Details

Time bar (total: 2.5m)

sample571.0ms

Algorithm
intervals
Results
329.0ms130×body1280valid
114.0ms56×body640valid
41.0ms256×pre80true
22.0ms22×body320valid
12.0ms40×body80valid
5.0ms8×body160valid

simplify569.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
568.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize22.0ms

Local error

Found 3 expressions with local error:

3.4b
(tan (+ y z))
0.1b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite74.0ms

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
34.0ms
(+ x (- (tan (+ y z)) (tan a)))
31.0ms
(- (tan (+ y z)) (tan a))
7.0ms
(tan (+ y z))

series469.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
199.0ms
(- (tan (+ y z)) (tan a))
197.0ms
(+ x (- (tan (+ y z)) (tan a)))
73.0ms
(tan (+ y z))

simplify7.8s

Counts
98 → 84
Calls
98 calls:
Slowest
543.0ms
(* (* (- (tan (+ y z)) (tan a)) (- (tan (+ y z)) (tan a))) (- (tan (+ y z)) (tan a)))
317.0ms
(+ x (fma (sqrt (tan (+ y z))) (sqrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))))
315.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
289.0ms
(+ x (fma (* (cbrt (tan (+ y z))) (cbrt (tan (+ y z)))) (cbrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))))
260.0ms
(+ (* x x) (- (* (- (tan (+ y z)) (tan a)) (- (tan (+ y z)) (tan a))) (* x (- (tan (+ y z)) (tan a)))))

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

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

rewrite225.0ms

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
118.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
77.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
19.0ms
(* (tan y) (tan z))
7.0ms
(+ (tan y) (tan z))

series1.7s

Counts
4 → 12
Calls
4 calls:
Slowest
716.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
681.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
231.0ms
(+ (tan y) (tan z))
121.0ms
(* (tan y) (tan z))

simplify41.8s

Counts
280 → 223
Calls
280 calls:
Slowest
581.0ms
(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)))))
576.0ms
(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
(+ x (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))))) (- (* (sqrt (tan a)) (sqrt (tan a))))))
505.0ms
(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))))))
502.0ms
(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))))))

prune2.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
28×associate-*l/
16×tan-quot
14×add-sqr-sqrt
13×add-cbrt-cube add-exp-log
12×frac-sub
10×*-un-lft-identity add-cube-cbrt
9×flip3-- flip--
8×pow1 associate-/l/
6×associate-*r* associate-*l* add-log-exp
4×expm1-log1p-u flip3-+ frac-add flip-+ insert-posit16 log1p-expm1-u
3×times-frac prod-exp cbrt-unprod associate-/l*
2×frac-times cbrt-undiv div-exp pow-prod-down associate-*r/ associate-/r/ *-commutative unswap-sqr
1×clear-num associate-/r* sub-neg frac-2neg fma-neg diff-log div-sub prod-diff div-inv
Counts
4 → 106
Calls
4 calls:
Slowest
64.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
39.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
26.0ms
(* (tan y) (tan z))
15.0ms
(* (tan y) (tan z))

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
796.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
494.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
158.0ms
(* (tan y) (tan z))
126.0ms
(* (tan y) (tan z))

simplify24.4s

Counts
134 → 118
Calls
134 calls:
Slowest
577.0ms
(* (+ (* (tan y) (tan y)) (- (* (tan z) (tan z)) (* (tan y) (tan z)))) (+ 1 (* (tan y) (tan z))))
573.0ms
(* (* (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))))
542.0ms
(/ (* (* (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))) (* (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (- 1 (* (tan y) (tan z))) (cos a))) (* (- 1 (* (tan y) (tan z))) (cos a))))
534.0ms
(* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (+ (* (tan y) (tan y)) (- (* (tan z) (tan z)) (* (tan y) (tan z)))) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))))
519.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z)))) (cos a)))

prune1.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
136×times-frac
109×add-sqr-sqrt
102×*-un-lft-identity
100×add-cube-cbrt
90×prod-diff
30×fma-neg
21×associate-/r/
17×div-inv
13×add-cbrt-cube add-exp-log cos-mult
8×pow1
6×associate-*r* associate-*l* add-log-exp
5×flip3-- tan-quot flip--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×prod-exp cbrt-unprod associate-/l*
2×cbrt-undiv div-exp pow-prod-down *-commutative difference-of-squares unswap-sqr
1×frac-times clear-num associate-/r* sub-neg frac-2neg diff-log associate-*l/ associate-*r/ frac-sub distribute-lft-out--
Counts
4 → 209
Calls
4 calls:
Slowest
95.0ms
(- (/ (/ (fma (sin z) (cos y) (* (cos z) (sin y))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a))
25.0ms
(/ (fma (sin z) (cos y) (* (cos z) (sin y))) (* (cos y) (cos z)))
14.0ms
(* (tan y) (tan z))
11.0ms
(* (cos z) (sin y))

series947.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
540.0ms
(- (/ (/ (fma (sin z) (cos y) (* (cos z) (sin y))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a))
208.0ms
(/ (fma (sin z) (cos y) (* (cos z) (sin y))) (* (cos y) (cos z)))
140.0ms
(* (tan y) (tan z))
59.0ms
(* (cos z) (sin y))

simplify45.7s

Counts
321 → 221
Calls
321 calls:
Slowest
888.0ms
(fma (/ (/ (* (cbrt (fma (sin z) (cos y) (* (cos z) (sin y)))) (cbrt (fma (sin z) (cos y) (* (cos z) (sin y))))) (cos y)) (* (cbrt (- 1 (* (tan y) (tan z)))) (cbrt (- 1 (* (tan y) (tan z)))))) (/ (/ (cbrt (fma (sin z) (cos y) (* (cos z) (sin y)))) (cos z)) (cbrt (- 1 (* (tan y) (tan z))))) (- (* (sqrt (tan a)) (sqrt (tan a)))))
639.0ms
(fma (/ (fma (sin z) (cos y) (* (cos z) (sin y))) (sqrt (- 1 (* (tan y) (tan z))))) (/ (/ 1 (* (cos y) (cos z))) (sqrt (- 1 (* (tan y) (tan z))))) (- (* (tan a) 1)))
620.0ms
(sqrt (- (/ (/ (fma (sin z) (cos y) (* (cos z) (sin y))) (* (cos y) (cos z))) (- 1 (* (tan y) (tan z)))) (tan a)))
582.0ms
(fma (/ (fma (sin z) (cos y) (* (cos z) (sin y))) (sqrt (- 1 (* (tan y) (tan z))))) (/ (/ 1 (* (cos y) (cos z))) (sqrt (- 1 (* (tan y) (tan z))))) (- (* (sqrt (tan a)) (sqrt (tan a)))))
522.0ms
(fma (/ 1 (sqrt (- 1 (* (tan y) (tan z))))) (/ (/ (fma (sin z) (cos y) (* (cos z) (sin y))) (* (cos y) (cos z))) (sqrt (- 1 (* (tan y) (tan z))))) (- (* (tan a) 1)))

prune3.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes670.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample13.6s

Algorithm
intervals
Results
7.0s3800×body1280valid
3.5s2057×body640valid
994.0ms8000×pre80true
598.0ms287×body160valid
493.0ms691×body320valid
375.0ms1165×body80valid