Details

Time bar (total: 3.3m)

sample510.0ms

Algorithm
intervals
Results
321.0ms131×body1280valid
75.0ms60×body640valid
36.0ms256×pre80true
25.0ms22×body320valid
8.0ms34×body80valid
5.0ms9×body160valid

simplify82.0ms

Calls
1 calls:
Slowest
82.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize486.0ms

Local error

Found 3 expressions with local error:

4.3b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt *-un-lft-identity prod-diff
16×add-cube-cbrt
11×associate-+r+
5×add-log-exp
4×tan-quot
3×expm1-log1p-u pow1 add-cbrt-cube fma-neg add-exp-log insert-posit16 log1p-expm1-u
2×tan-sum sub-neg frac-sub
1×+-commutative associate-+r- flip3-+ flip3-- diff-log flip-+ flip-- distribute-lft-out-- difference-of-squares
Calls
3 calls:
Slowest
21.0ms
(- (tan (+ y z)) (tan a))
8.0ms
(+ x (- (tan (+ y z)) (tan a)))
4.0ms
(tan (+ y z))

series341.0ms

Calls
3 calls:
Slowest
163.0ms
(+ x (- (tan (+ y z)) (tan a)))
127.0ms
(- (tan (+ y z)) (tan a))
50.0ms
(tan (+ y z))

simplify2.2s

Calls
50 calls:
Slowest
328.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
179.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
106.0ms
(- (+ (/ (sin (+ z y)) (cos (+ z y))) x) (/ (sin a) (cos a)))
80.0ms
(+ (* 1/3 (pow y 3)) (+ z y))
77.0ms
(- (+ (/ (sin (+ z y)) (cos (+ z y))) x) (/ (sin a) (cos a)))

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize52.0ms

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

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
145×*-un-lft-identity
108×prod-diff
104×add-sqr-sqrt
99×add-cube-cbrt
85×times-frac
56×associate-+r+
22×distribute-lft-out
18×fma-neg
14×associate-/r/
8×flip3-- flip-- add-log-exp
7×tan-quot div-inv
6×pow1 add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-def associate-*r* associate-*l*
2×+-commutative sub-neg flip3-+ flip-+ difference-of-squares
1×frac-times associate-+r- sum-log diff-log pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod distribute-lft-out--
Calls
4 calls:
Slowest
55.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
46.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
11.0ms
(* (tan y) (tan z))
10.0ms
(+ (tan y) (tan z))

series1.2s

Calls
4 calls:
Slowest
493.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
449.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
112.0ms
(* (tan y) (tan z))
105.0ms
(+ (tan y) (tan z))

simplify18.7s

Calls
220 calls:
Slowest
491.0ms
(fma (/ 1 (* (cbrt (- 1 (* (tan y) (tan z)))) (cbrt (- 1 (* (tan y) (tan z)))))) (/ (+ (tan y) (tan z)) (cbrt (- 1 (* (tan y) (tan z))))) (- (* (sqrt (tan a)) (sqrt (tan a)))))
478.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
471.0ms
(fma (/ 1 (* (cbrt (- 1 (* (tan y) (tan z)))) (cbrt (- 1 (* (tan y) (tan z)))))) (/ (+ (tan y) (tan z)) (cbrt (- 1 (* (tan y) (tan z))))) (- (* (sqrt (tan a)) (sqrt (tan a)))))
422.0ms
(/ (+ (tan y) (tan z)) (- (pow 1 3) (pow (* (tan y) (tan z)) 3)))
418.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (* (tan a) 1)))

prune3.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan y) (sin z))
0.2b
(/ (* (tan y) (sin z)) (cos z))
0.2b
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
0.1b
(+ (tan y) (tan z))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
87×*-un-lft-identity
64×add-sqr-sqrt
59×add-cube-cbrt
54×prod-diff
52×times-frac
18×fma-neg
13×distribute-lft-out
11×add-cbrt-cube add-exp-log
8×associate-/r/ add-log-exp
6×pow1
5×flip3-- tan-quot div-inv flip--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* fma-def 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-+ diff-log pow-prod-down frac-add *-commutative frac-sub flip-+ associate-/l* distribute-lft-out-- associate-/l/
Calls
4 calls:
Slowest
76.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
18.0ms
(/ (* (tan y) (sin z)) (cos z))
11.0ms
(* (tan y) (sin z))
5.0ms
(+ (tan y) (tan z))

series760.0ms

Calls
4 calls:
Slowest
456.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
117.0ms
(/ (* (tan y) (sin z)) (cos z))
97.0ms
(+ (tan y) (tan z))
90.0ms
(* (tan y) (sin z))

simplify16.4s

Calls
175 calls:
Slowest
532.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z))))) (+ 1 (/ (* (tan y) (sin z)) (cos z))) (- (* (tan a) 1)))
351.0ms
(/ (+ (tan y) (tan z)) (- (pow 1 3) (pow (/ (* (tan y) (sin z)) (cos z)) 3)))
306.0ms
(fma (/ (* (cbrt (+ (tan y) (tan z))) (cbrt (+ (tan y) (tan z)))) (* (cbrt (- 1 (/ (* (tan y) (sin z)) (cos z)))) (cbrt (- 1 (/ (* (tan y) (sin z)) (cos z)))))) (/ (cbrt (+ (tan y) (tan z))) (cbrt (- 1 (/ (* (tan y) (sin z)) (cos z))))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
298.0ms
(fma (/ 1 (* (cbrt (- 1 (/ (* (tan y) (sin z)) (cos z)))) (cbrt (- 1 (/ (* (tan y) (sin z)) (cos z)))))) (/ (+ (tan y) (tan z)) (cbrt (- 1 (/ (* (tan y) (sin z)) (cos z))))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
292.0ms
(fma (/ 1 (sqrt (- 1 (/ (* (tan y) (sin z)) (cos z))))) (/ (+ (tan y) (tan z)) (sqrt (- 1 (/ (* (tan y) (sin z)) (cos z))))) (- (* (sqrt (tan a)) (sqrt (tan a)))))

prune2.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

3.7b
(cbrt (* (* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))))
0.5b
(* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
0.3b
(* (* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
0.3b
(* (tan y) (sin z))

rewrite587.0ms

Algorithm
rewrite-expression-head
Rules
255×*-un-lft-identity
216×prod-diff
192×add-sqr-sqrt
177×add-cube-cbrt
171×frac-times
147×times-frac
116×flip3-- flip--
112×distribute-rgt-in distribute-lft-in
105×tan-quot
104×frac-sub
63×cbrt-div
58×associate-*l/
36×distribute-lft-out
33×associate-*r/
25×pow1
24×associate-/r/
15×associate-*r*
13×add-cbrt-cube add-exp-log
12×div-inv
10×associate-*l*
6×pow-plus pow-prod-up difference-of-squares
5×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u sub-neg insert-posit16 log1p-expm1-u add-log-exp
3×pow2 *-commutative distribute-lft-out--
2×pow3
1×cbrt-prod pow1/3 rem-cbrt-cube
Calls
4 calls:
Slowest
260.0ms
(* (* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
172.0ms
(cbrt (* (* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))))
138.0ms
(* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
5.0ms
(* (tan y) (sin z))

series1.4s

Calls
4 calls:
Slowest
549.0ms
(* (* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
426.0ms
(* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
359.0ms
(cbrt (* (* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))))
64.0ms
(* (tan y) (sin z))

simplify2.2m

Calls
481 calls:
Slowest
965.0ms
(cbrt (* (* (- (* (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z))))) (* (tan a) (tan a))) (- (* (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z))))) (* (tan a) (tan a)))) (- (* (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z))))) (* (tan a) (tan a)))))
946.0ms
(* (fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))) (* (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))))
827.0ms
(* (* (- (* (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z))))) (* (tan a) (tan a))) (- (* (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z))))) (* (tan a) (tan a)))) (- (* (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z))))) (* (tan a) (tan a))))
785.0ms
(* (* (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a))) (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a))))
776.0ms
(* (* (+ (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (cos a))) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (cos a)))

prune7.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes336.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample11.4s

Algorithm
intervals
Results
6.9s3906×body1280valid
2.3s2010×body640valid
854.0ms8000×pre80true
550.0ms1099×body80valid
466.0ms706×body320valid
110.0ms279×body160valid