Details

Time bar (total: 53.0s)

sample446.0ms

Algorithm
intervals
Results
227.0ms121×body1280valid
82.0ms72×body640valid
64.0ms22×body320valid
27.0ms256×pre80true
9.0ms33×body80valid
4.0ms8×body160valid

simplify105.0ms

Calls
1 calls:
Slowest
105.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize17.0ms

Local error

Found 3 expressions with local error:

1.6b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.2b
(+ x (- (tan (+ y z)) (tan a)))

rewrite23.0ms

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
13.0ms
(- (tan (+ y z)) (tan a))
6.0ms
(+ x (- (tan (+ y z)) (tan a)))
3.0ms
(tan (+ y z))

series269.0ms

Calls
3 calls:
Slowest
110.0ms
(- (tan (+ y z)) (tan a))
104.0ms
(+ x (- (tan (+ y z)) (tan a)))
54.0ms
(tan (+ y z))

simplify989.0ms

Calls
21 calls:
Slowest
379.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
120.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
83.0ms
(- (+ (/ (sin (+ z y)) (cos (+ z y))) x) (/ (sin a) (cos a)))
73.0ms
(- (+ (/ (sin (+ z y)) (cos (+ z y))) x) (/ (sin a) (cos a)))
61.0ms
(/ (exp (tan (+ y z))) (exp (tan a)))

prune489.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

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)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
28×associate-*l/
16×tan-quot
13×add-cbrt-cube add-exp-log
12×frac-sub
10×add-sqr-sqrt *-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
1×clear-num associate-/r* sub-neg frac-2neg diff-log div-sub div-inv
Calls
4 calls:
Slowest
30.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
15.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
5.0ms
(* (tan y) (tan z))
5.0ms
(* (tan y) (tan z))

series946.0ms

Calls
4 calls:
Slowest
460.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
276.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
109.0ms
(* (tan y) (tan z))
102.0ms
(* (tan y) (tan z))

simplify12.1s

Calls
73 calls:
Slowest
593.0ms
(/ (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (cos a)))
465.0ms
(/ (* (* (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (* (* (* (- 1 (* (tan y) (tan z))) (- 1 (* (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))) (* (* (cos a) (cos a)) (cos a))))
433.0ms
(* (* (cos y) (cos z)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z))))))
410.0ms
(- (* (* (+ (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))))
401.0ms
(/ (sqrt (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (cos a))

prune2.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

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))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
28×associate-*l/
16×frac-add tan-quot
13×add-cbrt-cube add-exp-log
12×distribute-neg-frac
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×pow1 add-log-exp associate-/l/
7×flip3-- flip--
6×flip3-+ associate-*r* associate-*l* flip-+
4×insert-posit16
3×times-frac div-sub prod-exp cbrt-unprod associate-/l*
2×neg-sub0 frac-times cbrt-undiv associate-+r- sum-log div-exp unsub-neg pow-prod-down associate-*r/ associate-/r/ *-commutative
1×+-commutative clear-num associate-/r* frac-2neg neg-log div-inv
Calls
4 calls:
Slowest
26.0ms
(/ (+ (* (+ (tan y) (tan z)) (cos a)) (- (* (- 1 (* (tan y) (tan z))) (sin a)))) (* (- 1 (* (tan y) (tan z))) (cos a)))
23.0ms
(+ (* (+ (tan y) (tan z)) (cos a)) (- (* (- 1 (* (tan y) (tan z))) (sin a))))
5.0ms
(* (tan y) (tan z))
5.0ms
(* (tan y) (tan z))

series978.0ms

Calls
4 calls:
Slowest
461.0ms
(/ (+ (* (+ (tan y) (tan z)) (cos a)) (- (* (- 1 (* (tan y) (tan z))) (sin a)))) (* (- 1 (* (tan y) (tan z))) (cos a)))
302.0ms
(+ (* (+ (tan y) (tan z)) (cos a)) (- (* (- 1 (* (tan y) (tan z))) (sin a))))
117.0ms
(* (tan y) (tan z))
99.0ms
(* (tan y) (tan z))

simplify13.1s

Calls
79 calls:
Slowest
619.0ms
(/ (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (cos a)))
595.0ms
(/ (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (cos a)))
558.0ms
(/ (* (* (+ (* (+ (tan y) (tan z)) (cos a)) (- (* (- 1 (* (tan y) (tan z))) (sin a)))) (+ (* (+ (tan y) (tan z)) (cos a)) (- (* (- 1 (* (tan y) (tan z))) (sin a))))) (+ (* (+ (tan y) (tan z)) (cos a)) (- (* (- 1 (* (tan y) (tan z))) (sin a))))) (* (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (- 1 (* (tan y) (tan z))) (cos a))) (* (- 1 (* (tan y) (tan z))) (cos a))))
538.0ms
(/ (* (* (+ (* (+ (tan y) (tan z)) (cos a)) (- (* (- 1 (* (tan y) (tan z))) (sin a)))) (+ (* (+ (tan y) (tan z)) (cos a)) (- (* (- 1 (* (tan y) (tan z))) (sin a))))) (+ (* (+ (tan y) (tan z)) (cos a)) (- (* (- 1 (* (tan y) (tan z))) (sin a))))) (* (* (* (- 1 (* (tan y) (tan z))) (- 1 (* (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))) (* (* (cos a) (cos a)) (cos a))))
465.0ms
(/ (+ (* (+ (tan y) (tan z)) (cos a)) 0) (* (- 1 (* (tan y) (tan z))) (cos a)))

prune1.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

4.2b
(log (exp (* (tan y) (tan z))))
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 (log (exp (* (tan y) (tan z))))) (cos a)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
16×associate-*l/
13×add-cbrt-cube add-exp-log
12×tan-quot
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×pow1
8×associate-/l/
6×associate-*r* associate-*l* frac-sub
5×flip3-- flip-- add-log-exp
4×insert-posit16
3×log-prod times-frac prod-exp log-pow cbrt-unprod associate-/l*
2×frac-times cbrt-undiv flip3-+ div-exp pow-prod-down frac-add associate-*r/ associate-/r/ *-commutative flip-+
1×exp-prod clear-num associate-/r* frac-2neg exp-to-pow div-sub rem-log-exp div-inv
Calls
4 calls:
Slowest
26.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (log (exp (* (tan y) (tan z))))) (cos a)))
5.0ms
(* (tan y) (tan z))
5.0ms
(* (tan y) (tan z))
3.0ms
(log (exp (* (tan y) (tan z))))

series655.0ms

Calls
4 calls:
Slowest
407.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (log (exp (* (tan y) (tan z))))) (cos a)))
83.0ms
(log (exp (* (tan y) (tan z))))
82.0ms
(* (tan y) (tan z))
82.0ms
(* (tan y) (tan z))

simplify6.0s

Calls
66 calls:
Slowest
324.0ms
(/ (* (* (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (* (* (* (- 1 (log (exp (* (tan y) (tan z))))) (cos a)) (* (- 1 (log (exp (* (tan y) (tan z))))) (cos a))) (* (- 1 (log (exp (* (tan y) (tan z))))) (cos a))))
305.0ms
(sqrt (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))))
303.0ms
(/ (cbrt (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (cos a))
298.0ms
(/ (sqrt (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (cos a))
297.0ms
(* (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)))))

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes915.0ms

Accuracy

0% (0.2b remaining)

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

bsearch9.0ms

end0.0ms

sample10.7s

Algorithm
intervals
Results
6.0s3884×body1280valid
2.7s2043×body640valid
918.0ms8000×pre80true
408.0ms676×body320valid
272.0ms1128×body80valid
159.0ms269×body160valid