Details

Time bar (total: 1.6m)

sample405.0ms

Algorithm
intervals
Results
258.0ms128×body1280valid
59.0ms63×body640valid
25.0ms256×pre80true
15.0ms23×body320valid
6.0ms31×body80valid
5.0ms11×body160valid

simplify108.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
108.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize24.0ms

Local error

Found 3 expressions with local error:

2.5b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite64.0ms

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
37.0ms
(- (tan (+ y z)) (tan a))
15.0ms
(+ x (- (tan (+ y z)) (tan a)))
10.0ms
(tan (+ y z))

series478.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
224.0ms
(+ x (- (tan (+ y z)) (tan a)))
182.0ms
(- (tan (+ y z)) (tan a))
72.0ms
(tan (+ y z))

simplify3.3s

Counts
56 → 84
Calls
56 calls:
Slowest
263.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
230.0ms
(fma (* (cbrt (tan (+ y z))) (cbrt (tan (+ y z)))) (cbrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
198.0ms
(fma (sqrt (tan (+ y z))) (sqrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
176.0ms
(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))
168.0ms
(fma 1 (tan (+ y z)) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan y) (tan z))
0.1b
(- (/ (+ (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))))

rewrite298.0ms

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
123.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
103.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
34.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
28.0ms
(* (tan y) (tan z))

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
622.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
460.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
373.0ms
(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
172.0ms
(* (tan y) (tan z))

simplify24.3s

Counts
258 → 243
Calls
258 calls:
Slowest
582.0ms
(fma (/ 1 1) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
452.0ms
(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)))))
433.0ms
(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)))))
393.0ms
(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))))))
360.0ms
(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)))))

prune3.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize89.0ms

Local error

Found 4 expressions with local error:

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

rewrite252.0ms

Algorithm
rewrite-expression-head
Rules
165×*-un-lft-identity
125×times-frac
108×add-sqr-sqrt
91×add-cube-cbrt
63×prod-diff
24×distribute-lft-out
21×fma-neg
20×add-cbrt-cube add-exp-log
13×associate-*r* associate-*l*
8×associate-/r/ div-inv
6×pow1 cbrt-undiv associate-/r* div-exp associate-/l* add-log-exp
5×flip3-- flip--
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u unswap-sqr
2×quot-tan clear-num frac-2neg difference-of-squares
1×frac-times sub-neg diff-log pow-prod-down associate-*l/ tan-quot associate-*r/ *-commutative frac-sub distribute-lft-out--
Counts
4 → 218
Calls
4 calls:
Slowest
203.0ms
(- (/ (+ (/ (sin z) (cos z)) (/ (sin y) (cos y))) (- 1 (* (/ (sin z) (cos z)) (/ (sin y) (cos y))))) (tan a))
18.0ms
(* (/ (sin z) (cos z)) (/ (sin y) (cos y)))
16.0ms
(/ (sin z) (cos z))
11.0ms
(/ (sin z) (cos z))

series779.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
550.0ms
(- (/ (+ (/ (sin z) (cos z)) (/ (sin y) (cos y))) (- 1 (* (/ (sin z) (cos z)) (/ (sin y) (cos y))))) (tan a))
168.0ms
(* (/ (sin z) (cos z)) (/ (sin y) (cos y)))
33.0ms
(/ (sin z) (cos z))
28.0ms
(/ (sin z) (cos z))

simplify32.0s

Counts
262 → 230
Calls
262 calls:
Slowest
630.0ms
(* (* (* (/ (sin z) (cos z)) (/ (sin z) (cos z))) (/ (sin z) (cos z))) (* (* (/ (sin y) (cos y)) (/ (sin y) (cos y))) (/ (sin y) (cos y))))
617.0ms
(fma (/ (sqrt (+ (/ (sin z) (cos z)) (/ (sin y) (cos y)))) (sqrt (- 1 (* (/ (sin z) (cos z)) (/ (sin y) (cos y)))))) (/ (sqrt (+ (/ (sin z) (cos z)) (/ (sin y) (cos y)))) (sqrt (- 1 (* (/ (sin z) (cos z)) (/ (sin y) (cos y)))))) (- (* (sqrt (tan a)) (sqrt (tan a)))))
458.0ms
(fma (/ 1 1) (/ (+ (/ (sin z) (cos z)) (/ (sin y) (cos y))) (- 1 (* (/ (sin z) (cos z)) (/ (sin y) (cos y))))) (- (* (sqrt (tan a)) (sqrt (tan a)))))
455.0ms
(fma 1 (/ (+ (/ (sin z) (cos z)) (/ (sin y) (cos y))) (- 1 (* (/ (sin z) (cos z)) (/ (sin y) (cos y))))) (- (* (sqrt (tan a)) (sqrt (tan a)))))
450.0ms
(fma (/ (+ (/ (sin z) (cos z)) (/ (sin y) (cos y))) (- (pow 1 3) (pow (* (/ (sin z) (cos z)) (/ (sin y) (cos y))) 3))) (+ (* 1 1) (+ (* (* (/ (sin z) (cos z)) (/ (sin y) (cos y))) (* (/ (sin z) (cos z)) (/ (sin y) (cos y)))) (* 1 (* (/ (sin z) (cos z)) (/ (sin y) (cos y)))))) (- (* (sqrt (tan a)) (sqrt (tan a)))))

prune2.7s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

2.6b
(exp (- (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (tan a)))
0.2b
(- (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (tan a))
0.2b
(* (tan y) (tan z))
0.1b
(+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))

rewrite509.0ms

Algorithm
rewrite-expression-head
Rules
49×*-un-lft-identity
29×add-sqr-sqrt
24×prod-diff
23×add-cube-cbrt
17×add-log-exp
15×exp-sum
10×distribute-lft-out
6×pow1 exp-prod add-cbrt-cube tan-quot add-exp-log
4×expm1-log1p-u fma-neg diff-log insert-posit16 log1p-expm1-u distribute-lft-out--
3×sum-log fma-def associate-*r* associate-*l* rem-exp-log
2×sub-neg flip3-+ associate--l+ frac-sub flip-+ difference-of-squares
1×frac-times +-commutative flip3-- exp-diff pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod flip-- unswap-sqr
Counts
4 → 115
Calls
4 calls:
Slowest
299.0ms
(exp (- (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (tan a)))
175.0ms
(- (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (tan a))
20.0ms
(+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
14.0ms
(* (tan y) (tan z))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
489.0ms
(exp (- (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (tan a)))
408.0ms
(- (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (tan a))
326.0ms
(+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))
108.0ms
(* (tan y) (tan z))

simplify8.8s

Counts
91 → 127
Calls
91 calls:
Slowest
475.0ms
(exp (* (cbrt (- (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (tan a))) (cbrt (- (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (tan a)))))
326.0ms
(exp (- (+ x (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))))) (/ (sin a) (cos a))))
324.0ms
(exp (fma (* (cbrt (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))) (cbrt (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))))) (cbrt (+ x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))) (- (* (tan a) 1))))
324.0ms
(exp (- (+ (/ (sin z) (* (cos z) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) (+ (/ (sin y) (* (cos y) (- 1 (/ (* (sin z) (sin y)) (* (cos y) (cos z)))))) x)) (/ (sin a) (cos a))))
278.0ms
(- (* (- (* x x) (* (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))))) (cos a)) (* (- x (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))) (sin a)))

prune1.4s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes305.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample11.6s

Algorithm
intervals
Results
6.7s3896×body1280valid
2.3s1994×body640valid
1.2s8000×pre80true
540.0ms700×body320valid
318.0ms1116×body80valid
148.0ms294×body160valid