Details

Time bar (total: 4.0m)

sample455.0ms

Algorithm
intervals
Results
240.0ms121×body1280valid
82.0ms68×body640valid
31.0ms256×pre80true
26.0ms24×body320valid
11.0ms37×body80valid
3.0ms6×body160valid

simplify46.0ms

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

localize35.0ms

Local error

Found 3 expressions with local error:

3.0b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite27.0ms

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
19.0ms
(- (tan (+ y z)) (tan a))
4.0ms
(+ x (- (tan (+ y z)) (tan a)))
4.0ms
(tan (+ y z))

series329.0ms

Calls
3 calls:
Slowest
139.0ms
(- (tan (+ y z)) (tan a))
126.0ms
(+ x (- (tan (+ y z)) (tan a)))
63.0ms
(tan (+ y z))

simplify930.0ms

Calls
21 calls:
Slowest
396.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
130.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
66.0ms
(- (+ (/ (sin (+ z y)) (cos (+ z y))) x) (/ (sin a) (cos a)))
65.0ms
(- (+ (/ (sin (+ z y)) (cos (+ z y))) x) (/ (sin a) (cos a)))
42.0ms
(/ (exp (tan (+ y z))) (exp (tan a)))

prune660.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite108.0ms

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
61.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
25.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
10.0ms
(* (tan y) (tan z))
9.0ms
(* (tan y) (tan z))

series1.0s

Calls
4 calls:
Slowest
514.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
301.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
107.0ms
(* (tan y) (tan z))
88.0ms
(* (tan y) (tan z))

simplify13.1s

Calls
73 calls:
Slowest
637.0ms
(/ (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (cos a)))
461.0ms
(sqrt (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))))
452.0ms
(/ (* (* (- (* (+ (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))))
443.0ms
(* (* (cos y) (cos z)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z))))))
437.0ms
(/ (* (* (- (* (+ (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))))

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize99.0ms

Local error

Found 4 expressions with local error:

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

rewrite743.0ms

Algorithm
rewrite-expression-head
Rules
42×add-cbrt-cube add-exp-log
16×prod-exp cbrt-unprod
14×*-un-lft-identity
13×add-log-exp
10×cbrt-undiv div-exp
9×pow1
7×add-sqr-sqrt
5×add-cube-cbrt
4×insert-posit16
3×sum-log diff-log associate-*l* pow-prod-down sin-mult distribute-lft-out distribute-lft-out--
2×clear-num associate-/r* frac-2neg times-frac associate-*r/ associate-/r/ cos-mult div-inv associate-/l* associate-/l/
1×sub-neg flip3-- associate-*r* associate--l+ *-commutative flip-- difference-of-squares
Calls
4 calls:
Slowest
688.0ms
(- (+ (/ (* (cos a) (sin z)) (cos z)) (+ (/ (* (sin a) (* (sin z) (sin y))) (* (cos y) (cos z))) (/ (* (cos a) (sin y)) (cos y)))) (sin a))
31.0ms
(/ (* (sin a) (* (sin z) (sin y))) (* (cos y) (cos z)))
11.0ms
(* (sin a) (* (sin z) (sin y)))
11.0ms
(/ (* (sin z) (sin y)) (* (cos y) (cos z)))

series747.0ms

Calls
4 calls:
Slowest
352.0ms
(- (+ (/ (* (cos a) (sin z)) (cos z)) (+ (/ (* (sin a) (* (sin z) (sin y))) (* (cos y) (cos z))) (/ (* (cos a) (sin y)) (cos y)))) (sin a))
188.0ms
(/ (* (sin a) (* (sin z) (sin y))) (* (cos y) (cos z)))
110.0ms
(/ (* (sin z) (sin y)) (* (cos y) (cos z)))
97.0ms
(* (sin a) (* (sin z) (sin y)))

simplify16.6s

Calls
60 calls:
Slowest
1.6s
(/ (* (* (* (sin a) (sin a)) (sin a)) (* (* (* (sin z) (sin z)) (sin z)) (* (* (sin y) (sin y)) (sin y)))) (* (* (* (cos y) (cos y)) (cos y)) (* (* (cos z) (cos z)) (cos z))))
1.3s
(/ (* (* (* (sin a) (sin a)) (sin a)) (* (* (* (sin z) (sin y)) (* (sin z) (sin y))) (* (sin z) (sin y)))) (* (* (* (cos y) (cos y)) (cos y)) (* (* (cos z) (cos z)) (cos z))))
1.3s
(/ (* (* (* (sin a) (* (sin z) (sin y))) (* (sin a) (* (sin z) (sin y)))) (* (sin a) (* (sin z) (sin y)))) (* (* (* (cos y) (cos y)) (cos y)) (* (* (cos z) (cos z)) (cos z))))
1.2s
(/ (* (* (* (sin a) (sin a)) (sin a)) (* (* (* (sin z) (sin z)) (sin z)) (* (* (sin y) (sin y)) (sin y)))) (* (* (* (cos y) (cos z)) (* (cos y) (cos z))) (* (cos y) (cos z))))
1.0s
(/ (* (* (* (sin a) (sin a)) (sin a)) (* (* (* (sin z) (sin y)) (* (sin z) (sin y))) (* (sin z) (sin y)))) (* (* (* (cos y) (cos z)) (* (cos y) (cos z))) (* (cos y) (cos z))))

prune2.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

1.3b
(/ (- (* (+ (tan y) (tan z)) (* (- (tan y) (tan z)) (+ (cos a) (* (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (cos a))))) (* (* (sin a) (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z)))))) (- (tan y) (tan z)))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (- (tan y) (tan z)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z))))))))
0.3b
(* (+ (tan y) (tan z)) (* (- (tan y) (tan z)) (+ (cos a) (* (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (cos a)))))
0.3b
(* (* (sin a) (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z)))))) (- (tan y) (tan z)))
0.2b
(* (* (tan y) (tan z)) (* (tan y) (tan z)))

rewrite355.0ms

Algorithm
rewrite-expression-head
Rules
1029×frac-times
922×tan-quot
817×frac-sub
791×associate-*r/
523×associate-/l/
504×flip3-- flip--
348×flip3-+ flip-+
326×associate-*l/
145×frac-add
44×add-cbrt-cube add-exp-log
41×pow1
35×associate-/r/
22×prod-exp cbrt-unprod
19×pow-prod-down
12×*-un-lft-identity
10×add-sqr-sqrt
8×add-cube-cbrt
7×associate-*r*
6×distribute-rgt-in distribute-lft-in associate-*l*
5×cbrt-undiv div-exp
4×pow-prod-up insert-posit16 sub-div add-log-exp
3×times-frac *-commutative associate-/l*
2×sub-neg pow-plus
1×pow2 clear-num associate-/r* frac-2neg div-sub div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Calls
4 calls:
Slowest
201.0ms
(/ (- (* (+ (tan y) (tan z)) (* (- (tan y) (tan z)) (+ (cos a) (* (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (cos a))))) (* (* (sin a) (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z)))))) (- (tan y) (tan z)))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (- (tan y) (tan z)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z))))))))
47.0ms
(* (+ (tan y) (tan z)) (* (- (tan y) (tan z)) (+ (cos a) (* (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (cos a)))))
35.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
26.0ms
(* (* (sin a) (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z)))))) (- (tan y) (tan z)))

series3.2s

Calls
4 calls:
Slowest
2.1s
(/ (- (* (+ (tan y) (tan z)) (* (- (tan y) (tan z)) (+ (cos a) (* (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (cos a))))) (* (* (sin a) (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z)))))) (- (tan y) (tan z)))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (- (tan y) (tan z)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z))))))))
691.0ms
(* (+ (tan y) (tan z)) (* (- (tan y) (tan z)) (+ (cos a) (* (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (cos a)))))
339.0ms
(* (* (sin a) (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z)))))) (- (tan y) (tan z)))
104.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))

simplify2.7m

Calls
764 calls:
Slowest
925.0ms
(- (* (* (+ (tan y) (tan z)) (* (- (tan y) (tan z)) (- (* (cos a) (cos a)) (* (* (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (cos a)) (* (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (cos a)))))) (+ 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z)))))) (* (- (cos a) (* (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (cos a))) (* (* (sin a) (- (* 1 1) (* (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z))))))) (- (tan y) (tan z)))))
885.0ms
(- (* (* (+ (tan y) (tan z)) (* (- (* (sin y) (cos z)) (* (cos y) (sin z))) (- (* (cos a) (cos a)) (* (* (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (cos a)) (* (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (cos a)))))) (* (cos y) (cos z))) (* (* (* (cos y) (cos z)) (- (cos a) (* (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (cos a)))) (* (* (sin a) (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z)))))) (- (* (sin y) (cos z)) (* (cos y) (sin z))))))
849.0ms
(* (* (* (+ (tan y) (tan z)) (+ (tan y) (tan z))) (+ (tan y) (tan z))) (* (* (* (- (tan y) (tan z)) (+ (cos a) (* (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (cos a)))) (* (- (tan y) (tan z)) (+ (cos a) (* (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (cos a))))) (* (- (tan y) (tan z)) (+ (cos a) (* (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (cos a))))))
836.0ms
(* (* (* (+ (tan y) (tan z)) (+ (tan y) (tan z))) (+ (tan y) (tan z))) (* (* (* (- (tan y) (tan z)) (- (tan y) (tan z))) (- (tan y) (tan z))) (* (* (+ (cos a) (* (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (cos a))) (+ (cos a) (* (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (cos a)))) (+ (cos a) (* (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (cos a))))))
807.0ms
(- (* (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (* (- (* (sin y) (cos z)) (* (cos y) (sin z))) (+ (cos a) (* (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (cos a))))) (* (cos y) (cos z))) (* (* (- (tan y) (tan z)) (* (cos y) (cos z))) (* (* (sin a) (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z)))))) (- (* (sin y) (cos z)) (* (cos y) (sin z))))))

prune21.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes731.0ms

Accuracy

0% (0.1b remaining)

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

bsearch8.0ms

end0.0ms

sample10.2s

Algorithm
intervals
Results
6.1s3894×body1280valid
1.9s2018×body640valid
900.0ms8000×pre80true
528.0ms1111×body80valid
445.0ms715×body320valid
166.0ms262×body160valid