Details

Time bar (total: 1.6m)

sample485.0ms

Algorithm
intervals
Results
247.0ms107×body1280valid
117.0ms63×body640valid
70.0ms18×body2560valid
19.0ms23×body320valid
9.0ms33×body80valid
7.0ms12×body160valid

simplify16.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
16.0ms
(- (tan (+ x eps)) (tan x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.2b

localize29.0ms

Local error

Found 2 expressions with local error:

3.5b
(tan (+ x eps))
1.2b
(- (tan (+ x eps)) (tan x))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×prod-diff add-cube-cbrt
4×tan-quot add-log-exp
3×fma-neg
2×expm1-log1p-u pow1 tan-sum add-cbrt-cube add-exp-log frac-sub insert-posit16 log1p-expm1-u
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 43
Calls
2 calls:
Slowest
27.0ms
(- (tan (+ x eps)) (tan x))
10.0ms
(tan (+ x eps))

series263.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
157.0ms
(- (tan (+ x eps)) (tan x))
105.0ms
(tan (+ x eps))

simplify2.6s

Counts
35 → 49
Calls
35 calls:
Slowest
439.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
237.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
205.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
194.0ms
(fma (sqrt (tan (+ x eps))) (sqrt (tan (+ x eps))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
181.0ms
(fma (* (cbrt (tan (+ x eps))) (cbrt (tan (+ x eps)))) (cbrt (tan (+ x eps))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))

prune483.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.4b

localize44.0ms

Local error

Found 4 expressions with local error:

2.5b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
0.2b
(* (tan x) (tan eps))
0.1b
(+ (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
102×*-un-lft-identity
73×add-sqr-sqrt
66×add-cube-cbrt
61×times-frac
54×prod-diff
18×fma-neg
17×distribute-lft-out
10×associate-/r/
9×tan-quot
8×add-cbrt-cube add-exp-log add-log-exp
6×pow1 flip3-- flip--
5×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l*
3×associate-/r* fma-def associate-*r* associate-*l* associate-/l/
2×flip3-+ frac-add flip-+ difference-of-squares
1×frac-times cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg diff-log div-exp pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod distribute-lft-out-- unswap-sqr
Counts
4 → 173
Calls
4 calls:
Slowest
97.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
37.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
14.0ms
(* (tan x) (tan eps))
11.0ms
(+ (tan x) (tan eps))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
502.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
296.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
126.0ms
(+ (tan x) (tan eps))
100.0ms
(* (tan x) (tan eps))

simplify24.0s

Counts
201 → 185
Calls
201 calls:
Slowest
544.0ms
(fma (/ (sqrt (+ (tan x) (tan eps))) 1) (/ (sqrt (+ (tan x) (tan eps))) (- 1 (* (tan x) (tan eps)))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
520.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
503.0ms
(fma (/ (* (cbrt (+ (tan x) (tan eps))) (cbrt (+ (tan x) (tan eps)))) (sqrt (- 1 (* (tan x) (tan eps))))) (/ (cbrt (+ (tan x) (tan eps))) (sqrt (- 1 (* (tan x) (tan eps))))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
501.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
498.0ms
(fma (/ (sqrt (+ (tan x) (tan eps))) 1) (/ (sqrt (+ (tan x) (tan eps))) (- 1 (* (tan x) (tan eps)))) (- (* (sqrt (tan x)) (sqrt (tan x)))))

prune1.9s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.2b

localize58.0ms

Local error

Found 4 expressions with local error:

2.5b
(fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
0.2b
(* (tan eps) (tan x))

rewrite212.0ms

Algorithm
rewrite-expression-head
Rules
84×pow1
68×tan-quot
35×frac-times pow-prod-down
30×add-cbrt-cube add-exp-log
23×associate-*l/ associate-*r/
17×prod-exp cbrt-unprod
8×add-sqr-sqrt pow-sqr pow-prod-up
6×*-un-lft-identity add-cube-cbrt
5×associate-*r* associate-*l*
4×expm1-log1p-u pow-plus insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×pow2 swap-sqr
1×fma-udef unswap-sqr
Counts
4 → 139
Calls
4 calls:
Slowest
99.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
96.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
14.0ms
(* (tan eps) (tan x))
0.0ms
(fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
1.2s
(fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))
169.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
139.0ms
(* (tan eps) (tan x))
134.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))

simplify9.4s

Counts
142 → 151
Calls
142 calls:
Slowest
941.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
729.0ms
(* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))
715.0ms
(* (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))) (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))))
706.0ms
(* (* (* (* (tan eps) (tan eps)) (tan eps)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan eps) (tan eps)) (tan eps)) (* (* (tan x) (tan x)) (tan x))))
507.0ms
(- (+ (/ (* (pow (sin x) 2) (sin eps)) (* (pow (cos x) 2) (* (cos eps) (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3))))))) (+ (/ (* (pow (sin x) 3) (pow (sin eps) 2)) (* (pow (cos x) 3) (* (pow (cos eps) 2) (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3))))))) (+ (/ (* (sin x) (pow (sin eps) 2)) (* (cos x) (* (pow (cos eps) 2) (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3))))))) (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (pow (cos x) 2) (* (pow (cos eps) 3) (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3))))))) (+ (/ (sin eps) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos eps))) (/ (sin x) (* (cos x) (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3))))))))))) (/ (sin x) (cos x)))

prune2.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.4b

localize260.0ms

Local error

Found 4 expressions with local error:

2.5b
(- (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))))) (/ (sin x) (cos x)))
0.3b
(* (sin eps) (sin eps))
0.3b
(* (sin eps) (sin eps))
0.3b
(* (sin eps) (sin eps))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
53×*-un-lft-identity
51×add-cube-cbrt
39×prod-diff
28×times-frac
25×pow1
10×add-cbrt-cube add-exp-log
9×swap-sqr associate-*r* associate-*l*
6×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×pow2 pow-plus fma-neg pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod sqr-sin div-inv sin-mult unswap-sqr
2×difference-of-squares
1×sub-neg flip3-- diff-log associate--l+ fma-udef flip-- distribute-lft-out--
Counts
4 → 151
Calls
4 calls:
Slowest
24.0ms
(* (sin eps) (sin eps))
21.0ms
(* (sin eps) (sin eps))
13.0ms
(* (sin eps) (sin eps))
11.0ms
(- (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))))) (/ (sin x) (cos x)))

series1.8s

Counts
4 → 12
Calls
4 calls:
Slowest
1.7s
(- (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))))) (/ (sin x) (cos x)))
34.0ms
(* (sin eps) (sin eps))
33.0ms
(* (sin eps) (sin eps))
32.0ms
(* (sin eps) (sin eps))

simplify37.3s

Counts
168 → 163
Calls
168 calls:
Slowest
1.5s
(fma (* (cbrt (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))))))) (cbrt (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))))))) (cbrt (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))))))) (- (* (sqrt (/ (sin x) (cos x))) (sqrt (/ (sin x) (cos x))))))
1.3s
(fma (* (cbrt (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))))))) (cbrt (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))))))) (cbrt (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))))))) (- (* (/ (sqrt (sin x)) (cos x)) (/ (sqrt (sin x)) 1))))
1.3s
(fma (* (cbrt (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))))))) (cbrt (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))))))) (cbrt (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))))))) (- (* (cbrt (/ (sin x) (cos x))) (* (cbrt (/ (sin x) (cos x))) (cbrt (/ (sin x) (cos x)))))))
1.2s
(fma (sqrt (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))))))) (sqrt (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))))))) (- (* (/ (sin x) (cos x)) 1)))
1.2s
(fma (* (cbrt (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))))))) (cbrt (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))))))) (cbrt (fma (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (fma (/ (sin x) (cos x)) (/ (/ (* (sin eps) (sin eps)) (* (cos eps) (cos eps))) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))) (+ (fma (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (cos eps)) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin eps) (cos eps)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps)))))) (/ (/ (sin x) (cos x)) (- 1 (/ (* (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (/ (sin x) (cos x))) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))))))) (- (* (/ (sin x) (cos x)) 1)))

prune2.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes134.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch20.0ms

end0.0ms

sample11.2s

Algorithm
intervals
Results
5.8s3273×body1280valid
2.1s1868×body640valid
1.8s644×body2560valid
566.0ms755×body320valid
559.0ms1107×body80valid
168.0ms353×body160valid