Details

Time bar (total: 1.1m)

sample532.0ms

Algorithm
intervals
Results
305.0ms125×body1280valid
91.0ms62×body640valid
49.0ms256×pre80true
24.0ms22×body320valid
14.0ms42×body80valid
3.0ms5×body160valid

simplify498.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
497.0ms
(+ x (- (tan (+ y z)) (tan a)))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize19.0ms

Local error

Found 3 expressions with local error:

3.4b
(tan (+ y z))
0.2b
(+ x (- (tan (+ y z)) (tan a)))
0.1b
(- (tan (+ y z)) (tan a))

rewrite41.0ms

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
19.0ms
(+ x (- (tan (+ y z)) (tan a)))
16.0ms
(- (tan (+ y z)) (tan a))
6.0ms
(tan (+ y z))

series469.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
210.0ms
(- (tan (+ y z)) (tan a))
183.0ms
(+ x (- (tan (+ y z)) (tan a)))
76.0ms
(tan (+ y z))

simplify3.7s

Counts
56 → 84
Calls
56 calls:
Slowest
312.0ms
(- (* (+ (tan y) (tan z)) (cos a)) (* (- 1 (* (tan y) (tan z))) (sin a)))
252.0ms
(fma (* (cbrt (tan (+ y z))) (cbrt (tan (+ y z)))) (cbrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
234.0ms
(+ (* 1/3 (pow y 3)) (+ z y))
216.0ms
(fma (sqrt (tan (+ y z))) (sqrt (tan (+ y z))) (- (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a))))))
190.0ms
(fma (- (cbrt (tan a))) (* (cbrt (tan a)) (cbrt (tan a))) (* (cbrt (tan a)) (* (cbrt (tan a)) (cbrt (tan a)))))

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite270.0ms

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
133.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
91.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
31.0ms
(* (tan y) (tan z))
10.0ms
(+ (tan y) (tan z))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
571.0ms
(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
546.0ms
(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
184.0ms
(* (tan y) (tan z))
132.0ms
(+ (tan y) (tan z))

simplify26.1s

Counts
228 → 223
Calls
228 calls:
Slowest
571.0ms
(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)))))
520.0ms
(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (* (tan a) 1)))
494.0ms
(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)))))
460.0ms
(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))))))
454.0ms
(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))))))

prune3.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize79.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan z) (tan y))
0.2b
(* (tan z) (tan y))
0.2b
(* (tan z) (tan y))
0.2b
(+ x (+ (- (/ (/ (+ (tan y) (tan z)) (cbrt (- 1 (* (tan z) (tan y))))) (* (cbrt (- 1 (* (tan z) (tan y)))) (cbrt (- 1 (* (tan z) (tan y)))))) (tan a)) 0))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
17×add-sqr-sqrt
13×add-log-exp
12×tan-quot
11×add-cube-cbrt
10×pow1 add-cbrt-cube add-exp-log
9×associate-*r* associate-*l*
5×sum-log distribute-lft-out
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×frac-times fma-def pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
1×+-commutative associate-+r+ associate-+r- flip3-+ diff-log associate-+l- flip-+ distribute-lft-out--
Counts
4 → 96
Calls
4 calls:
Slowest
1.7s
(+ x (+ (- (/ (/ (+ (tan y) (tan z)) (cbrt (- 1 (* (tan z) (tan y))))) (* (cbrt (- 1 (* (tan z) (tan y)))) (cbrt (- 1 (* (tan z) (tan y)))))) (tan a)) 0))
40.0ms
(* (tan z) (tan y))
30.0ms
(* (tan z) (tan y))
29.0ms
(* (tan z) (tan y))

series932.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
552.0ms
(+ x (+ (- (/ (/ (+ (tan y) (tan z)) (cbrt (- 1 (* (tan z) (tan y))))) (* (cbrt (- 1 (* (tan z) (tan y)))) (cbrt (- 1 (* (tan z) (tan y)))))) (tan a)) 0))
145.0ms
(* (tan z) (tan y))
119.0ms
(* (tan z) (tan y))
115.0ms
(* (tan z) (tan y))

simplify4.6s

Counts
63 → 108
Calls
63 calls:
Slowest
378.0ms
(* (* (* (tan z) (tan z)) (tan z)) (* (* (tan y) (tan y)) (tan y)))
356.0ms
(* (* (* (tan z) (tan z)) (tan z)) (* (* (tan y) (tan y)) (tan y)))
329.0ms
(- (+ (/ (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)))
320.0ms
(* (* (* (tan z) (tan z)) (tan z)) (* (* (tan y) (tan y)) (tan y)))
317.0ms
(+ (* 1/3 (* (pow z 3) y)) (+ (* 1/3 (* z (pow y 3))) (* z y)))

prune1.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize91.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan z) (tan y))
0.2b
(* (tan z) (tan y))
0.2b
(* (sin z) (tan y))
0.2b
(+ x (+ (- (/ (/ (+ (tan y) (tan z)) (cbrt (- 1 (* (tan z) (tan y))))) (* (cbrt (- 1 (/ (* (sin z) (tan y)) (cos z)))) (cbrt (- 1 (* (tan z) (tan y)))))) (tan a)) 0))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
17×add-sqr-sqrt
13×add-log-exp
11×add-cube-cbrt
10×pow1 add-cbrt-cube add-exp-log
9×associate-*r* associate-*l* tan-quot
5×sum-log distribute-lft-out
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-def pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
2×frac-times associate-*l/
1×+-commutative associate-+r+ associate-+r- flip3-+ diff-log associate-+l- flip-+ distribute-lft-out--
Counts
4 → 94
Calls
4 calls:
Slowest
1.2s
(+ x (+ (- (/ (/ (+ (tan y) (tan z)) (cbrt (- 1 (* (tan z) (tan y))))) (* (cbrt (- 1 (/ (* (sin z) (tan y)) (cos z)))) (cbrt (- 1 (* (tan z) (tan y)))))) (tan a)) 0))
23.0ms
(* (sin z) (tan y))
18.0ms
(* (tan z) (tan y))
15.0ms
(* (tan z) (tan y))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
740.0ms
(+ x (+ (- (/ (/ (+ (tan y) (tan z)) (cbrt (- 1 (* (tan z) (tan y))))) (* (cbrt (- 1 (/ (* (sin z) (tan y)) (cos z)))) (cbrt (- 1 (* (tan z) (tan y)))))) (tan a)) 0))
144.0ms
(* (tan z) (tan y))
134.0ms
(* (tan z) (tan y))
104.0ms
(* (sin z) (tan y))

simplify4.8s

Counts
60 → 106
Calls
60 calls:
Slowest
404.0ms
(* (exp x) (exp (+ (- (/ (/ (+ (tan y) (tan z)) (cbrt (- 1 (* (tan z) (tan y))))) (* (cbrt (- 1 (/ (* (sin z) (tan y)) (cos z)))) (cbrt (- 1 (* (tan z) (tan y)))))) (tan a)) 0)))
378.0ms
(* (exp x) (* (exp (- (/ (/ (+ (tan y) (tan z)) (cbrt (- 1 (* (tan z) (tan y))))) (* (cbrt (- 1 (/ (* (sin z) (tan y)) (cos z)))) (cbrt (- 1 (* (tan z) (tan y)))))) (tan a))) (exp 0)))
334.0ms
(- (+ (* 1/3 (* z (pow y 3))) (* z y)) (* 1/6 (* (pow z 3) y)))
315.0ms
(* (* (* (tan z) (tan z)) (tan z)) (* (* (tan y) (tan y)) (tan y)))
312.0ms
(* (* (* (tan z) (tan z)) (tan z)) (* (* (tan y) (tan y)) (tan y)))

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes416.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample11.5s

Algorithm
intervals
Results
6.7s3875×body1280valid
2.8s1980×body640valid
761.0ms8000×pre80true
450.0ms674×body320valid
240.0ms1186×body80valid
136.0ms285×body160valid