Details

Time bar (total: 44.5s)

sample431.0ms

Algorithm
intervals
Results
249.0ms128×body1280valid
65.0ms63×body640valid
45.0ms23×body320valid
25.0ms256×pre80true
7.0ms31×body80valid
7.0ms11×body160valid

simplify46.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
46.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize34.0ms

Local error

Found 3 expressions with local error:

2.5b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite44.0ms

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
24.0ms
(- (tan (+ y z)) (tan a))
10.0ms
(+ x (- (tan (+ y z)) (tan a)))
9.0ms
(tan (+ y z))

series382.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
160.0ms
(+ x (- (tan (+ y z)) (tan a)))
138.0ms
(- (tan (+ y z)) (tan a))
84.0ms
(tan (+ y z))

simplify1.5s

Counts
25 → 54
Calls
25 calls:
Slowest
375.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
156.0ms
(+ (* 1/3 (pow y 3)) (+ z y))
141.0ms
(* (exp x) (exp (- (tan (+ y z)) (tan a))))
133.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
129.0ms
(* (exp x) (/ (exp (tan (+ y z))) (exp (tan a))))

prune551.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

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

rewrite281.0ms

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity
22×add-sqr-sqrt
15×add-cube-cbrt
13×times-frac
11×add-log-exp
8×add-cbrt-cube add-exp-log
7×tan-quot
6×pow1 distribute-lft-out
4×insert-posit16 associate-/l*
3×associate-/r* associate-*r* associate-*l* associate-/l/
2×associate-+r+ sum-log sub-neg flip3-+ flip3-- diff-log associate-/r/ flip-+ flip-- distribute-lft-out-- difference-of-squares
1×frac-times cbrt-undiv +-commutative clear-num associate-+r- frac-2neg div-exp pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod div-inv unswap-sqr
Counts
4 → 94
Calls
4 calls:
Slowest
112.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
95.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
38.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
34.0ms
(* (tan y) (tan z))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
491.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
490.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
286.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
100.0ms
(* (tan y) (tan z))

simplify6.0s

Counts
77 → 106
Calls
77 calls:
Slowest
497.0ms
(/ (* (* (+ (tan y) (tan z)) (+ (tan y) (tan z))) (+ (tan y) (tan z))) (* (* (- 1 (* (tan y) (tan z))) (- 1 (* (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))))
402.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
363.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
316.0ms
(- (+ (/ (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)))
316.0ms
(- (+ (/ (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)))

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize96.0ms

Local error

Found 4 expressions with local error:

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

rewrite284.0ms

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube add-exp-log
17×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-cube-cbrt
6×associate-*r* associate-*l* prod-exp cbrt-unprod add-log-exp
4×cbrt-undiv div-exp insert-posit16
2×times-frac pow-prod-down cos-mult *-commutative sin-mult difference-of-squares unswap-sqr
1×clear-num associate-/r* sub-neg frac-2neg flip3-- diff-log tan-quot associate-/r/ frac-sub div-inv flip-- associate-/l* distribute-lft-out-- associate-/l/
Counts
4 → 81
Calls
4 calls:
Slowest
234.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z))))) (tan a))
21.0ms
(/ (* (sin z) (sin y)) (* (cos y) (cos z)))
14.0ms
(* (sin z) (sin y))
12.0ms
(* (cos y) (cos z))

series838.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
556.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z))))) (tan a))
143.0ms
(/ (* (sin z) (sin y)) (* (cos y) (cos z)))
81.0ms
(* (sin z) (sin y))
59.0ms
(* (cos y) (cos z))

simplify8.1s

Counts
55 → 93
Calls
55 calls:
Slowest
1.2s
(/ (* (* (* (sin z) (sin z)) (sin z)) (* (* (sin y) (sin y)) (sin y))) (* (* (* (cos y) (cos z)) (* (cos y) (cos z))) (* (cos y) (cos z))))
1.1s
(/ (* (* (* (sin z) (sin y)) (* (sin z) (sin y))) (* (sin z) (sin y))) (* (* (* (cos y) (cos z)) (* (cos y) (cos z))) (* (cos y) (cos z))))
693.0ms
(/ (* (* (* (sin z) (sin z)) (sin z)) (* (* (sin y) (sin y)) (sin y))) (* (* (* (cos y) (cos y)) (cos y)) (* (* (cos z) (cos z)) (cos z))))
676.0ms
(/ (* (* (* (sin z) (sin y)) (* (sin z) (sin y))) (* (sin z) (sin y))) (* (* (* (cos y) (cos y)) (cos y)) (* (* (cos z) (cos z)) (cos z))))
298.0ms
(- (+ (log (sin z)) (log (sin y))) (log (* (cos y) (cos z))))

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite231.0ms

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity
19×add-sqr-sqrt
15×add-cube-cbrt
12×times-frac
11×add-log-exp
8×add-cbrt-cube tan-quot add-exp-log
6×pow1 distribute-lft-out
4×insert-posit16 associate-/l*
3×associate-/r* flip3-+ associate-*r* associate-*l* flip-+ associate-/l/
2×sum-log flip3-- diff-log associate-/r/ frac-sub flip-- distribute-lft-out--
1×frac-times cbrt-undiv +-commutative clear-num sub-neg frac-2neg div-exp pow-prod-down associate-*l/ frac-add prod-exp associate--l+ associate-*r/ *-commutative cbrt-unprod div-inv difference-of-squares unswap-sqr
Counts
4 → 92
Calls
4 calls:
Slowest
168.0ms
(- (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (tan a))
26.0ms
(+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
22.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
14.0ms
(* (tan y) (tan z))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
408.0ms
(- (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (tan a))
346.0ms
(+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
241.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
129.0ms
(* (tan y) (tan z))

simplify5.3s

Counts
74 → 104
Calls
74 calls:
Slowest
401.0ms
(/ (* (* (+ (tan y) (tan z)) (+ (tan y) (tan z))) (+ (tan y) (tan z))) (* (* (- 1 (* (tan y) (tan z))) (- 1 (* (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))))
293.0ms
(- (+ (/ (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)))
275.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
274.0ms
(+ (/ (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))
269.0ms
(- (+ (/ (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)))

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes370.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample13.2s

Algorithm
intervals
Results
8.0s3896×body1280valid
2.6s1994×body640valid
892.0ms700×body320valid
847.0ms8000×pre80true
332.0ms1116×body80valid
166.0ms294×body160valid