Details

Time bar (total: 49.6s)

sample481.0ms

Algorithm
intervals
Results
306.0ms126×body1280valid
81.0ms67×body640valid
28.0ms256×pre80true
16.0ms19×body320valid
10.0ms35×body80valid
5.0ms9×body160valid

simplify72.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
72.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize24.0ms

Local error

Found 3 expressions with local error:

2.3b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite30.0ms

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
13.0ms
(- (tan (+ y z)) (tan a))
12.0ms
(+ x (- (tan (+ y z)) (tan a)))
5.0ms
(tan (+ y z))

series390.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
153.0ms
(+ x (- (tan (+ y z)) (tan a)))
140.0ms
(- (tan (+ y z)) (tan a))
97.0ms
(tan (+ y z))

simplify1.6s

Counts
25 → 54
Calls
25 calls:
Slowest
399.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
187.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
172.0ms
(+ (* 1/3 (pow y 3)) (+ z y))
126.0ms
(* (exp x) (exp (- (tan (+ y z)) (tan a))))
96.0ms
(- (+ (/ (sin (+ z y)) (cos (+ z y))) x) (/ (sin a) (cos a)))

prune624.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

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))

rewrite235.0ms

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
142.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
65.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
14.0ms
(+ (tan y) (tan z))
13.0ms
(* (tan y) (tan z))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
528.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
497.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
143.0ms
(* (tan y) (tan z))
99.0ms
(+ (tan y) (tan z))

simplify3.7s

Counts
45 → 83
Calls
45 calls:
Slowest
419.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
344.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
332.0ms
(- (+ (/ (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)))
299.0ms
(- (+ (/ (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)))
279.0ms
(- (+ (/ (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)))

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite371.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt *-un-lft-identity
11×add-cbrt-cube add-exp-log add-log-exp
8×add-cube-cbrt
6×pow1
4×times-frac insert-posit16
3×associate-/r* associate-*r* associate-*l* tan-quot
2×cbrt-undiv associate-+r+ sum-log sub-neg diff-log div-exp associate-*l/ prod-exp cbrt-unprod distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative clear-num associate-+r- frac-2neg flip3-+ flip3-- pow-prod-down *-commutative frac-sub flip-+ div-inv flip-- associate-/l* unswap-sqr associate-/l/
Counts
4 → 78
Calls
4 calls:
Slowest
166.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
157.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
29.0ms
(/ (* (tan y) (sin z)) (cos z))
18.0ms
(* (tan y) (sin z))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
541.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
540.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
124.0ms
(/ (* (tan y) (sin z)) (cos z))
96.0ms
(* (tan y) (sin z))

simplify5.5s

Counts
53 → 90
Calls
53 calls:
Slowest
440.0ms
(* (- 1 (/ (* (tan y) (sin z)) (cos z))) (cos a))
383.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a)))
346.0ms
(- (+ (/ (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)))
345.0ms
(- (+ (* 1/3 (* z (pow y 3))) (* z y)) (* 1/6 (* (pow z 3) y)))
342.0ms
(- (+ (/ (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)))

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

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

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
19×associate-*l/
18×add-sqr-sqrt
15×add-cbrt-cube add-exp-log
14×*-un-lft-identity
12×add-cube-cbrt
10×pow1 associate-*l*
9×associate-*r*
8×tan-quot associate-/l/
6×frac-sub
5×flip3-- flip--
4×prod-exp cbrt-unprod insert-posit16 add-log-exp
3×flip3-+ times-frac pow-prod-down frac-add *-commutative flip-+ associate-/l* unswap-sqr
2×cbrt-undiv div-exp associate-/r/
1×clear-num associate-/r* frac-2neg div-sub div-inv distribute-lft-out
Counts
4 → 96
Calls
4 calls:
Slowest
78.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a))) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (cos a)))
44.0ms
(* (+ (tan y) (tan z)) (cos a))
23.0ms
(* (tan y) (sin z))
12.0ms
(* (tan y) (sin z))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
688.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a))) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (cos a)))
464.0ms
(* (tan y) (sin z))
173.0ms
(* (+ (tan y) (tan z)) (cos a))
121.0ms
(* (tan y) (sin z))

simplify10.4s

Counts
71 → 108
Calls
71 calls:
Slowest
586.0ms
(/ (* (* (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a))) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a)))) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a)))) (* (* (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (cos a))) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (cos a))))
568.0ms
(- (* (* (+ (pow (tan y) 3) (pow (tan z) 3)) (cos a)) (+ (* 1 1) (+ (* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z))) (* 1 (/ (* (tan y) (sin z)) (cos z)))))) (* (+ (* (tan y) (tan y)) (- (* (tan z) (tan z)) (* (tan y) (tan z)))) (* (- (pow 1 3) (pow (/ (* (tan y) (sin z)) (cos z)) 3)) (sin a))))
523.0ms
(/ (* (cbrt (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a)))) (cbrt (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a))))) (- 1 (/ (* (tan y) (sin z)) (cos z))))
505.0ms
(- (* (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (cos a)) (+ (* 1 1) (+ (* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z))) (* 1 (/ (* (tan y) (sin z)) (cos z)))))) (* (- (tan y) (tan z)) (* (- (pow 1 3) (pow (/ (* (tan y) (sin z)) (cos z)) 3)) (sin a))))
476.0ms
(/ (* (* (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a))) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a)))) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a)))) (* (* (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (* (* (cos a) (cos a)) (cos a))))

prune2.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes492.0ms

Accuracy

0% (0.2b remaining)

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

bsearch6.0ms

end0.0ms

sample16.7s

Algorithm
intervals
Results
9.7s4030×body1280valid
3.8s1900×body640valid
1.5s8000×pre80true
777.0ms670×body320valid
346.0ms1123×body80valid
195.0ms277×body160valid