calls
45 calls:
Slowest
340.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
270.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
268.0ms
(- (+ (/ (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)))
262.0ms
(- (+ (/ (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)))
257.0ms
(- (+ (/ (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)))

prune995.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan y) (tan z))
0.3b
(* (tan y) (tan z))
0.2b
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
0.2b
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
28×associate-*l/
16×tan-quot
14×add-sqr-sqrt
13×add-cbrt-cube add-exp-log
12×frac-sub
10×*-un-lft-identity add-cube-cbrt
9×flip3-- flip--
8×pow1 associate-/l/
6×associate-*r* associate-*l* add-log-exp
4×flip3-+ frac-add flip-+ insert-posit16
3×times-frac prod-exp cbrt-unprod associate-/l*
2×frac-times cbrt-undiv div-exp pow-prod-down associate-*r/ associate-/r/ *-commutative unswap-sqr
1×clear-num associate-/r* sub-neg frac-2neg diff-log div-sub div-inv
Counts
4 → 96
Calls
4 calls:
Slowest
68.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
43.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
26.0ms
(* (tan y) (tan z))
21.0ms
(* (tan y) (tan z))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
623.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
402.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
129.0ms
(* (tan y) (tan z))
111.0ms
(* (tan y) (tan z))

simplify12.0s

Counts
77 → 108
Calls
77 calls:
Slowest
538.0ms
(/ (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (cos a)))
426.0ms
(- (* (* (+ (pow (tan y) 3) (pow (tan z) 3)) (cos a)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))) (* (+ (* (tan y) (tan y)) (- (* (tan z) (tan z)) (* (tan y) (tan z)))) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (sin a))))
404.0ms
(* (cbrt (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (cbrt (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))))
396.0ms
(- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))) (* (* (cos y) (cos z)) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (sin a))))
395.0ms
(sqrt (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))))

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize91.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan y) (tan z))
0.3b
(* (tan y) (tan z))
0.3b
(* (tan y) (tan z))
0.3b
(* (tan y) (tan z))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
16×tan-quot
12×pow1 *-un-lft-identity add-cbrt-cube associate-*r* associate-*l* add-exp-log add-cube-cbrt
4×frac-times pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod insert-posit16 add-log-exp unswap-sqr
Counts
4 → 88
Calls
4 calls:
Slowest
21.0ms
(* (tan y) (tan z))
19.0ms
(* (tan y) (tan z))
17.0ms
(* (tan y) (tan z))
17.0ms
(* (tan y) (tan z))

series494.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
128.0ms
(* (tan y) (tan z))
125.0ms
(* (tan y) (tan z))
122.0ms
(* (tan y) (tan z))
119.0ms
(* (tan y) (tan z))

simplify3.0s

Counts
68 → 100
Calls
68 calls:
Slowest
616.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
336.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
325.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
311.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
227.0ms
(+ (* 1/3 (* (pow z 3) y)) (+ (* 1/3 (* z (pow y 3))) (* z y)))

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

regimes412.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch5.0ms

end0.0ms

sample13.3s

Algorithm
intervals
Results
8.6s3988×body1280valid
2.4s1903×body640valid
864.0ms8000×pre80true
646.0ms719×body320valid
352.0ms1132×body80valid
231.0ms258×body160valid