Details

Time bar (total: 1.6m)

sample544.0ms

Algorithm
intervals
Results
331.0ms121×body1280valid
93.0ms68×body640valid
37.0ms256×pre80true
23.0ms24×body320valid
11.0ms37×body80valid
4.0ms6×body160valid

simplify45.0ms

Calls
1 calls:
Slowest
45.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

localize19.0ms

Local error

Found 3 expressions with local error:

3.0b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite16.0ms

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
7.0ms
(- (tan (+ y z)) (tan a))
5.0ms
(+ x (- (tan (+ y z)) (tan a)))
2.0ms
(tan (+ y z))

series344.0ms

Calls
3 calls:
Slowest
145.0ms
(- (tan (+ y z)) (tan a))
143.0ms
(+ x (- (tan (+ y z)) (tan a)))
56.0ms
(tan (+ y z))

simplify2.0s

Calls
50 calls:
Slowest
310.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
175.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
78.0ms
(- (+ (/ (sin (+ z y)) (cos (+ z y))) x) (/ (sin a) (cos a)))
71.0ms
(- (+ (/ (sin (+ z y)) (cos (+ z y))) x) (/ (sin a) (cos a)))
69.0ms
(+ (* 1/3 (pow y 3)) (+ z y))

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize65.0ms

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

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
28×associate-*l/
16×tan-quot
13×add-cbrt-cube add-exp-log
12×frac-sub
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×flip3-- flip--
8×pow1 associate-/l/
6×associate-*r* associate-*l* add-log-exp
4×expm1-log1p-u flip3-+ frac-add flip-+ insert-posit16 log1p-expm1-u
3×times-frac prod-exp cbrt-unprod associate-/l*
2×frac-times cbrt-undiv div-exp pow-prod-down associate-*r/ associate-/r/ *-commutative
1×clear-num associate-/r* sub-neg frac-2neg fma-neg diff-log div-sub prod-diff div-inv
Calls
4 calls:
Slowest
42.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
19.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
5.0ms
(* (tan y) (tan z))
5.0ms
(* (tan y) (tan z))

series1.7s

Calls
4 calls:
Slowest
1.1s
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
401.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
115.0ms
(* (tan y) (tan z))
111.0ms
(* (tan y) (tan z))

simplify14.5s

Calls
76 calls:
Slowest
720.0ms
(* (- (tan y) (tan z)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z))))))
614.0ms
(* (+ (* (tan y) (tan y)) (- (* (tan z) (tan z)) (* (tan y) (tan z)))) (+ 1 (* (tan y) (tan z))))
551.0ms
(/ (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (cos a)))
494.0ms
(* (- (tan y) (tan z)) (+ 1 (* (tan y) (tan z))))
463.0ms
(- (* (* (+ (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

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize90.0ms

Local error

Found 4 expressions with local error:

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

rewrite319.0ms

Algorithm
rewrite-expression-head
Rules
114×associate-*l/
72×frac-times
59×add-cbrt-cube add-exp-log
51×associate-*r/
45×pow1
42×associate-/l/
40×frac-sub
36×flip3-+ tan-quot cos-mult flip-+
32×prod-exp cbrt-unprod
25×flip3-- flip--
22×pow-prod-down
17×associate-/r/
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×cbrt-undiv div-exp
5×associate-*r* associate-*l*
4×expm1-log1p-u pow-prod-up insert-posit16 log1p-expm1-u add-log-exp
3×times-frac *-commutative associate-/l*
2×pow-plus
1×pow2 clear-num associate-/r* frac-2neg div-sub div-inv
Calls
4 calls:
Slowest
228.0ms
(/ (- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ 1 (* (tan y) (tan z)))) (* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (* (cos y) (cos z)) (+ 1 (* (tan y) (tan z))))))
41.0ms
(* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))
40.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
5.0ms
(* (tan y) (tan z))

series1.8s

Calls
4 calls:
Slowest
1.3s
(/ (- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ 1 (* (tan y) (tan z)))) (* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (* (cos y) (cos z)) (+ 1 (* (tan y) (tan z))))))
232.0ms
(* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))
129.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
120.0ms
(* (tan y) (tan z))

simplify29.8s

Calls
175 calls:
Slowest
863.0ms
(/ (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ 1 (* (tan y) (tan z)))) (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (* (cos y) (cos z)) (+ 1 (* (tan y) (tan z))))))
815.0ms
(/ (- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ 1 (* (tan y) (tan z)))) (* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a)))) (* (* (cos y) (cos z)) (+ 1 (* (tan y) (tan z)))))
672.0ms
(* (+ 1 (* (tan y) (tan z))) (* 2 (- 1 (* (tan y) (tan z)))))
660.0ms
(* (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z))))) (* 2 (- 1 (* (tan y) (tan z)))))
575.0ms
(- (log (- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ 1 (* (tan y) (tan z)))) (* (* (cos y) (cos z)) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (sin a))))) (+ (+ (log (- 1 (* (tan y) (tan z)))) (log (cos a))) (+ (+ (log (cos y)) (log (cos z))) (log (+ 1 (* (tan y) (tan z)))))))

prune5.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

1.3b
(/ (fma (+ (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))) (* (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (* (- (tan y) (tan z)) (- (sin a))))) (* (* (- 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))))))))
0.4b
(fma (+ (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))) (* (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (* (- (tan y) (tan z)) (- (sin a)))))
0.3b
(* (- (tan y) (tan z)) (- (sin a)))
0.2b
(* (* (tan y) (tan z)) (* (tan y) (tan z)))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
57×frac-times
52×tan-quot
49×associate-*l/
36×add-cbrt-cube add-exp-log
35×associate-/r/
33×pow1
28×associate-*r/
22×flip3-- flip--
17×prod-exp cbrt-unprod
14×pow-prod-down
12×add-sqr-sqrt *-un-lft-identity flip3-+ flip-+
11×associate-*r*
10×frac-sub add-cube-cbrt
6×associate-*l*
5×cbrt-undiv div-exp
4×expm1-log1p-u pow-prod-up insert-posit16 log1p-expm1-u add-log-exp
3×distribute-lft-neg-in distribute-rgt-neg-in times-frac associate-/l*
2×pow-plus *-commutative
1×pow2 clear-num associate-/r* neg-mul-1 frac-2neg distribute-rgt-neg-out fma-udef div-inv distribute-lft-out-- difference-of-squares
Calls
4 calls:
Slowest
73.0ms
(/ (fma (+ (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))) (* (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (* (- (tan y) (tan z)) (- (sin a))))) (* (* (- 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))))))))
20.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
13.0ms
(* (- (tan y) (tan z)) (- (sin a)))
0.0ms
(fma (+ (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))) (* (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (* (- (tan y) (tan z)) (- (sin a)))))

series2.7s

Calls
4 calls:
Slowest
1.5s
(/ (fma (+ (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))) (* (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (* (- (tan y) (tan z)) (- (sin a))))) (* (* (- 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))))))))
937.0ms
(fma (+ (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))) (* (- 1 (* (* (tan y) (tan z)) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (* (- (tan y) (tan z)) (- (sin a)))))
145.0ms
(* (- (tan y) (tan z)) (- (sin a)))
96.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))

simplify19.6s

Calls
133 calls:
Slowest
696.0ms
(/ (- (+ (/ (* (sin a) (sin z)) (cos z)) (+ (/ (* (cos a) (pow (sin y) 2)) (pow (cos y) 2)) (+ (/ (* (cos a) (* (sin z) (pow (sin y) 3))) (* (pow (cos y) 3) (cos z))) (+ (/ (* (sin a) (* (pow (sin z) 3) (pow (sin y) 4))) (* (pow (cos y) 4) (pow (cos z) 3))) (/ (* (cos a) (* (pow (sin z) 2) (pow (sin y) 4))) (* (pow (cos y) 4) (pow (cos z) 2))))))) (+ (/ (* (cos a) (* (pow (sin z) 4) (pow (sin y) 2))) (* (pow (cos y) 2) (pow (cos z) 4))) (+ (/ (* (sin a) (sin y)) (cos y)) (+ (/ (* (cos a) (* (pow (sin z) 3) (sin y))) (* (cos y) (pow (cos z) 3))) (+ (/ (* (sin a) (* (pow (sin z) 4) (pow (sin y) 3))) (* (pow (cos y) 3) (pow (cos z) 4))) (/ (* (cos a) (pow (sin z) 2)) (pow (cos z) 2))))))) (* (cos a) (* (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))) (* (- (/ (sin y) (cos y)) (/ (sin z) (cos z))) (+ (/ (* (pow (sin z) 2) (pow (sin y) 2)) (* (pow (cos y) 2) (pow (cos z) 2))) (+ (/ (* (sin z) (sin y)) (* (cos y) (cos z))) 1))))))
691.0ms
(* (+ (* 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)))))))))
561.0ms
(* (+ (* 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))))))
522.0ms
(* (+ 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)))))))))
498.0ms
(* (- (tan y) (tan z)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z))))))

prune3.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes842.0ms

Accuracy

0% (0.1b remaining)

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

bsearch9.0ms

end0.0ms

sample11.9s

Algorithm
intervals
Results
6.8s3894×body1280valid
2.6s2018×body640valid
715.0ms8000×pre80true
599.0ms1111×body80valid
598.0ms715×body320valid
166.0ms262×body160valid