Details

Time bar (total: 1.0m)

sample414.0ms

Algorithm
intervals
Results
209.0ms131×body1280valid
102.0ms58×body640valid
39.0ms23×body320valid
28.0ms256×pre80true
9.0ms37×body80valid
3.0ms7×body160valid

simplify70.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
69.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize29.0ms

Local error

Found 3 expressions with local error:

2.0b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite60.0ms

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
27.0ms
(- (tan (+ y z)) (tan a))
21.0ms
(+ x (- (tan (+ y z)) (tan a)))
10.0ms
(tan (+ y z))

series417.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
184.0ms
(- (tan (+ y z)) (tan a))
157.0ms
(+ x (- (tan (+ y z)) (tan a)))
76.0ms
(tan (+ y z))

simplify3.7s

Counts
56 → 84
Calls
56 calls:
Slowest
343.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
199.0ms
(fma (sqrt (tan (+ y z))) (sqrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
181.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
179.0ms
(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))
175.0ms
(fma 1 (tan (+ y z)) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

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))

rewrite269.0ms

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
130.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
104.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
24.0ms
(* (tan y) (tan z))
7.0ms
(+ (tan y) (tan z))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
576.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
536.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
126.0ms
(+ (tan y) (tan z))
118.0ms
(* (tan y) (tan z))

simplify24.1s

Counts
228 → 223
Calls
228 calls:
Slowest
556.0ms
(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)))))
500.0ms
(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)))))
455.0ms
(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)))))
449.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (* (tan a) 1)))
423.0ms
(fma (- (sqrt (tan a))) (sqrt (tan a)) (* (sqrt (tan a)) (sqrt (tan a))))

prune2.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize81.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (tan y) (tan z))
0.3b
(* (tan y) (tan z))
0.3b
(* (tan y) (tan z))
0.2b
(* (* (tan y) (tan z)) (* (tan y) (tan z)))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
49×pow1
44×tan-quot
22×add-cbrt-cube add-exp-log
20×frac-times pow-prod-down
16×add-sqr-sqrt
14×associate-*l/ associate-*r/
11×prod-exp cbrt-unprod
10×*-un-lft-identity associate-*r* associate-*l* add-cube-cbrt
4×expm1-log1p-u pow-sqr *-commutative pow-prod-up insert-posit16 log1p-expm1-u add-log-exp
3×unswap-sqr
2×pow-plus
1×pow2 swap-sqr
Counts
4 → 124
Calls
4 calls:
Slowest
78.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
20.0ms
(* (tan y) (tan z))
15.0ms
(* (tan y) (tan z))
14.0ms
(* (tan y) (tan z))

series491.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
148.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
116.0ms
(* (tan y) (tan z))
114.0ms
(* (tan y) (tan z))
113.0ms
(* (tan y) (tan z))

simplify5.4s

Counts
112 → 136
Calls
112 calls:
Slowest
699.0ms
(* (* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z))) (* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z))))
629.0ms
(* (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))))
369.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
339.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
312.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

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

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1 add-cbrt-cube tan-quot add-exp-log
12×add-sqr-sqrt
11×associate-*l/
10×pow-prod-down prod-exp cbrt-unprod
8×*-un-lft-identity add-cube-cbrt
7×frac-times associate-*r* associate-*l*
5×associate-*r/
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×unswap-sqr
1×fma-udef
Counts
4 → 91
Calls
4 calls:
Slowest
83.0ms
(* (* (tan y) (tan z)) (* (tan y) (sin z)))
18.0ms
(* (tan y) (tan z))
14.0ms
(* (tan y) (tan z))
0.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (/ (* (* (tan y) (tan z)) (* (tan y) (sin z))) (cos z)))) (+ 1 (* (tan y) (tan z))) (- (tan a)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
766.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (/ (* (* (tan y) (tan z)) (* (tan y) (sin z))) (cos z)))) (+ 1 (* (tan y) (tan z))) (- (tan a)))
140.0ms
(* (* (tan y) (tan z)) (* (tan y) (sin z)))
103.0ms
(* (tan y) (tan z))
100.0ms
(* (tan y) (tan z))

simplify4.0s

Counts
64 → 103
Calls
64 calls:
Slowest
649.0ms
(- (+ (/ (sin y) (* (- 1 (/ (* (pow (sin z) 2) (pow (sin y) 2)) (* (pow (cos y) 2) (pow (cos z) 2)))) (cos y))) (+ (/ (* (sin z) (pow (sin y) 2)) (* (- 1 (/ (* (pow (sin z) 2) (pow (sin y) 2)) (* (pow (cos y) 2) (pow (cos z) 2)))) (* (pow (cos y) 2) (cos z)))) (+ (/ (* (pow (sin z) 2) (sin y)) (* (- 1 (/ (* (pow (sin z) 2) (pow (sin y) 2)) (* (pow (cos y) 2) (pow (cos z) 2)))) (* (cos y) (pow (cos z) 2)))) (/ (sin z) (* (- 1 (/ (* (pow (sin z) 2) (pow (sin y) 2)) (* (pow (cos y) 2) (pow (cos z) 2)))) (cos z)))))) (/ (sin a) (cos a)))
598.0ms
(- (+ (/ (sin y) (* (- 1 (/ (* (pow (sin z) 2) (pow (sin y) 2)) (* (pow (cos y) 2) (pow (cos z) 2)))) (cos y))) (+ (/ (* (sin z) (pow (sin y) 2)) (* (- 1 (/ (* (pow (sin z) 2) (pow (sin y) 2)) (* (pow (cos y) 2) (pow (cos z) 2)))) (* (pow (cos y) 2) (cos z)))) (+ (/ (sin z) (* (- 1 (/ (* (pow (sin z) 2) (pow (sin y) 2)) (* (pow (cos y) 2) (pow (cos z) 2)))) (cos z))) (/ (* (pow (sin z) 2) (sin y)) (* (- 1 (/ (* (pow (sin z) 2) (pow (sin y) 2)) (* (pow (cos y) 2) (pow (cos z) 2)))) (* (cos y) (pow (cos z) 2))))))) (/ (sin a) (cos a)))
235.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
233.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
229.0ms
(+ (* 1/3 (* (pow z 3) y)) (+ (* 1/3 (* z (pow y 3))) (* z y)))

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes331.0ms

Accuracy

0% (0.1b remaining)

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

bsearch5.0ms

end0.0ms

sample11.4s

Algorithm
intervals
Results
7.3s3988×body1280valid
2.0s1903×body640valid
776.0ms719×body320valid
664.0ms8000×pre80true
289.0ms1132×body80valid
101.0ms258×body160valid