Details

Time bar (total: 2.3m)

sample492.0ms

Algorithm
intervals
Results
242.0ms104×body1280valid
87.0ms70×body640valid
65.0ms23×body320valid
32.0ms256×pre80true
19.0ms52×body80valid
5.0ms7×body160valid

simplify63.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
63.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.6b

localize33.0ms

Local error

Found 3 expressions with local error:

2.9b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
19×add-sqr-sqrt
18×prod-diff
17×add-cube-cbrt
11×associate-+r+
10×add-log-exp
4×tan-quot
3×expm1-log1p-u pow1 fma-def add-cbrt-cube fma-neg add-exp-log insert-posit16 log1p-expm1-u
2×tan-sum 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 → 75
Calls
3 calls:
Slowest
23.0ms
(+ x (- (tan (+ y z)) (tan a)))
20.0ms
(- (tan (+ y z)) (tan a))
6.0ms
(tan (+ y z))

series460.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
198.0ms
(+ x (- (tan (+ y z)) (tan a)))
183.0ms
(- (tan (+ y z)) (tan a))
79.0ms
(tan (+ y z))

simplify3.8s

Counts
56 → 84
Calls
56 calls:
Slowest
282.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
224.0ms
(fma 1 (tan (+ y z)) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
208.0ms
(fma (* (cbrt (tan (+ y z))) (cbrt (tan (+ y z)))) (cbrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
189.0ms
(+ (* 1/3 (pow y 3)) (+ z y))
177.0ms
(* (exp x) (exp (- (tan (+ y z)) (tan a))))

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize67.0ms

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))

rewrite141.0ms

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×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* 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 → 108
Calls
4 calls:
Slowest
76.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
35.0ms
(* (+ (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
741.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
233.0ms
(* (+ (tan y) (tan z)) (cos a))
140.0ms
(* (tan y) (tan z))
130.0ms
(* (tan y) (tan z))

simplify11.4s

Counts
77 → 120
Calls
77 calls:
Slowest
563.0ms
(- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))) (* (* (cos y) (cos z)) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (sin a))))
558.0ms
(- (* (* (- (* (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))))
533.0ms
(/ (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (cos a)))
529.0ms
(/ (* (* (- (* (+ (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))))
504.0ms
(- (* (* (+ (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))))

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize144.0ms

Local error

Found 4 expressions with local error:

2.3b
(/ (fma (+ (tan y) (tan z)) (* (- (tan y) (tan z)) (fma (cos a) (fma (* (tan y) (tan z)) (* (tan y) (tan z)) (* (tan y) (tan z))) (cos a))) (- (* (* (- (tan y) (tan z)) (sin a)) (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z)))))))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (- (tan y) (tan z)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z))))))))
0.3b
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
0.3b
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
0.3b
(fma (+ (tan y) (tan z)) (* (- (tan y) (tan z)) (fma (cos a) (fma (* (tan y) (tan z)) (* (tan y) (tan z)) (* (tan y) (tan z))) (cos a))) (- (* (* (- (tan y) (tan z)) (sin a)) (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z))))))))

rewrite958.0ms

Algorithm
rewrite-expression-head
Rules
82×pow1 tan-quot
74×frac-times
57×associate-*l/
46×add-cbrt-cube add-exp-log
39×associate-*r/
35×associate-/r/
34×pow-prod-down
24×prod-exp cbrt-unprod
21×flip3-- flip--
12×flip3-+ flip-+
9×frac-sub
8×pow-sqr pow-prod-up
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×cbrt-undiv div-exp
4×expm1-log1p-u pow-plus insert-posit16 log1p-expm1-u add-log-exp
3×times-frac associate-/l*
2×pow2 swap-sqr associate-*r* associate-*l* *-commutative
1×clear-num associate-/r* frac-2neg fma-udef div-inv
Counts
4 → 180
Calls
4 calls:
Slowest
728.0ms
(/ (fma (+ (tan y) (tan z)) (* (- (tan y) (tan z)) (fma (cos a) (fma (* (tan y) (tan z)) (* (tan y) (tan z)) (* (tan y) (tan z))) (cos a))) (- (* (* (- (tan y) (tan z)) (sin a)) (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z)))))))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (- (tan y) (tan z)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z))))))))
127.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
95.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
1.0ms
(fma (+ (tan y) (tan z)) (* (- (tan y) (tan z)) (fma (cos a) (fma (* (tan y) (tan z)) (* (tan y) (tan z)) (* (tan y) (tan z))) (cos a))) (- (* (* (- (tan y) (tan z)) (sin a)) (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z))))))))

series5.2s

Counts
4 → 12
Calls
4 calls:
Slowest
2.9s
(/ (fma (+ (tan y) (tan z)) (* (- (tan y) (tan z)) (fma (cos a) (fma (* (tan y) (tan z)) (* (tan y) (tan z)) (* (tan y) (tan z))) (cos a))) (- (* (* (- (tan y) (tan z)) (sin a)) (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z)))))))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (- (tan y) (tan z)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z))))))))
1.9s
(fma (+ (tan y) (tan z)) (* (- (tan y) (tan z)) (fma (cos a) (fma (* (tan y) (tan z)) (* (tan y) (tan z)) (* (tan y) (tan z))) (cos a))) (- (* (* (- (tan y) (tan z)) (sin a)) (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z))))))))
196.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
180.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))

simplify32.7s

Counts
182 → 192
Calls
182 calls:
Slowest
1.1s
(* (+ (* 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)))) (+ (* (* 1 1) (* 1 1)) (- (* (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z))))) (* (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))))))
900.0ms
(* (* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z))) (* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z))))
890.0ms
(* (* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z))) (* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z))))
858.0ms
(* (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z))))) (- (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z))))))
806.0ms
(* (+ 1 (* (tan y) (tan z))) (* (+ (* (tan y) (tan y)) (+ (* (tan z) (tan z)) (* (tan y) (tan z)))) (+ (* (* 1 1) (* 1 1)) (- (* (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z))))) (* (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))))))

prune4.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize65.0ms

Local error

Found 4 expressions with local error:

8.3b
(cbrt (* (* (+ (tan y) (tan z)) (cos a)) (* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a)))))
0.4b
(* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a)))
0.3b
(* (* (+ (tan y) (tan z)) (cos a)) (* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a))))
0.2b
(* (tan y) (tan z))

rewrite744.0ms

Algorithm
rewrite-expression-head
Rules
346×associate-*l/
212×tan-quot
173×pow1
172×frac-times
104×flip3-+ frac-add flip-+
78×pow-prod-down
63×cbrt-div
59×add-cbrt-cube add-exp-log
58×associate-*r/
40×prod-exp cbrt-unprod
34×pow-prod-up
12×pow-sqr
8×add-sqr-sqrt
6×*-un-lft-identity pow-plus add-cube-cbrt
5×associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow2 *-commutative
2×cube-unmult
1×cbrt-prod pow1/3 swap-sqr rem-cbrt-cube unswap-sqr
Counts
4 → 281
Calls
4 calls:
Slowest
345.0ms
(* (* (+ (tan y) (tan z)) (cos a)) (* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a))))
279.0ms
(cbrt (* (* (+ (tan y) (tan z)) (cos a)) (* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a)))))
93.0ms
(* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a)))
13.0ms
(* (tan y) (tan z))

series761.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
244.0ms
(* (* (+ (tan y) (tan z)) (cos a)) (* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a))))
212.0ms
(* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a)))
184.0ms
(cbrt (* (* (+ (tan y) (tan z)) (cos a)) (* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a)))))
122.0ms
(* (tan y) (tan z))

simplify53.9s

Counts
333 → 293
Calls
333 calls:
Slowest
903.0ms
(* (* (* (* (+ (tan y) (tan z)) (+ (tan y) (tan z))) (+ (tan y) (tan z))) (* (* (cos a) (cos a)) (cos a))) (* (* (* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a))) (* (+ (tan y) (tan z)) (cos a))) (* (* (* (+ (tan y) (tan z)) (+ (tan y) (tan z))) (+ (tan y) (tan z))) (* (* (cos a) (cos a)) (cos a)))))
768.0ms
(* (* (* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a))) (* (+ (tan y) (tan z)) (cos a))) (* (* (* (* (+ (tan y) (tan z)) (+ (tan y) (tan z))) (+ (tan y) (tan z))) (* (* (cos a) (cos a)) (cos a))) (* (* (* (+ (tan y) (tan z)) (+ (tan y) (tan z))) (+ (tan y) (tan z))) (* (* (cos a) (cos a)) (cos a)))))
674.0ms
(* (* (* (* (+ (tan y) (tan z)) (+ (tan y) (tan z))) (+ (tan y) (tan z))) (* (* (cos a) (cos a)) (cos a))) (* (* (* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a))) (* (+ (tan y) (tan z)) (cos a))) (* (* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a))) (* (+ (tan y) (tan z)) (cos a)))))
645.0ms
(* (* (* (* (+ (tan y) (tan z)) (+ (tan y) (tan z))) (+ (tan y) (tan z))) (* (* (cos a) (cos a)) (cos a))) (* (* (* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a))) (* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a)))) (* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a)))))
616.0ms
(* (* (* (* (+ (tan y) (tan z)) (+ (tan y) (tan z))) (+ (tan y) (tan z))) (* (* (cos a) (cos a)) (cos a))) (* (* (* (* (+ (tan y) (tan z)) (+ (tan y) (tan z))) (+ (tan y) (tan z))) (* (* (cos a) (cos a)) (cos a))) (* (* (* (+ (tan y) (tan z)) (cos a)) (* (+ (tan y) (tan z)) (cos a))) (* (+ (tan y) (tan z)) (cos a)))))

prune4.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

regimes845.0ms

Accuracy

0% (0.1b remaining)

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

bsearch13.0ms

end0.0ms

sample11.6s

Algorithm
intervals
Results
7.2s3913×body1280valid
2.4s2012×body640valid
719.0ms8000×pre80true
427.0ms665×body320valid
282.0ms1132×body80valid
165.0ms278×body160valid