Details

Time bar (total: 56.4s)

sample530.0ms

Algorithm
intervals
Results
303.0ms132×body1280valid
129.0ms61×body640valid
31.0ms256×pre80true
19.0ms21×body320valid
10.0ms35×body80valid
4.0ms7×body160valid

simplify80.0ms

Calls
1 calls:
Slowest
80.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize46.0ms

Local error

Found 3 expressions with local error:

2.8b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite55.0ms

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
Calls
3 calls:
Slowest
25.0ms
(- (tan (+ y z)) (tan a))
20.0ms
(+ x (- (tan (+ y z)) (tan a)))
10.0ms
(tan (+ y z))

series429.0ms

Calls
3 calls:
Slowest
178.0ms
(+ x (- (tan (+ y z)) (tan a)))
157.0ms
(- (tan (+ y z)) (tan a))
94.0ms
(tan (+ y z))

simplify1.5s

Calls
25 calls:
Slowest
411.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
142.0ms
(+ (* 1/3 (pow y 3)) (+ z y))
121.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
115.0ms
(* (exp x) (/ (exp (tan (+ y z))) (exp (tan a))))
107.0ms
(* (exp x) (exp (- (tan (+ y z)) (tan a))))

prune575.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

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

rewrite238.0ms

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
Calls
4 calls:
Slowest
97.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
96.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
23.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
21.0ms
(* (tan y) (tan z))

series1.5s

Calls
4 calls:
Slowest
519.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
510.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
339.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
156.0ms
(* (tan y) (tan z))

simplify6.2s

Calls
77 calls:
Slowest
528.0ms
(/ (* (* (+ (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)))))
459.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
396.0ms
(- (+ (/ (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)))
325.0ms
(- (+ (/ (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)))
301.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))

prune1.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

3.5b
(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))))
0.3b
(* (tan z) (tan z))
0.3b
(* (tan y) (tan y))
0.3b
(* (tan y) (tan z))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
42×tan-quot
22×add-sqr-sqrt
20×pow1
16×*-un-lft-identity add-cube-cbrt
15×frac-times add-cbrt-cube add-exp-log
12×associate-*r/ frac-sub
11×associate-*l/ associate-/r/ associate-/l/
9×associate-*r* associate-*l*
8×flip3-- flip--
6×swap-sqr
4×times-frac prod-exp cbrt-unprod insert-posit16 associate-/l* add-log-exp
3×pow-prod-down *-commutative unswap-sqr
2×pow2 cbrt-undiv pow-plus div-exp pow-sqr pow-prod-up difference-of-squares
1×clear-num associate-/r* frac-2neg div-sub div-inv
Calls
4 calls:
Slowest
81.0ms
(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))))
26.0ms
(* (tan y) (tan z))
13.0ms
(* (tan z) (tan z))
13.0ms
(* (tan y) (tan y))

series616.0ms

Calls
4 calls:
Slowest
412.0ms
(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))))
109.0ms
(* (tan y) (tan z))
53.0ms
(* (tan y) (tan y))
41.0ms
(* (tan z) (tan z))

simplify10.5s

Calls
115 calls:
Slowest
892.0ms
(/ (* (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (* (tan y) (tan y)) (* (tan z) (tan z)))) (- (* (tan y) (tan y)) (* (tan z) (tan z)))) (* (* (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z)))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z)))))
624.0ms
(/ (* (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (* (tan y) (tan y)) (* (tan z) (tan z)))) (- (* (tan y) (tan y)) (* (tan z) (tan z)))) (* (* (* (- 1 (* (tan y) (tan z))) (- 1 (* (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))) (* (* (- (tan y) (tan z)) (- (tan y) (tan z))) (- (tan y) (tan z)))))
588.0ms
(* (+ (* 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)))))
548.0ms
(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))
466.0ms
(- (log (- (* (tan y) (tan y)) (* (tan z) (tan z)))) (log (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z)))))

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

16.1b
(log (* (tan y) (tan y)))
3.5b
(/ (- (exp (log (* (tan y) (tan y)))) (* (tan z) (tan z))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))))
1.5b
(exp (log (* (tan y) (tan y))))
0.3b
(* (tan z) (tan z))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
42×tan-quot
27×pow1
15×add-sqr-sqrt frac-times log-div
14×add-exp-log
12×exp-diff associate-*r/ log-pow frac-sub
11×*-un-lft-identity add-cbrt-cube associate-*l/ associate-/r/ add-cube-cbrt associate-/l/
9×exp-prod
8×flip3-- flip--
5×times-frac associate-/l*
4×log-prod insert-posit16 add-log-exp difference-of-squares
3×pow2 pow-plus swap-sqr associate-*r* associate-*l* exp-sum pow-prod-down prod-exp pow-sqr pow-prod-up
2×cbrt-undiv div-exp rem-log-exp cbrt-unprod
1×clear-num associate-/r* frac-2neg div-sub *-commutative div-inv unswap-sqr rem-exp-log
Calls
4 calls:
Slowest
137.0ms
(/ (- (exp (log (* (tan y) (tan y)))) (* (tan z) (tan z))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))))
36.0ms
(log (* (tan y) (tan y)))
27.0ms
(* (tan z) (tan z))
19.0ms
(exp (log (* (tan y) (tan y))))

series711.0ms

Calls
4 calls:
Slowest
490.0ms
(/ (- (exp (log (* (tan y) (tan y)))) (* (tan z) (tan z))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))))
125.0ms
(log (* (tan y) (tan y)))
57.0ms
(exp (log (* (tan y) (tan y))))
40.0ms
(* (tan z) (tan z))

simplify9.2s

Calls
102 calls:
Slowest
704.0ms
(/ (* (* (- (exp (log (* (tan y) (tan y)))) (* (tan z) (tan z))) (- (exp (log (* (tan y) (tan y)))) (* (tan z) (tan z)))) (- (exp (log (* (tan y) (tan y)))) (* (tan z) (tan z)))) (* (* (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z)))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z)))))
468.0ms
(/ (* (* (- (exp (log (* (tan y) (tan y)))) (* (tan z) (tan z))) (- (exp (log (* (tan y) (tan y)))) (* (tan z) (tan z)))) (- (exp (log (* (tan y) (tan y)))) (* (tan z) (tan z)))) (* (* (* (- 1 (* (tan y) (tan z))) (- 1 (* (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))) (* (* (- (tan y) (tan z)) (- (tan y) (tan z))) (- (tan y) (tan z)))))
415.0ms
(/ (exp (log (* (tan y) (tan y)))) (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z))))
395.0ms
(- (log (- (exp (log (* (tan y) (tan y)))) (* (tan z) (tan z)))) (log (* (- 1 (* (tan y) (tan z))) (- (tan y) (tan z)))))
338.0ms
(* (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z))))) (+ (tan y) (tan z)))

prune2.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes682.0ms

Accuracy

0% (0.2b remaining)

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

bsearch4.0ms

end0.0ms

sample16.6s

Algorithm
intervals
Results
10.3s3952×body1280valid
2.9s1973×body640valid
1.3s669×body320valid
1.0s8000×pre80true
387.0ms1094×body80valid
225.0ms312×body160valid