Details

Time bar (total: 39.0s)

sample524.0ms

Algorithm
intervals
Results
292.0ms122×body1280valid
133.0ms74×body640valid
34.0ms256×pre80true
15.0ms16×body320valid
10.0ms36×body80valid
4.0ms8×body160valid

simplify55.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
55.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize35.0ms

Local error

Found 3 expressions with local error:

2.3b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite43.0ms

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
22.0ms
(- (tan (+ y z)) (tan a))
11.0ms
(+ x (- (tan (+ y z)) (tan a)))
9.0ms
(tan (+ y z))

series423.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
187.0ms
(+ x (- (tan (+ y z)) (tan a)))
173.0ms
(- (tan (+ y z)) (tan a))
63.0ms
(tan (+ y z))

simplify1.3s

Counts
25 → 54
Calls
25 calls:
Slowest
367.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
137.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
132.0ms
(+ (* 1/3 (pow y 3)) (+ z y))
97.0ms
(* (exp x) (/ (exp (tan (+ y z))) (exp (tan a))))
93.0ms
(* (exp x) (exp (- (tan (+ y z)) (tan a))))

prune523.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan y) (tan z))
0.2b
(- (/ (+ (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))

rewrite192.0ms

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
116.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
50.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
18.0ms
(* (tan y) (tan z))
7.0ms
(+ (tan y) (tan z))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
536.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
479.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
155.0ms
(+ (tan y) (tan z))
116.0ms
(* (tan y) (tan z))

simplify3.6s

Counts
45 → 83
Calls
45 calls:
Slowest
383.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
381.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
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))))))) (/ (sin a) (cos a)))
297.0ms
(- (+ (/ (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)))
273.0ms
(- (+ (/ (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)))

prune936.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite315.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt *-un-lft-identity
11×add-cbrt-cube add-exp-log add-log-exp
8×add-cube-cbrt
6×pow1
4×times-frac insert-posit16
3×associate-/r* associate-*r* associate-*l* tan-quot
2×cbrt-undiv associate-+r+ sum-log sub-neg diff-log div-exp associate-*l/ prod-exp cbrt-unprod distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative clear-num associate-+r- frac-2neg flip3-+ flip3-- pow-prod-down *-commutative frac-sub flip-+ div-inv flip-- associate-/l* unswap-sqr associate-/l/
Counts
4 → 78
Calls
4 calls:
Slowest
184.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
101.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
14.0ms
(/ (* (tan y) (sin z)) (cos z))
14.0ms
(* (tan y) (sin z))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
527.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
454.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
130.0ms
(/ (* (tan y) (sin z)) (cos z))
99.0ms
(* (tan y) (sin z))

simplify4.6s

Counts
53 → 90
Calls
53 calls:
Slowest
338.0ms
(* (- 1 (/ (* (tan y) (sin z)) (cos z))) (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)))))) x)) (/ (sin a) (cos a)))
281.0ms
(- (+ (* 1/3 (* z (pow y 3))) (* z y)) (* 1/6 (* (pow z 3) y)))
280.0ms
(- (+ (/ (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)))
276.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a)))

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize73.0ms

Local error

Found 4 expressions with local error:

3.1b
(log (exp (* (tan y) (sin z))))
0.2b
(* (tan y) (sin z))
0.2b
(- (/ (+ (tan y) (tan z)) (- 1 (/ (log (exp (* (tan y) (sin z)))) (cos z)))) (tan a))
0.1b
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (log (exp (* (tan y) (sin z)))) (cos z)))) (tan a)))

rewrite482.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt *-un-lft-identity
12×add-log-exp
7×pow1 add-cube-cbrt
6×add-cbrt-cube add-exp-log
4×insert-posit16
3×log-prod associate-*r* associate-*l* log-pow
2×associate-+r+ sum-log sub-neg diff-log tan-quot distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative exp-prod associate-+r- flip3-+ times-frac flip3-- exp-to-pow rem-log-exp pow-prod-down associate-*l/ prod-exp *-commutative frac-sub cbrt-unprod flip-+ flip-- unswap-sqr
Counts
4 → 70
Calls
4 calls:
Slowest
255.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (log (exp (* (tan y) (sin z)))) (cos z)))) (tan a)))
209.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (log (exp (* (tan y) (sin z)))) (cos z)))) (tan a))
12.0ms
(* (tan y) (sin z))
5.0ms
(log (exp (* (tan y) (sin z))))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
555.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (log (exp (* (tan y) (sin z)))) (cos z)))) (tan a))
437.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (log (exp (* (tan y) (sin z)))) (cos z)))) (tan a)))
112.0ms
(* (tan y) (sin z))
78.0ms
(log (exp (* (tan y) (sin z))))

simplify5.5s

Counts
44 → 82
Calls
44 calls:
Slowest
387.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (sin z) (sin z)) (sin z)))
364.0ms
(* (exp x) (/ (exp (/ (+ (tan y) (tan z)) (- 1 (/ (log (exp (* (tan y) (sin z)))) (cos z))))) (exp (tan a))))
329.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (log (exp (* (tan y) (sin z)))) (cos z))) (sin a)))
305.0ms
(- (+ (/ (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)))
304.0ms
(/ (exp (/ (+ (tan y) (tan z)) (- 1 (/ (log (exp (* (tan y) (sin z)))) (cos z))))) (exp (tan a)))

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes462.0ms

Accuracy

0% (0.2b remaining)

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

bsearch7.0ms

end0.0ms

sample13.6s

Algorithm
intervals
Results
8.2s3885×body1280valid
3.1s1935×body640valid
862.0ms8000×pre80true
618.0ms714×body320valid
335.0ms1189×body80valid
167.0ms277×body160valid