Details

Time bar (total: 1.5m)

sample951.0ms

Algorithm
intervals
Results
719.0ms113×body1280valid
118.0ms77×body640valid
36.0ms256×pre80true
17.0ms17×body320valid
13.0ms39×body80valid
7.0ms10×body160valid

simplify101.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
101.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize20.0ms

Local error

Found 3 expressions with local error:

4.0b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite55.0ms

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
29.0ms
(- (tan (+ y z)) (tan a))
13.0ms
(+ x (- (tan (+ y z)) (tan a)))
6.0ms
(tan (+ y z))

series523.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
214.0ms
(+ x (- (tan (+ y z)) (tan a)))
200.0ms
(- (tan (+ y z)) (tan a))
109.0ms
(tan (+ y z))

simplify3.5s

Counts
56 → 84
Calls
56 calls:
Slowest
338.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
234.0ms
(fma (sqrt (tan (+ y z))) (sqrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
211.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
206.0ms
(fma (* (cbrt (tan (+ y z))) (cbrt (tan (+ y z)))) (cbrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
182.0ms
(fma 1 (tan (+ y z)) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

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

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
165×*-un-lft-identity
115×add-sqr-sqrt
108×prod-diff add-cube-cbrt
97×times-frac
56×associate-+r+
27×distribute-lft-out
18×fma-neg
16×associate-/r/
11×add-log-exp
9×flip3-- flip--
8×add-cbrt-cube add-exp-log div-inv
7×tan-quot
6×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l*
3×associate-/r* fma-def associate-*r* associate-*l* associate-/l/
2×sum-log sub-neg flip3-+ diff-log flip-+ distribute-lft-out-- difference-of-squares
1×frac-times cbrt-undiv +-commutative clear-num associate-+r- frac-2neg div-exp pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod unswap-sqr
Counts
4 → 231
Calls
4 calls:
Slowest
107.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
74.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
44.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
31.0ms
(* (tan y) (tan z))

series1.7s

Counts
4 → 12
Calls
4 calls:
Slowest
656.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
562.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
361.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
152.0ms
(* (tan y) (tan z))

simplify26.4s

Counts
258 → 243
Calls
258 calls:
Slowest
564.0ms
(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)))))
532.0ms
(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)))))
524.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (* (tan a) 1)))
515.0ms
(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)))))
440.0ms
(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))))))

prune3.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

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

rewrite602.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt prod-diff
32×*-un-lft-identity
30×add-cube-cbrt
25×associate-/r/
17×add-cbrt-cube add-exp-log
15×times-frac cos-mult
12×fma-neg
11×frac-times flip3-- associate-*l/ flip--
8×pow1
6×associate-*r* associate-*l* associate-*r/ add-log-exp
5×prod-exp tan-quot cbrt-unprod div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv div-exp associate-/l*
2×pow-prod-down *-commutative unswap-sqr
1×clear-num associate-/r* sub-neg frac-2neg diff-log frac-sub distribute-lft-out-- difference-of-squares
Counts
4 → 142
Calls
4 calls:
Slowest
544.0ms
(- (/ (fma (sin z) (cos y) (* (cos z) (sin y))) (* (- 1 (* (tan y) (tan z))) (* (cos y) (cos z)))) (tan a))
24.0ms
(* (tan y) (tan z))
21.0ms
(/ (fma (sin z) (cos y) (* (cos z) (sin y))) (* (- 1 (* (tan y) (tan z))) (* (cos y) (cos z))))
10.0ms
(* (cos z) (sin y))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
549.0ms
(- (/ (fma (sin z) (cos y) (* (cos z) (sin y))) (* (- 1 (* (tan y) (tan z))) (* (cos y) (cos z)))) (tan a))
403.0ms
(/ (fma (sin z) (cos y) (* (cos z) (sin y))) (* (- 1 (* (tan y) (tan z))) (* (cos y) (cos z))))
105.0ms
(* (tan y) (tan z))
64.0ms
(* (cos z) (sin y))

simplify24.2s

Counts
144 → 154
Calls
144 calls:
Slowest
710.0ms
(/ (* (* (fma (sin z) (cos y) (* (cos z) (sin y))) (fma (sin z) (cos y) (* (cos z) (sin y)))) (fma (sin z) (cos y) (* (cos z) (sin y)))) (* (* (* (- 1 (* (tan y) (tan z))) (* (cos y) (cos z))) (* (- 1 (* (tan y) (tan z))) (* (cos y) (cos z)))) (* (- 1 (* (tan y) (tan z))) (* (cos y) (cos z)))))
668.0ms
(+ (* 1/3 (* (pow z 3) y)) (+ (* 1/3 (* z (pow y 3))) (* z y)))
546.0ms
(/ (* (* (fma (sin z) (cos y) (* (cos z) (sin y))) (fma (sin z) (cos y) (* (cos z) (sin y)))) (fma (sin z) (cos y) (* (cos z) (sin y)))) (* (* (* (- 1 (* (tan y) (tan z))) (- 1 (* (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))) (* (* (* (cos y) (cos z)) (* (cos y) (cos z))) (* (cos y) (cos z)))))
546.0ms
(/ (* (* (fma (sin z) (cos y) (* (cos z) (sin y))) (fma (sin z) (cos y) (* (cos z) (sin y)))) (fma (sin z) (cos y) (* (cos z) (sin y)))) (* (* (* (- 1 (* (tan y) (tan z))) (- 1 (* (tan y) (tan z)))) (- 1 (* (tan y) (tan z)))) (* (* (* (cos y) (cos y)) (cos y)) (* (* (cos z) (cos z)) (cos z)))))
491.0ms
(/ (fma (sin z) (cos y) (* (cos z) (sin y))) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (* (cos y) (cos z))))

prune2.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize101.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-cbrt-cube add-exp-log
11×*-un-lft-identity add-cube-cbrt
8×pow1
7×tan-quot
6×associate-*r* associate-*l* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×times-frac prod-diff prod-exp frac-sub cbrt-unprod associate-/l*
2×frac-times cbrt-undiv div-exp pow-prod-down associate-*l/ associate-*r/ *-commutative unswap-sqr
1×clear-num associate-/r* sub-neg frac-2neg flip3-- fma-neg diff-log associate-/r/ cos-mult div-inv flip--
Counts
4 → 92
Calls
4 calls:
Slowest
43.0ms
(- (* (/ 1 (- 1 (* (tan y) (tan z)))) (/ (fma (sin z) (cos y) (* (cos z) (sin y))) (* (cos y) (cos z)))) (tan a))
21.0ms
(* (cos z) (sin y))
14.0ms
(* (tan y) (tan z))
9.0ms
(/ (fma (sin z) (cos y) (* (cos z) (sin y))) (* (cos y) (cos z)))

series904.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
499.0ms
(- (* (/ 1 (- 1 (* (tan y) (tan z)))) (/ (fma (sin z) (cos y) (* (cos z) (sin y))) (* (cos y) (cos z)))) (tan a))
219.0ms
(/ (fma (sin z) (cos y) (* (cos z) (sin y))) (* (cos y) (cos z)))
119.0ms
(* (tan y) (tan z))
68.0ms
(* (cos z) (sin y))

simplify5.8s

Counts
63 → 104
Calls
63 calls:
Slowest
445.0ms
(+ z (+ (* 1/3 (pow z 3)) y))
333.0ms
(fma (/ 1 (- 1 (* (tan y) (tan z)))) (/ (fma (sin z) (cos y) (* (cos z) (sin y))) (* (cos y) (cos z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
331.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
320.0ms
(- (* (* 1 (fma (sin z) (cos y) (* (cos z) (sin y)))) (cos a)) (* (* (- 1 (* (tan y) (tan z))) (* (cos y) (cos z))) (sin a)))
319.0ms
(* (* (* (cos z) (cos z)) (cos z)) (* (* (sin y) (sin y)) (sin y)))

prune1.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes466.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample15.4s

Algorithm
intervals
Results
9.1s3857×body1280valid
3.6s1983×body640valid
1.0s8000×pre80true
760.0ms700×body320valid
367.0ms1201×body80valid
171.0ms259×body160valid