Details

Time bar (total: 47.6s)

sample543.0ms

Algorithm
intervals
Results
303.0ms122×body1280valid
131.0ms68×body640valid
31.0ms256×pre80true
22.0ms23×body320valid
9.0ms32×body80valid
7.0ms11×body160valid

simplify425.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
425.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize37.0ms

Local error

Found 3 expressions with local error:

3.8b
(tan (+ y z))
0.1b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite56.0ms

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
25.0ms
(- (tan (+ y z)) (tan a))
21.0ms
(+ x (- (tan (+ y z)) (tan a)))
9.0ms
(tan (+ y z))

series502.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
205.0ms
(- (tan (+ y z)) (tan a))
197.0ms
(+ x (- (tan (+ y z)) (tan a)))
100.0ms
(tan (+ y z))

simplify1.5s

Counts
25 → 54
Calls
25 calls:
Slowest
412.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
158.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
144.0ms
(+ (* 1/3 (pow y 3)) (+ z y))
101.0ms
(* (exp x) (/ (exp (tan (+ y z))) (exp (tan a))))
95.0ms
(* (exp x) (exp (- (tan (+ y z)) (tan a))))

prune586.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize64.0ms

Local error

Found 4 expressions with local error:

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

rewrite205.0ms

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
113.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
68.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
15.0ms
(* (tan y) (tan z))
9.0ms
(+ (tan y) (tan z))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
536.0ms
(- (/ (+ (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)))
127.0ms
(* (tan y) (tan z))
111.0ms
(+ (tan y) (tan z))

simplify3.8s

Counts
45 → 83
Calls
45 calls:
Slowest
384.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
341.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
336.0ms
(- (+ (/ (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)))
334.0ms
(- (+ (/ (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)))
322.0ms
(- (+ (/ (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)))

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

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

rewrite275.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
11×add-cbrt-cube add-exp-log add-log-exp
10×add-sqr-sqrt
8×add-cube-cbrt
6×pow1
4×tan-quot insert-posit16
3×associate-/r* sum-log times-frac associate-*r* associate-*l* distribute-lft-out
2×cbrt-undiv +-commutative associate-+r+ flip3-+ div-exp associate-*l/ prod-exp cbrt-unprod flip-+
1×clear-num associate-+r- sub-neg frac-2neg diff-log pow-prod-down frac-add *-commutative div-inv associate-/l* distribute-lft-out-- unswap-sqr associate-/l/
Counts
4 → 75
Calls
4 calls:
Slowest
228.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
17.0ms
(* (tan y) (sin z))
14.0ms
(+ (tan y) (tan z))
14.0ms
(/ (* (tan y) (sin z)) (cos z))

series844.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
501.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
131.0ms
(+ (tan y) (tan z))
122.0ms
(/ (* (tan y) (sin z)) (cos z))
90.0ms
(* (tan y) (sin z))

simplify3.4s

Counts
49 → 87
Calls
49 calls:
Slowest
362.0ms
(- (+ (/ (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)))
345.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (sin z) (sin z)) (sin z)))
335.0ms
(- (+ (/ (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
(- (+ (* 1/3 (* z (pow y 3))) (* z y)) (* 1/6 (* (pow z 3) y)))
267.0ms
(+ (* 1/3 (* (pow z 3) y)) (+ (* 1/3 (* z (pow y 3))) (* z y)))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize85.0ms

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

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
19×associate-*l/
18×add-sqr-sqrt
15×add-cbrt-cube add-exp-log
14×*-un-lft-identity tan-quot
12×add-cube-cbrt
10×pow1 associate-*l*
9×associate-*r*
8×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×frac-times cbrt-undiv div-exp associate-*r/ associate-/r/
1×clear-num associate-/r* frac-2neg div-sub div-inv distribute-lft-out
Counts
4 → 100
Calls
4 calls:
Slowest
68.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
26.0ms
(* (+ (tan y) (tan z)) (cos a))
14.0ms
(* (tan y) (tan z))
14.0ms
(* (tan y) (tan z))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
679.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
191.0ms
(* (+ (tan y) (tan z)) (cos a))
162.0ms
(* (tan y) (tan z))
141.0ms
(* (tan y) (tan z))

simplify11.1s

Counts
77 → 112
Calls
77 calls:
Slowest
664.0ms
(/ (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (cos a)))
573.0ms
(/ (* (* (- (* (+ (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))))
508.0ms
(- (* (* (+ (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))))
499.0ms
(/ (sqrt (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (- 1 (* (tan y) (tan z))))
482.0ms
(- (* (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (cos a)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))) (* (- (tan y) (tan z)) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (sin a))))

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes551.0ms

Accuracy

0% (0.1b remaining)

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

bsearch6.0ms

end0.0ms

sample16.4s

Algorithm
intervals
Results
10.3s3904×body1280valid
3.2s1955×body640valid
1.0s8000×pre80true
698.0ms722×body320valid
461.0ms1147×body80valid
194.0ms272×body160valid