Details

Time bar (total: 1.0m)

sample531.0ms

Algorithm
intervals
Results
309.0ms130×body1280valid
112.0ms56×body640valid
32.0ms256×pre80true
22.0ms22×body320valid
12.0ms40×body80valid
5.0ms8×body160valid

simplify453.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
453.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize18.0ms

Local error

Found 3 expressions with local error:

3.4b
(tan (+ y z))
0.1b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite38.0ms

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
19.0ms
(+ x (- (tan (+ y z)) (tan a)))
13.0ms
(- (tan (+ y z)) (tan a))
6.0ms
(tan (+ y z))

series404.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
164.0ms
(- (tan (+ y z)) (tan a))
160.0ms
(+ x (- (tan (+ y z)) (tan a)))
79.0ms
(tan (+ y z))

simplify4.1s

Counts
62 → 54
Calls
62 calls:
Slowest
467.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
448.0ms
(- (* x x) (* (- (tan (+ y z)) (tan a)) (- (tan (+ y z)) (tan a))))
423.0ms
(* (* (- (tan (+ y z)) (tan a)) (- (tan (+ y z)) (tan a))) (- (tan (+ y z)) (tan a)))
237.0ms
(- (pow (tan (+ y z)) 3) (pow (tan a) 3))
216.0ms
(+ (* x x) (- (* (- (tan (+ y z)) (tan a)) (- (tan (+ y z)) (tan a))) (* x (- (tan (+ y z)) (tan a)))))

prune645.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite184.0ms

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
104.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
54.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
18.0ms
(* (tan y) (tan z))
7.0ms
(+ (tan y) (tan z))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
567.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
565.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
145.0ms
(+ (tan y) (tan z))
120.0ms
(* (tan y) (tan z))

simplify8.8s

Counts
92 → 83
Calls
92 calls:
Slowest
714.0ms
(* (* (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))) (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
461.0ms
(+ (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (+ (* (tan a) (tan a)) (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))))
422.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
409.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
375.0ms
(- (+ (/ (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)))

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite226.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
12×*-un-lft-identity
11×add-cbrt-cube add-exp-log
8×add-cube-cbrt add-log-exp
6×pow1
5×tan-quot
4×times-frac insert-posit16
3×associate-/r* associate-*r* associate-*l*
2×cbrt-undiv div-exp associate-*l/ prod-exp cbrt-unprod difference-of-squares
1×+-commutative clear-num sum-log sub-neg frac-2neg flip3-+ flip3-- diff-log pow-prod-down frac-add *-commutative frac-sub flip-+ div-inv flip-- distribute-lft-out associate-/l* distribute-lft-out-- unswap-sqr associate-/l/
Counts
4 → 74
Calls
4 calls:
Slowest
157.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
31.0ms
(* (tan y) (sin z))
29.0ms
(/ (* (tan y) (sin z)) (cos z))
7.0ms
(+ (tan y) (tan z))

series933.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
566.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
143.0ms
(+ (tan y) (tan z))
122.0ms
(/ (* (tan y) (sin z)) (cos z))
103.0ms
(* (tan y) (sin z))

simplify7.7s

Counts
97 → 86
Calls
97 calls:
Slowest
392.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (sin z) (sin z)) (sin z)))
388.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a)))
380.0ms
(- (pow (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) 3) (pow (tan a) 3))
344.0ms
(- (+ (* 1/3 (* z (pow y 3))) (* z y)) (* 1/6 (* (pow z 3) y)))
339.0ms
(* (* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z))) (/ (* (tan y) (sin z)) (cos z)))

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize84.0ms

Local error

Found 4 expressions with local error:

3.6b
(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))
0.3b
(* (tan y) (tan y))
0.2b
(* (tan z) (tan z))
0.2b
(/ (* (tan y) (sin z)) (cos z))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
35×*-un-lft-identity tan-quot
25×add-cube-cbrt
23×times-frac
18×pow1
15×add-cbrt-cube add-exp-log
12×associate-/l/
11×difference-of-squares
10×frac-sub
9×associate-*l/
8×frac-times associate-/r* associate-*r/
6×swap-sqr associate-*r* associate-*l*
5×associate-/l* distribute-lft-out--
4×insert-posit16 add-log-exp
3×cbrt-undiv div-exp prod-exp associate-/r/ cbrt-unprod
2×pow2 clear-num frac-2neg pow-plus flip3-- pow-prod-down pow-sqr *-commutative pow-prod-up div-inv flip-- unswap-sqr
1×div-sub
Counts
4 → 138
Calls
4 calls:
Slowest
73.0ms
(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))
29.0ms
(/ (* (tan y) (sin z)) (cos z))
29.0ms
(* (tan z) (tan z))
27.0ms
(* (tan y) (tan y))

series555.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
311.0ms
(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))
140.0ms
(/ (* (tan y) (sin z)) (cos z))
52.0ms
(* (tan y) (tan y))
51.0ms
(* (tan z) (tan z))

simplify16.2s

Counts
182 → 150
Calls
182 calls:
Slowest
568.0ms
(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z)))
552.0ms
(/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (sqrt (- (tan y) (tan z))))
513.0ms
(sqrt (/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z))))
504.0ms
(cbrt (/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z))))
491.0ms
(real->posit16 (/ (- (* (tan y) (tan y)) (* (tan z) (tan z))) (- (tan y) (tan z))))

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

regimes381.0ms

Accuracy

0% (0.2b remaining)

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

bsearch6.0ms

end0.0ms

sample14.3s

Algorithm
intervals
Results
8.7s3800×body1280valid
2.8s2057×body640valid
1.0s691×body320valid
856.0ms8000×pre80true
332.0ms1165×body80valid
176.0ms287×body160valid