Details

Time bar (total: 1.3m)

sample449.0ms

Algorithm
intervals
Results
259.0ms122×body1280valid
106.0ms73×body640valid
26.0ms256×pre80true
14.0ms18×body320valid
9.0ms35×body80valid
5.0ms8×body160valid

simplify82.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
82.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize35.0ms

Local error

Found 3 expressions with local error:

2.8b
(tan (+ y z))
0.1b
(- (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
29.0ms
(- (tan (+ y z)) (tan a))
23.0ms
(+ x (- (tan (+ y z)) (tan a)))
10.0ms
(tan (+ y z))

series419.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
163.0ms
(+ x (- (tan (+ y z)) (tan a)))
162.0ms
(- (tan (+ y z)) (tan a))
94.0ms
(tan (+ y z))

simplify7.8s

Counts
98 → 84
Calls
98 calls:
Slowest
625.0ms
(- (* x x) (* (- (tan (+ y z)) (tan a)) (- (tan (+ y z)) (tan a))))
457.0ms
(* (* (- (tan (+ y z)) (tan a)) (- (tan (+ y z)) (tan a))) (- (tan (+ y z)) (tan a)))
357.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
286.0ms
(- (pow (tan (+ y z)) 3) (pow (tan a) 3))
273.0ms
(+ x (fma (* (cbrt (tan (+ y z))) (cbrt (tan (+ y z)))) (cbrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))))

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize56.0ms

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))

rewrite319.0ms

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
141.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
130.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
24.0ms
(* (tan y) (tan z))
15.0ms
(+ (tan y) (tan z))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
555.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
512.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
166.0ms
(* (tan y) (tan z))
117.0ms
(+ (tan y) (tan z))

simplify31.8s

Counts
280 → 223
Calls
280 calls:
Slowest
504.0ms
(fma (/ (sqrt (+ (tan y) (tan z))) (* (cbrt (- 1 (* (tan y) (tan z)))) (cbrt (- 1 (* (tan y) (tan z)))))) (/ (sqrt (+ (tan y) (tan z))) (cbrt (- 1 (* (tan y) (tan z))))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
496.0ms
(- (+ (/ (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)))
407.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
398.0ms
(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))))))
376.0ms
(fma (/ (* (cbrt (+ (tan y) (tan z))) (cbrt (+ (tan y) (tan z)))) 1) (/ (cbrt (+ (tan y) (tan z))) (- 1 (* (tan y) (tan z)))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite117.0ms

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
70.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
16.0ms
(* (tan y) (tan z))
15.0ms
(* (tan y) (tan z))
15.0ms
(* (tan y) (tan z))

series395.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
113.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
94.0ms
(* (tan y) (tan z))
94.0ms
(* (tan y) (tan z))
94.0ms
(* (tan y) (tan z))

simplify5.4s

Counts
147 → 136
Calls
147 calls:
Slowest
535.0ms
(* (* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z))) (* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z))))
458.0ms
(* (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))))
240.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
239.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
237.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

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

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
40×tan-quot
19×frac-times associate-*r/
17×pow1 add-cbrt-cube add-exp-log
13×add-sqr-sqrt
9×*-un-lft-identity associate-*l* associate-*l/ add-cube-cbrt
8×pow-prod-down prod-exp cbrt-unprod
7×associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×unswap-sqr
1×fma-udef
Counts
4 → 98
Calls
4 calls:
Slowest
125.0ms
(* (tan y) (* (tan z) (* (tan y) (tan z))))
19.0ms
(* (tan y) (tan z))
15.0ms
(* (tan y) (tan z))
0.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (tan y) (* (tan z) (* (tan y) (tan z)))))) (+ 1 (* (tan y) (tan z))) (- (tan a)))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
709.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (tan y) (* (tan z) (* (tan y) (tan z)))))) (+ 1 (* (tan y) (tan z))) (- (tan a)))
118.0ms
(* (tan y) (* (tan z) (* (tan y) (tan z))))
97.0ms
(* (tan y) (tan z))
95.0ms
(* (tan y) (tan z))

simplify8.7s

Counts
118 → 110
Calls
118 calls:
Slowest
761.0ms
(- (+ (/ (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)))
530.0ms
(- (+ (/ (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)))
373.0ms
(* (* (* (tan y) (* (tan z) (* (tan y) (tan z)))) (* (tan y) (* (tan z) (* (tan y) (tan z))))) (* (tan y) (* (tan z) (* (tan y) (tan z)))))
352.0ms
(log1p (fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (tan y) (* (tan z) (* (tan y) (tan z)))))) (+ 1 (* (tan y) (tan z))) (- (tan a))))
351.0ms
(expm1 (fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (tan y) (* (tan z) (* (tan y) (tan z)))))) (+ 1 (* (tan y) (tan z))) (- (tan a))))

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes356.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample10.5s

Algorithm
intervals
Results
5.9s3939×body1280valid
2.5s2001×body640valid
712.0ms652×body320valid
666.0ms8000×pre80true
270.0ms1129×body80valid
153.0ms279×body160valid