Details

Time bar (total: 1.2m)

sample510.0ms

Algorithm
intervals
Results
265.0ms118×body1280valid
122.0ms68×body640valid
34.0ms256×pre80true
22.0ms26×body320valid
10.0ms33×body80valid
8.0ms11×body160valid

simplify86.0ms

Calls
1 calls:
Slowest
86.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize49.0ms

Local error

Found 3 expressions with local error:

3.0b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite63.0ms

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
Calls
3 calls:
Slowest
27.0ms
(- (tan (+ y z)) (tan a))
23.0ms
(+ x (- (tan (+ y z)) (tan a)))
11.0ms
(tan (+ y z))

series494.0ms

Calls
3 calls:
Slowest
210.0ms
(- (tan (+ y z)) (tan a))
194.0ms
(+ x (- (tan (+ y z)) (tan a)))
90.0ms
(tan (+ y z))

simplify3.7s

Calls
56 calls:
Slowest
292.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
199.0ms
(fma (sqrt (tan (+ y z))) (sqrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
182.0ms
(fma (* (cbrt (tan (+ y z))) (cbrt (tan (+ y z)))) (cbrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
174.0ms
(+ (* 1/3 (pow y 3)) (+ z y))
167.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

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))

rewrite222.0ms

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
Calls
4 calls:
Slowest
128.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
68.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
15.0ms
(* (tan y) (tan z))
8.0ms
(+ (tan y) (tan z))

series1.6s

Calls
4 calls:
Slowest
664.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
599.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
184.0ms
(* (tan y) (tan z))
147.0ms
(+ (tan y) (tan z))

simplify26.4s

Calls
228 calls:
Slowest
803.0ms
(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))))))
586.0ms
(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)))))
561.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (* (tan a) 1)))
525.0ms
(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)))))
482.0ms
(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)))))

prune3.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize65.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (tan y) (tan z)) (* (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))
0.2b
(* (tan y) (tan z))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
47×pow1
40×tan-quot
20×add-cbrt-cube add-exp-log
19×frac-times pow-prod-down
13×associate-*l/ associate-*r/
12×add-sqr-sqrt
10×prod-exp cbrt-unprod
8×*-un-lft-identity add-cube-cbrt
7×associate-*r* associate-*l*
4×expm1-log1p-u pow-sqr pow-prod-up insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×pow-plus unswap-sqr
1×pow2 swap-sqr fma-udef
Calls
4 calls:
Slowest
104.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
29.0ms
(* (tan y) (tan z))
16.0ms
(* (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)))

series1.4s

Calls
4 calls:
Slowest
975.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (tan a)))
163.0ms
(* (* (tan y) (tan z)) (* (tan y) (tan z)))
159.0ms
(* (tan y) (tan z))
137.0ms
(* (tan y) (tan z))

simplify7.9s

Calls
98 calls:
Slowest
1.0s
(- (+ (/ (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)))
1.0s
(- (+ (/ (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)))
958.0ms
(* (* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z))) (* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z))))
779.0ms
(* (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))) (* (* (* (tan y) (tan z)) (* (tan y) (tan z))) (* (tan y) (tan z))))
367.0ms
(+ (* 1/3 (* (pow z 3) y)) (+ (* 1/3 (* z (pow y 3))) (* z y)))

prune2.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
10×add-sqr-sqrt
8×add-cube-cbrt add-log-exp
6×pow1 fma-def add-cbrt-cube tan-quot add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-*r* associate-*l*
2×+-commutative sum-log flip3-+ flip-+ fma-udef distribute-lft-out
1×frac-times associate-+r+ pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
Calls
4 calls:
Slowest
28.0ms
(* (tan y) (tan z))
7.0ms
(+ (tan y) (tan z))
4.0ms
(+ x (fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z)))) (- (* (tan a) 1))))
1.0ms
(fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z)))) (- (* (tan a) 1)))

series1.3s

Calls
4 calls:
Slowest
535.0ms
(fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z)))) (- (* (tan a) 1)))
425.0ms
(+ x (fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z)))) (- (* (tan a) 1))))
178.0ms
(+ (tan y) (tan z))
139.0ms
(* (tan y) (tan z))

simplify3.1s

Calls
37 calls:
Slowest
366.0ms
(* (* (* (tan y) (tan y)) (tan y)) (* (* (tan z) (tan z)) (tan z)))
365.0ms
(- (+ (/ (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)))
346.0ms
(- (+ (/ (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)))
342.0ms
(* (exp x) (exp (fma (+ (tan y) (tan z)) (/ 1 (- 1 (* (tan y) (tan z)))) (- (* (tan a) 1)))))
323.0ms
(+ (* 1/3 (* (pow z 3) y)) (+ (* 1/3 (* z (pow y 3))) (* z y)))

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes408.0ms

Accuracy

0% (0.1b remaining)

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

bsearch6.0ms

end0.0ms

sample14.0s

Algorithm
intervals
Results
8.1s3847×body1280valid
3.0s2051×body640valid
1.0s8000×pre80true
597.0ms286×body160valid
589.0ms670×body320valid
327.0ms1146×body80valid