Details

Time bar (total: 58.7s)

sample481.0ms

Algorithm
intervals
Results
301.0ms132×body1280valid
75.0ms61×body640valid
35.0ms256×pre80true
18.0ms21×body320valid
9.0ms35×body80valid
5.0ms7×body160valid

simplify79.0ms

Calls
1 calls:
Slowest
79.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize28.0ms

Local error

Found 3 expressions with local error:

2.8b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite24.0ms

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
13.0ms
(+ x (- (tan (+ y z)) (tan a)))
7.0ms
(- (tan (+ y z)) (tan a))
2.0ms
(tan (+ y z))

series449.0ms

Calls
3 calls:
Slowest
193.0ms
(+ x (- (tan (+ y z)) (tan a)))
187.0ms
(- (tan (+ y z)) (tan a))
69.0ms
(tan (+ y z))

simplify2.0s

Calls
50 calls:
Slowest
295.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
127.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
75.0ms
(fma (sqrt (tan (+ y z))) (sqrt (tan (+ y z))) (- (* (sqrt (tan a)) (sqrt (tan a)))))
69.0ms
(- (+ (/ (sin (+ z y)) (cos (+ z y))) x) (/ (sin a) (cos a)))
67.0ms
(fma 1 (tan (+ y z)) (- (* (sqrt (tan a)) (sqrt (tan a)))))

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
159×*-un-lft-identity
112×add-sqr-sqrt
108×prod-diff
107×add-cube-cbrt
97×times-frac
56×associate-+r+
25×distribute-lft-out
18×fma-neg
16×associate-/r/
9×flip3-- flip--
8×add-cbrt-cube add-exp-log div-inv
7×tan-quot
6×pow1 add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l*
3×associate-/r* associate-*r* associate-*l* associate-/l/
2×sub-neg flip3-+ flip-+ difference-of-squares
1×frac-times cbrt-undiv +-commutative clear-num associate-+r- frac-2neg diff-log div-exp pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod distribute-lft-out--
Calls
4 calls:
Slowest
74.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
30.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
26.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
5.0ms
(* (tan y) (tan z))

series1.8s

Calls
4 calls:
Slowest
659.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
628.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
343.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
162.0ms
(* (tan y) (tan z))

simplify21.6s

Calls
250 calls:
Slowest
696.0ms
(/ (* (* (+ (tan y) (tan z)) (+ (tan y) (tan z))) (+ (tan y) (tan z))) (* (* (- 1 (* (tan y) (tan z))) (- 1 (* (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))))
618.0ms
(fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z)))) (- (* (tan a) 1)))
534.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (* (tan a) 1)))
486.0ms
(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)))))
477.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (* (sqrt (tan a)) (sqrt (tan a)))))

prune3.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan y) (tan z))
0.3b
(* (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))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
19×associate-*l/
15×add-cbrt-cube add-exp-log
14×*-un-lft-identity tan-quot
12×add-sqr-sqrt add-cube-cbrt
10×pow1 associate-*l*
9×associate-*r*
8×associate-/l/
6×frac-sub
5×flip3-- flip--
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×flip3-+ times-frac pow-prod-down frac-add *-commutative flip-+ associate-/l*
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
Calls
4 calls:
Slowest
37.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
11.0ms
(* (+ (tan y) (tan z)) (cos a))
6.0ms
(* (tan y) (tan z))
5.0ms
(* (tan y) (tan z))

series1.3s

Calls
4 calls:
Slowest
721.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
235.0ms
(* (+ (tan y) (tan z)) (cos a))
187.0ms
(* (tan y) (tan z))
138.0ms
(* (tan y) (tan z))

simplify8.0s

Calls
71 calls:
Slowest
659.0ms
(/ (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (cos a)))
394.0ms
(- (* (* (+ (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))))
371.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (cos a))
366.0ms
(- (* (* (- (* (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))))
358.0ms
(/ (* (* (- (* (+ (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))))

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (* (tan y) (tan z)) 3)
0.3b
(* (tan y) (tan z))
0.3b
(* (tan y) (tan z))
0.3b
(* (tan y) (tan z))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
16×tan-quot
13×pow1 add-cbrt-cube add-exp-log
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×associate-*r* associate-*l*
4×expm1-log1p-u frac-times pow-prod-down associate-*l/ prod-exp associate-*r/ cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×cube-div *-commutative
2×pow-pow pow-exp rem-cube-cbrt
1×cube-mult pow-to-exp unpow-prod-down unpow3 cube-prod
Calls
4 calls:
Slowest
10.0ms
(* (tan y) (tan z))
5.0ms
(* (tan y) (tan z))
5.0ms
(* (tan y) (tan z))
5.0ms
(pow (* (tan y) (tan z)) 3)

series472.0ms

Calls
4 calls:
Slowest
136.0ms
(pow (* (tan y) (tan z)) 3)
122.0ms
(* (tan y) (tan z))
108.0ms
(* (tan y) (tan z))
106.0ms
(* (tan y) (tan z))

simplify2.1s

Calls
59 calls:
Slowest
279.0ms
(/ (* (pow (sin z) 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow (cos z) 3)))
279.0ms
(/ (* (pow (sin z) 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow (cos z) 3)))
239.0ms
(+ (* (pow z 5) (pow y 3)) (+ (* (pow z 3) (pow y 3)) (* (pow z 3) (pow y 5))))
130.0ms
(+ (* 1/3 (* (pow z 3) y)) (+ (* 1/3 (* z (pow y 3))) (* z y)))
130.0ms
(+ (* 1/3 (* (pow z 3) y)) (+ (* 1/3 (* z (pow y 3))) (* z y)))

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes471.0ms

Accuracy

0% (0.2b remaining)

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

bsearch7.0ms

end0.0ms

sample11.7s

Algorithm
intervals
Results
6.3s3952×body1280valid
2.3s1973×body640valid
1.4s8000×pre80true
532.0ms1094×body80valid
498.0ms669×body320valid
202.0ms312×body160valid