Details

Time bar (total: 1.4m)

sample501.0ms

Algorithm
intervals
Results
287.0ms135×body1280valid
62.0ms57×body640valid
53.0ms13×body160valid
34.0ms256×pre80true
20.0ms22×body320valid
9.0ms29×body80valid

simplify55.0ms

Calls
1 calls:
Slowest
55.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize18.0ms

Local error

Found 3 expressions with local error:

4.0b
(tan (+ y z))
0.2b
(- (tan (+ y z)) (tan a))
0.1b
(+ x (- (tan (+ y z)) (tan a)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt *-un-lft-identity prod-diff
16×add-cube-cbrt
11×associate-+r+
5×add-log-exp
4×tan-quot
3×expm1-log1p-u pow1 add-cbrt-cube fma-neg add-exp-log insert-posit16 log1p-expm1-u
2×tan-sum sub-neg frac-sub
1×+-commutative associate-+r- flip3-+ flip3-- diff-log flip-+ flip-- distribute-lft-out-- difference-of-squares
Calls
3 calls:
Slowest
7.0ms
(- (tan (+ y z)) (tan a))
7.0ms
(+ x (- (tan (+ y z)) (tan a)))
2.0ms
(tan (+ y z))

series507.0ms

Calls
3 calls:
Slowest
226.0ms
(+ x (- (tan (+ y z)) (tan a)))
196.0ms
(- (tan (+ y z)) (tan a))
84.0ms
(tan (+ y z))

simplify2.0s

Calls
50 calls:
Slowest
294.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
190.0ms
(* (- 1 (* (tan y) (tan z))) (cos a))
88.0ms
(fma (sqrt (tan (+ y z))) (sqrt (tan (+ y z))) (- (* (sqrt (tan a)) (sqrt (tan a)))))
64.0ms
(- (+ (/ (sin (+ z y)) (cos (+ z y))) x) (/ (sin a) (cos a)))
62.0ms
(fma 1 (tan (+ y z)) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))

prune945.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

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)))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
145×*-un-lft-identity
108×prod-diff
104×add-sqr-sqrt
99×add-cube-cbrt
85×times-frac
56×associate-+r+
22×distribute-lft-out
18×fma-neg
14×associate-/r/
8×flip3-- flip-- add-log-exp
7×tan-quot div-inv
6×pow1 add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-def associate-*r* associate-*l*
2×+-commutative sub-neg flip3-+ flip-+ difference-of-squares
1×frac-times associate-+r- sum-log diff-log pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod distribute-lft-out--
Calls
4 calls:
Slowest
60.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
57.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
9.0ms
(* (tan y) (tan z))
9.0ms
(+ (tan y) (tan z))

series1.7s

Calls
4 calls:
Slowest
739.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
588.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
194.0ms
(* (tan y) (tan z))
172.0ms
(+ (tan y) (tan z))

simplify19.1s

Calls
220 calls:
Slowest
559.0ms
(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)))))
559.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
512.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (* (tan a) 1)))
466.0ms
(/ (+ (tan y) (tan z)) (- (pow 1 3) (pow (* (tan y) (tan z)) 3)))
447.0ms
(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)))))

prune3.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
87×*-un-lft-identity
64×add-sqr-sqrt
59×add-cube-cbrt
54×prod-diff
52×times-frac
18×fma-neg
13×distribute-lft-out
11×add-cbrt-cube add-exp-log
8×associate-/r/ add-log-exp
6×pow1
5×flip3-- tan-quot div-inv flip--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* fma-def associate-*r* associate-*l*
2×cbrt-undiv div-exp prod-exp associate-*r/ cbrt-unprod difference-of-squares
1×+-commutative clear-num sum-log sub-neg frac-2neg flip3-+ diff-log pow-prod-down frac-add *-commutative frac-sub flip-+ associate-/l* distribute-lft-out-- associate-/l/
Calls
4 calls:
Slowest
108.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (tan z)) (cos y)))) (tan a))
21.0ms
(/ (* (sin y) (tan z)) (cos y))
12.0ms
(* (sin y) (tan z))
10.0ms
(+ (tan y) (tan z))

series1.7s

Calls
4 calls:
Slowest
753.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (/ (* (sin y) (tan z)) (cos y)))) (tan a))
575.0ms
(* (sin y) (tan z))
204.0ms
(/ (* (sin y) (tan z)) (cos y))
198.0ms
(+ (tan y) (tan z))

simplify20.2s

Calls
175 calls:
Slowest
401.0ms
(fma (/ 1 (sqrt (- 1 (/ (* (sin y) (tan z)) (cos y))))) (/ (+ (tan y) (tan z)) (sqrt (- 1 (/ (* (sin y) (tan z)) (cos y))))) (- (* (sqrt (tan a)) (sqrt (tan a)))))
399.0ms
(/ (+ (tan y) (tan z)) (- (pow 1 3) (pow (/ (* (sin y) (tan z)) (cos y)) 3)))
381.0ms
(fma (/ 1 (sqrt (- 1 (/ (* (sin y) (tan z)) (cos y))))) (/ (+ (tan y) (tan z)) (sqrt (- 1 (/ (* (sin y) (tan z)) (cos y))))) (- (* (tan a) 1)))
372.0ms
(fma (/ 1 (sqrt (- 1 (/ (* (sin y) (tan z)) (cos y))))) (/ (+ (tan y) (tan z)) (sqrt (- 1 (/ (* (sin y) (tan z)) (cos y))))) (- (* (tan a) 1)))
368.0ms
(fma (/ (* (cbrt (+ (tan y) (tan z))) (cbrt (+ (tan y) (tan z)))) 1) (/ (cbrt (+ (tan y) (tan z))) (- 1 (/ (* (sin y) (tan z)) (cos y)))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))

prune3.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

26.7b
(cbrt (* (* (/ (* (tan z) (sin y)) (cos y)) (/ (* (tan z) (sin y)) (cos y))) (/ (* (tan z) (sin y)) (cos y))))
0.3b
(* (/ (* (tan z) (sin y)) (cos y)) (/ (* (tan z) (sin y)) (cos y)))
0.2b
(* (tan z) (sin y))
0.2b
(* (tan z) (sin y))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
44×add-cbrt-cube add-exp-log
17×prod-exp cbrt-unprod
13×pow1 associate-*r* associate-*l*
12×add-sqr-sqrt cbrt-undiv *-un-lft-identity div-exp add-cube-cbrt
8×associate-*l/
7×cbrt-div
6×frac-times times-frac
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
3×pow-prod-down *-commutative
2×tan-quot div-inv
1×cbrt-prod pow2 pow-plus pow1/3 pow3 pow-prod-up rem-cbrt-cube
Calls
4 calls:
Slowest
47.0ms
(cbrt (* (* (/ (* (tan z) (sin y)) (cos y)) (/ (* (tan z) (sin y)) (cos y))) (/ (* (tan z) (sin y)) (cos y))))
30.0ms
(* (/ (* (tan z) (sin y)) (cos y)) (/ (* (tan z) (sin y)) (cos y)))
10.0ms
(* (tan z) (sin y))
10.0ms
(* (tan z) (sin y))

series633.0ms

Calls
4 calls:
Slowest
216.0ms
(* (/ (* (tan z) (sin y)) (cos y)) (/ (* (tan z) (sin y)) (cos y)))
181.0ms
(cbrt (* (* (/ (* (tan z) (sin y)) (cos y)) (/ (* (tan z) (sin y)) (cos y))) (/ (* (tan z) (sin y)) (cos y))))
141.0ms
(* (tan z) (sin y))
94.0ms
(* (tan z) (sin y))

simplify12.4s

Calls
78 calls:
Slowest
724.0ms
(* (/ (* (* (* (tan z) (sin y)) (* (tan z) (sin y))) (* (tan z) (sin y))) (* (* (cos y) (cos y)) (cos y))) (/ (* (* (* (tan z) (tan z)) (tan z)) (* (* (sin y) (sin y)) (sin y))) (* (* (cos y) (cos y)) (cos y))))
666.0ms
(* (/ (* (* (* (tan z) (tan z)) (tan z)) (* (* (sin y) (sin y)) (sin y))) (* (* (cos y) (cos y)) (cos y))) (/ (* (* (* (tan z) (sin y)) (* (tan z) (sin y))) (* (tan z) (sin y))) (* (* (cos y) (cos y)) (cos y))))
644.0ms
(- (+ (* 1/3 (* (pow z 3) y)) (* z y)) (* 1/6 (* z (pow y 3))))
603.0ms
(+ (log (/ (* (tan z) (sin y)) (cos y))) (- (log (* (tan z) (sin y))) (log (cos y))))
568.0ms
(* (* (* (/ (* (tan z) (sin y)) (cos y)) (/ (* (tan z) (sin y)) (cos y))) (/ (* (tan z) (sin y)) (cos y))) (/ (* (* (* (tan z) (sin y)) (* (tan z) (sin y))) (* (tan z) (sin y))) (* (* (cos y) (cos y)) (cos y))))

prune2.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

regimes583.0ms

Accuracy

0% (0.1b remaining)

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

bsearch3.0ms

end0.0ms

sample15.1s

Algorithm
intervals
Results
8.9s3880×body1280valid
3.3s1961×body640valid
1.1s8000×pre80true
713.0ms711×body320valid
367.0ms1165×body80valid
165.0ms283×body160valid