Details

Time bar (total: 1.7m)

sample447.0ms

Algorithm
intervals
Results
269.0ms126×body1280valid
88.0ms67×body640valid
30.0ms256×pre80true
16.0ms19×body320valid
9.0ms35×body80valid
5.0ms9×body160valid

simplify81.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
81.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.0b

localize34.0ms

Local error

Found 3 expressions with local error:

2.3b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite63.0ms

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
38.0ms
(- (tan (+ y z)) (tan a))
14.0ms
(+ x (- (tan (+ y z)) (tan a)))
10.0ms
(tan (+ y z))

series492.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
219.0ms
(+ x (- (tan (+ y z)) (tan a)))
197.0ms
(- (tan (+ y z)) (tan a))
76.0ms
(tan (+ y z))

simplify3.7s

Counts
56 → 84
Calls
56 calls:
Slowest
247.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
220.0ms
(fma (sqrt (tan (+ y z))) (sqrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
204.0ms
(fma (* (cbrt (tan (+ y z))) (cbrt (tan (+ y z)))) (cbrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
192.0ms
(+ (* 1/3 (pow y 3)) (+ z y))
173.0ms
(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize53.0ms

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

rewrite236.0ms

Algorithm
rewrite-expression-head
Rules
151×*-un-lft-identity
108×prod-diff
107×add-sqr-sqrt
100×add-cube-cbrt
85×times-frac
56×associate-+r+
24×distribute-lft-out
18×fma-neg
14×associate-/r/
13×add-log-exp
8×flip3-- flip--
7×tan-quot div-inv
6×pow1 fma-def add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×sum-log associate-*r* associate-*l*
2×+-commutative sub-neg flip3-+ diff-log flip-+ distribute-lft-out-- difference-of-squares
1×frac-times associate-+r- pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod unswap-sqr
Counts
4 → 211
Calls
4 calls:
Slowest
110.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
99.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
13.0ms
(* (tan y) (tan z))
7.0ms
(+ (tan y) (tan z))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
671.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
545.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
167.0ms
(+ (tan y) (tan z))
146.0ms
(* (tan y) (tan z))

simplify25.7s

Counts
228 → 223
Calls
228 calls:
Slowest
882.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (* (tan a) 1)))
529.0ms
(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)))))
519.0ms
(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)))))
479.0ms
(fma (/ (* (cbrt (+ (tan y) (tan z))) (cbrt (+ (tan y) (tan z)))) (* (cbrt (- 1 (* (tan y) (tan z)))) (cbrt (- 1 (* (tan y) (tan z)))))) (/ (cbrt (+ (tan y) (tan z))) (cbrt (- 1 (* (tan y) (tan z))))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
473.0ms
(fma (/ 1 (sqrt (- 1 (* (tan y) (tan z))))) (/ (+ (tan y) (tan z)) (sqrt (- 1 (* (tan y) (tan z))))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))

prune2.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite329.0ms

Algorithm
rewrite-expression-head
Rules
321×*-un-lft-identity
237×add-sqr-sqrt
180×prod-diff
172×times-frac
146×add-cube-cbrt
92×associate-+r+
58×difference-of-squares
44×distribute-lft-out
30×fma-neg distribute-lft-out--
14×associate-/r/
11×add-cbrt-cube add-exp-log add-log-exp
8×flip3-- div-inv flip--
6×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* fma-def associate-*r* associate-*l* tan-quot
2×cbrt-undiv sum-log sub-neg diff-log div-exp associate-*l/ prod-exp cbrt-unprod
1×+-commutative clear-num associate-+r- frac-2neg flip3-+ pow-prod-down *-commutative frac-sub flip-+ associate-/l* unswap-sqr associate-/l/
Counts
4 → 299
Calls
4 calls:
Slowest
165.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
119.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
21.0ms
(/ (* (tan y) (sin z)) (cos z))
13.0ms
(* (tan y) (sin z))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
464.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
413.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
114.0ms
(/ (* (tan y) (sin z)) (cos z))
77.0ms
(* (tan y) (sin z))

simplify34.4s

Counts
354 → 311
Calls
354 calls:
Slowest
537.0ms
(fma (/ 1 (+ (sqrt 1) (sqrt (/ (* (tan y) (sin z)) (cos z))))) (/ (+ (tan y) (tan z)) (- (sqrt 1) (sqrt (/ (* (tan y) (sin z)) (cos z))))) (- (* (sqrt (tan a)) (sqrt (tan a)))))
486.0ms
(/ (+ (tan y) (tan z)) (- (pow 1 3) (pow (/ (* (tan y) (sin z)) (cos z)) 3)))
344.0ms
(fma (/ (* (cbrt (+ (tan y) (tan z))) (cbrt (+ (tan y) (tan z)))) 1) (/ (cbrt (+ (tan y) (tan z))) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
342.0ms
(fma (/ (* (cbrt (+ (tan y) (tan z))) (cbrt (+ (tan y) (tan z)))) (+ 1 (sqrt (/ (* (tan y) (sin z)) (cos z))))) (/ (cbrt (+ (tan y) (tan z))) (- 1 (sqrt (/ (* (tan y) (sin z)) (cos z))))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
333.0ms
(fma (/ (* (cbrt (+ (tan y) (tan z))) (cbrt (+ (tan y) (tan z)))) 1) (/ (cbrt (+ (tan y) (tan z))) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))

prune4.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
19×associate-*l/
18×add-sqr-sqrt
15×add-cbrt-cube add-exp-log
14×*-un-lft-identity
12×add-cube-cbrt
10×pow1 associate-*l*
9×associate-*r*
8×tan-quot 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×cbrt-undiv div-exp associate-/r/
1×clear-num associate-/r* frac-2neg div-sub div-inv distribute-lft-out
Counts
4 → 104
Calls
4 calls:
Slowest
54.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a))) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (cos a)))
24.0ms
(* (+ (tan y) (tan z)) (cos a))
21.0ms
(* (tan y) (sin z))
13.0ms
(* (tan y) (sin z))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
568.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a))) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (cos a)))
497.0ms
(* (+ (tan y) (tan z)) (cos a))
80.0ms
(* (tan y) (sin z))
79.0ms
(* (tan y) (sin z))

simplify8.4s

Counts
71 → 116
Calls
71 calls:
Slowest
474.0ms
(- (* (* (+ (pow (tan y) 3) (pow (tan z) 3)) (cos a)) (+ (* 1 1) (+ (* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z))) (* 1 (/ (* (tan y) (sin z)) (cos z)))))) (* (+ (* (tan y) (tan y)) (- (* (tan z) (tan z)) (* (tan y) (tan z)))) (* (- (pow 1 3) (pow (/ (* (tan y) (sin z)) (cos z)) 3)) (sin a))))
433.0ms
(- (* (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (cos a)) (+ (* 1 1) (+ (* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z))) (* 1 (/ (* (tan y) (sin z)) (cos z)))))) (* (- (tan y) (tan z)) (* (- (pow 1 3) (pow (/ (* (tan y) (sin z)) (cos z)) 3)) (sin a))))
429.0ms
(/ (* (* (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a))) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a)))) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a)))) (* (* (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (cos a))) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (cos a))))
394.0ms
(- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ (* 1 1) (+ (* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z))) (* 1 (/ (* (tan y) (sin z)) (cos z)))))) (* (* (cos y) (cos z)) (* (- (pow 1 3) (pow (/ (* (tan y) (sin z)) (cos z)) 3)) (sin a))))
370.0ms
(/ (* (cbrt (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a)))) (cbrt (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (tan y) (sin z)) (cos z))) (sin a))))) (- 1 (/ (* (tan y) (sin z)) (cos z))))

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes404.0ms

Accuracy

0% (0.2b remaining)

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

bsearch6.0ms

end0.0ms

sample12.8s

Algorithm
intervals
Results
8.4s4030×body1280valid
2.2s1900×body640valid
835.0ms8000×pre80true
576.0ms670×body320valid
255.0ms1123×body80valid
151.0ms277×body160valid