Details

Time bar (total: 2.2m)

sample535.0ms

Algorithm
intervals
Results
288.0ms122×body1280valid
132.0ms74×body640valid
35.0ms256×pre80true
17.0ms16×body320valid
10.0ms36×body80valid
5.0ms8×body160valid

simplify82.0ms

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

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize22.0ms

Local error

Found 3 expressions with local error:

2.3b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite37.0ms

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
14.0ms
(- (tan (+ y z)) (tan a))
11.0ms
(+ x (- (tan (+ y z)) (tan a)))
10.0ms
(tan (+ y z))

series538.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
233.0ms
(+ x (- (tan (+ y z)) (tan a)))
215.0ms
(- (tan (+ y z)) (tan a))
89.0ms
(tan (+ y z))

simplify3.9s

Counts
56 → 84
Calls
56 calls:
Slowest
368.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
261.0ms
(fma (sqrt (tan (+ y z))) (sqrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
224.0ms
(fma (* (cbrt (tan (+ y z))) (cbrt (tan (+ y z)))) (cbrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
207.0ms
(fma 1 (tan (+ y z)) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
183.0ms
(+ (* 1/3 (pow y 3)) (+ z y))

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (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))

rewrite295.0ms

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
135.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
131.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
16.0ms
(* (tan y) (tan z))
7.0ms
(+ (tan y) (tan z))

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
660.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
556.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
179.0ms
(+ (tan y) (tan z))
173.0ms
(* (tan y) (tan z))

simplify27.3s

Counts
228 → 223
Calls
228 calls:
Slowest
712.0ms
(fma (/ 1 (* (cbrt (- 1 (* (tan y) (tan z)))) (cbrt (- 1 (* (tan y) (tan z)))))) (/ (+ (tan y) (tan z)) (cbrt (- 1 (* (tan y) (tan z))))) (- (* (tan a) 1)))
551.0ms
(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)))))
531.0ms
(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)))))
520.0ms
(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)))))
518.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (* (tan a) 1)))

prune3.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite531.0ms

Algorithm
rewrite-expression-head
Rules
321×*-un-lft-identity
237×add-sqr-sqrt
180×prod-diff
172×times-frac
146×add-cube-cbrt
92×associate-+r+
58×difference-of-squares
44×distribute-lft-out
30×fma-neg distribute-lft-out--
14×associate-/r/
11×add-cbrt-cube add-exp-log add-log-exp
8×flip3-- div-inv flip--
6×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* fma-def associate-*r* associate-*l* tan-quot
2×cbrt-undiv sum-log sub-neg diff-log div-exp associate-*l/ prod-exp cbrt-unprod
1×+-commutative clear-num associate-+r- frac-2neg flip3-+ pow-prod-down *-commutative frac-sub flip-+ associate-/l* unswap-sqr associate-/l/
Counts
4 → 299
Calls
4 calls:
Slowest
308.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
188.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
15.0ms
(/ (* (tan y) (sin z)) (cos z))
13.0ms
(* (tan y) (sin z))

series1.9s

Counts
4 → 12
Calls
4 calls:
Slowest
850.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a))
696.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (tan a)))
216.0ms
(/ (* (tan y) (sin z)) (cos z))
123.0ms
(* (tan y) (sin z))

simplify45.1s

Counts
354 → 311
Calls
354 calls:
Slowest
826.0ms
(fma (/ (sqrt (+ (tan y) (tan z))) (+ (sqrt 1) (sqrt (/ (* (tan y) (sin z)) (cos z))))) (/ (sqrt (+ (tan y) (tan z))) (- (sqrt 1) (sqrt (/ (* (tan y) (sin z)) (cos z))))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
577.0ms
(/ (+ (tan y) (tan z)) (- (pow 1 3) (pow (/ (* (tan y) (sin z)) (cos z)) 3)))
504.0ms
(fma (/ (* (cbrt (+ (tan y) (tan z))) (cbrt (+ (tan y) (tan z)))) (+ (sqrt 1) (sqrt (/ (* (tan y) (sin z)) (cos z))))) (/ (cbrt (+ (tan y) (tan z))) (- (sqrt 1) (sqrt (/ (* (tan y) (sin z)) (cos z))))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
491.0ms
(fma (/ (* (cbrt (+ (tan y) (tan z))) (cbrt (+ (tan y) (tan z)))) 1) (/ (cbrt (+ (tan y) (tan z))) (- 1 (/ (* (tan y) (sin z)) (cos z)))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
471.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (sin z) (sin z)) (sin z)))

prune5.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize92.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ (* (tan y) (sin z)) (cos z)) 3)
0.2b
(* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z)))
0.2b
(fma (/ (+ (tan y) (tan z)) (- (pow 1 3) (pow (/ (* (tan y) (sin z)) (cos z)) 3))) (+ (* 1 1) (+ (* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z))) (* 1 (/ (* (tan y) (sin z)) (cos z))))) (- (* (tan a) 1)))
0.2b
(* (tan y) (sin z))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
48×add-cbrt-cube add-exp-log
23×add-sqr-sqrt
19×*-un-lft-identity add-cube-cbrt
18×times-frac
17×prod-exp cbrt-unprod
14×pow1 cbrt-undiv div-exp
10×associate-*r* associate-*l*
7×unpow-prod-down cube-prod swap-sqr
6×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow pow-exp rem-cube-cbrt
2×pow-prod-down associate-*l/ *-commutative unswap-sqr
1×cube-div pow2 cube-mult frac-times pow-to-exp pow-pow pow-plus unpow3 tan-quot associate-*r/ pow-sqr pow-prod-up fma-udef sqr-pow
Counts
4 → 131
Calls
4 calls:
Slowest
38.0ms
(* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z)))
15.0ms
(* (tan y) (sin z))
8.0ms
(pow (/ (* (tan y) (sin z)) (cos z)) 3)
0.0ms
(fma (/ (+ (tan y) (tan z)) (- (pow 1 3) (pow (/ (* (tan y) (sin z)) (cos z)) 3))) (+ (* 1 1) (+ (* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z))) (* 1 (/ (* (tan y) (sin z)) (cos z))))) (- (* (tan a) 1)))

series2.2s

Counts
4 → 12
Calls
4 calls:
Slowest
1.7s
(fma (/ (+ (tan y) (tan z)) (- (pow 1 3) (pow (/ (* (tan y) (sin z)) (cos z)) 3))) (+ (* 1 1) (+ (* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z))) (* 1 (/ (* (tan y) (sin z)) (cos z))))) (- (* (tan a) 1)))
203.0ms
(pow (/ (* (tan y) (sin z)) (cos z)) 3)
163.0ms
(* (/ (* (tan y) (sin z)) (cos z)) (/ (* (tan y) (sin z)) (cos z)))
94.0ms
(* (tan y) (sin z))

simplify18.2s

Counts
104 → 143
Calls
104 calls:
Slowest
1.1s
(* (/ (* (* (* (tan y) (sin z)) (* (tan y) (sin z))) (* (tan y) (sin z))) (* (* (cos z) (cos z)) (cos z))) (/ (* (* (* (tan y) (tan y)) (tan y)) (* (* (sin z) (sin z)) (sin z))) (* (* (cos z) (cos z)) (cos z))))
1.1s
(* (/ (* (* (* (tan y) (tan y)) (tan y)) (* (* (sin z) (sin z)) (sin z))) (* (* (cos z) (cos z)) (cos z))) (/ (* (* (* (tan y) (sin z)) (* (tan y) (sin z))) (* (tan y) (sin z))) (* (* (cos z) (cos z)) (cos z))))
943.0ms
(/ (* (pow (sin z) 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow (cos z) 3)))
923.0ms
(/ (* (pow (sin z) 3) (pow (sin y) 3)) (* (pow (cos y) 3) (pow (cos z) 3)))
639.0ms
(* (/ (* (* (* (tan y) (tan y)) (tan y)) (* (* (sin z) (sin z)) (sin z))) (* (* (cos z) (cos z)) (cos z))) (/ (* (* (* (tan y) (tan y)) (tan y)) (* (* (sin z) (sin z)) (sin z))) (* (* (cos z) (cos z)) (cos z))))

prune3.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes561.0ms

Accuracy

0% (0.1b remaining)

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

bsearch18.0ms

end0.0ms

sample14.7s

Algorithm
intervals
Results
8.1s3885×body1280valid
3.0s1935×body640valid
1.4s8000×pre80true
1.1s714×body320valid
381.0ms1189×body80valid
172.0ms277×body160valid