Details

Time bar (total: 1.4m)

sample408.0ms

Algorithm
intervals
Results
228.0ms124×body1280valid
79.0ms69×body640valid
52.0ms256×pre80true
10.0ms38×body80valid
9.0ms15×body320valid
5.0ms10×body160valid

simplify99.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
99.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.8b

localize34.0ms

Local error

Found 3 expressions with local error:

3.1b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite30.0ms

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
13.0ms
(- (tan (+ y z)) (tan a))
11.0ms
(+ x (- (tan (+ y z)) (tan a)))
5.0ms
(tan (+ y z))

series418.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
178.0ms
(+ x (- (tan (+ y z)) (tan a)))
160.0ms
(- (tan (+ y z)) (tan a))
80.0ms
(tan (+ y z))

simplify3.5s

Counts
56 → 84
Calls
56 calls:
Slowest
234.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
217.0ms
(fma (sqrt (tan (+ y z))) (sqrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
198.0ms
(+ (* 1/3 (pow y 3)) (+ z y))
185.0ms
(fma (* (cbrt (tan (+ y z))) (cbrt (tan (+ y z)))) (cbrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
146.0ms
(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize52.0ms

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

rewrite279.0ms

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
148.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
102.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
18.0ms
(* (tan y) (tan z))
7.0ms
(+ (tan y) (tan z))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
606.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
494.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
150.0ms
(* (tan y) (tan z))
111.0ms
(+ (tan y) (tan z))

simplify25.0s

Counts
228 → 223
Calls
228 calls:
Slowest
597.0ms
(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)))))
516.0ms
(fma (/ (sqrt (+ (tan y) (tan z))) (sqrt (- 1 (* (tan y) (tan z))))) (/ (sqrt (+ (tan y) (tan z))) (sqrt (- 1 (* (tan y) (tan z))))) (- (* (sqrt (tan a)) (sqrt (tan a)))))
457.0ms
(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))))))
434.0ms
(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)))))
413.0ms
(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))))))

prune3.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

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

rewrite221.0ms

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
103.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
61.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
28.0ms
(* (tan y) (tan z))
26.0ms
(* (tan y) (tan z))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
722.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
488.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
142.0ms
(* (tan y) (tan z))
131.0ms
(* (tan y) (tan z))

simplify14.7s

Counts
80 → 118
Calls
80 calls:
Slowest
590.0ms
(/ (* (* (- (* (+ (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))))
564.0ms
(- (* (* (+ (pow (tan y) 3) (pow (tan z) 3)) (cos a)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))) (* (+ (* (tan y) (tan y)) (- (* (tan z) (tan z)) (* (tan y) (tan z)))) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (sin a))))
548.0ms
(* (* (cos y) (cos z)) (+ 1 (* (tan y) (tan z))))
518.0ms
(- (* (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (cos a)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))) (* (- (tan y) (tan z)) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (sin a))))
509.0ms
(- (* (* (+ (* (sin y) (cos z)) (* (cos y) (sin z))) (cos a)) (+ (* 1 1) (+ (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* 1 (* (tan y) (tan z)))))) (* (* (cos y) (cos z)) (* (- (pow 1 3) (pow (* (tan y) (tan z)) 3)) (sin a))))

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize99.0ms

Local error

Found 4 expressions with local error:

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

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
27×associate-*l/
14×add-sqr-sqrt
13×add-cbrt-cube tan-quot 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×cbrt-undiv div-exp pow-prod-down associate-*r/ associate-/r/ *-commutative unswap-sqr
1×frac-times clear-num associate-/r* sub-neg frac-2neg fma-neg diff-log div-sub prod-diff div-inv
Counts
4 → 104
Calls
4 calls:
Slowest
70.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
56.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (sin a)))
16.0ms
(* (tan y) (tan z))
12.0ms
(* (sin y) (tan z))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
583.0ms
(/ (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (sin a))) (* (- 1 (* (tan y) (tan z))) (cos a)))
400.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (sin a)))
101.0ms
(* (tan y) (tan z))
95.0ms
(* (sin y) (tan z))

simplify12.6s

Counts
77 → 116
Calls
77 calls:
Slowest
532.0ms
(/ (* (* (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (sin a))) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (sin a)))) (- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (/ (* (sin y) (tan z)) (cos y))) (sin a)))) (* (* (* (- 1 (* (tan y) (tan z))) (cos a)) (* (- 1 (* (tan y) (tan z))) (cos a))) (* (- 1 (* (tan y) (tan z))) (cos a))))
509.0ms
(- (* (* (+ (pow (tan y) 3) (pow (tan z) 3)) (cos a)) (+ (* 1 1) (+ (* (/ (* (sin y) (tan z)) (cos y)) (/ (* (sin y) (tan z)) (cos y))) (* 1 (/ (* (sin y) (tan z)) (cos y)))))) (* (+ (* (tan y) (tan y)) (- (* (tan z) (tan z)) (* (tan y) (tan z)))) (* (- (pow 1 3) (pow (/ (* (sin y) (tan z)) (cos y)) 3)) (sin a))))
489.0ms
(* (+ (* (tan y) (tan y)) (- (* (tan z) (tan z)) (* (tan y) (tan z)))) (+ 1 (/ (* (sin y) (tan z)) (cos y))))
452.0ms
(- (* (* (- (* (tan y) (tan y)) (* (tan z) (tan z))) (cos a)) (+ (* 1 1) (+ (* (/ (* (sin y) (tan z)) (cos y)) (/ (* (sin y) (tan z)) (cos y))) (* 1 (/ (* (sin y) (tan z)) (cos y)))))) (* (- (tan y) (tan z)) (* (- (pow 1 3) (pow (/ (* (sin y) (tan z)) (cos y)) 3)) (sin a))))
439.0ms
(- (* (* (+ (pow (tan y) 3) (pow (tan z) 3)) (cos a)) (+ (* 1 1) (+ (* (/ (* (sin y) (tan z)) (cos y)) (/ (* (sin y) (tan z)) (cos y))) (* 1 (/ (* (sin y) (tan z)) (cos y)))))) (* (+ (* (tan y) (tan y)) (- (* (tan z) (tan z)) (* (tan y) (tan z)))) (* (- (pow 1 3) (pow (/ (* (sin y) (tan z)) (cos y)) 3)) (sin a))))

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes369.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample11.4s

Algorithm
intervals
Results
6.7s3933×body1280valid
2.4s1961×body640valid
850.0ms675×body320valid
672.0ms8000×pre80true
268.0ms1131×body80valid
149.0ms300×body160valid