Details

Time bar (total: 46.5s)

sample459.0ms

Algorithm
intervals
Results
260.0ms109×body1280valid
86.0ms62×body640valid
68.0ms16×body2560valid
19.0ms23×body320valid
10.0ms35×body80valid
6.0ms11×body160valid

simplify11.0ms

Calls
1 calls:
Slowest
11.0ms
(- (tan (+ x eps)) (tan x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize55.0ms

Local error

Found 2 expressions with local error:

2.6b
(tan (+ x eps))
1.1b
(- (tan (+ x eps)) (tan x))

rewrite9.0ms

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
Calls
2 calls:
Slowest
7.0ms
(- (tan (+ x eps)) (tan x))
2.0ms
(tan (+ x eps))

series132.0ms

Calls
2 calls:
Slowest
86.0ms
(- (tan (+ x eps)) (tan x))
45.0ms
(tan (+ x eps))

simplify1.6s

Calls
35 calls:
Slowest
262.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
186.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
121.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))
113.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
71.0ms
(fma (* (cbrt (tan (+ x eps))) (cbrt (tan (+ x eps)))) (cbrt (tan (+ x eps))) (- (* (tan x) 1)))

prune477.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.4b

localize25.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
0.2b
(* (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b
(+ (tan x) (tan eps))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
102×*-un-lft-identity
71×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--
Calls
4 calls:
Slowest
48.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
15.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
8.0ms
(+ (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))

series870.0ms

Calls
4 calls:
Slowest
415.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
243.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
118.0ms
(* (tan x) (tan eps))
94.0ms
(+ (tan x) (tan eps))

simplify18.5s

Calls
199 calls:
Slowest
617.0ms
(/ (* (* (+ (tan x) (tan eps)) (+ (tan x) (tan eps))) (+ (tan x) (tan eps))) (* (* (- 1 (* (tan x) (tan eps))) (- 1 (* (tan x) (tan eps)))) (- 1 (* (tan x) (tan eps)))))
441.0ms
(fma (/ 1 (sqrt (- 1 (* (tan x) (tan eps))))) (/ (+ (tan x) (tan eps)) (sqrt (- 1 (* (tan x) (tan eps))))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
421.0ms
(fma (/ 1 (sqrt (- 1 (* (tan x) (tan eps))))) (/ (+ (tan x) (tan eps)) (sqrt (- 1 (* (tan x) (tan eps))))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
354.0ms
(/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3)))
339.0ms
(fma (/ (* (cbrt (+ (tan x) (tan eps))) (cbrt (+ (tan x) (tan eps)))) 1) (/ (cbrt (+ (tan x) (tan eps))) (- 1 (* (tan x) (tan eps)))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))

prune2.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.3b

localize8.0ms

Local error

Found 4 expressions with local error:

2.7b
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))
0.2b
(* (tan x) (tan eps))
0.1b
(+ (tan x) (tan eps))
0.1b
(- 1 (* (tan x) (tan eps)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
7×add-sqr-sqrt add-cube-cbrt
6×pow1 add-cbrt-cube tan-quot add-exp-log add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-def associate-*r* associate-*l*
1×frac-times +-commutative sum-log sub-neg flip3-+ flip3-- pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative cbrt-unprod flip-+ fma-udef flip-- distribute-lft-out
Calls
4 calls:
Slowest
5.0ms
(* (tan x) (tan eps))
4.0ms
(+ (tan x) (tan eps))
1.0ms
(- 1 (* (tan x) (tan eps)))
0.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

series610.0ms

Calls
4 calls:
Slowest
310.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))
106.0ms
(+ (tan x) (tan eps))
102.0ms
(- 1 (* (tan x) (tan eps)))
92.0ms
(* (tan x) (tan eps))

simplify1.7s

Calls
30 calls:
Slowest
275.0ms
(- 1 (+ (* 1/3 (* (pow x 3) eps)) (* x eps)))
217.0ms
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))))) (/ (sin x) (cos x)))
204.0ms
(- (+ (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))))) (/ (sin x) (cos x)))
182.0ms
(- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))
170.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))

prune838.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 14.3b

localize18.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
0.4b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.2b
(* (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
45×tan-quot
35×pow1
21×frac-times
20×add-cbrt-cube add-exp-log
15×pow-prod-down associate-*r/
14×associate-*l/
10×prod-exp cbrt-unprod
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×associate-*r* associate-*l*
6×add-log-exp
5×frac-sub
4×expm1-log1p-u pow-prod-up insert-posit16 log1p-expm1-u
3×prod-diff *-commutative
2×flip3-+ pow-plus associate--l+ flip-+
1×pow2 distribute-rgt-in sub-neg distribute-lft-in flip3-- fma-neg diff-log flip--
Calls
4 calls:
Slowest
22.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
12.0ms
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
7.0ms
(* (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))

series968.0ms

Calls
4 calls:
Slowest
724.0ms
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
91.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
77.0ms
(* (tan x) (tan eps))
77.0ms
(* (tan x) (tan eps))

simplify6.8s

Calls
104 calls:
Slowest
543.0ms
(- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2)))))) (+ (/ (* (sin x) (pow (sin eps) 2)) (* (cos x) (* (pow (cos eps) 2) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))) (+ (/ (* (pow (sin x) 2) (sin eps)) (* (pow (cos x) 2) (* (cos eps) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))) (/ (sin eps) (* (cos eps) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))))) (/ (sin x) (cos x)))
541.0ms
(- (+ (/ (sin x) (* (cos x) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2)))))) (+ (/ (* (sin x) (pow (sin eps) 2)) (* (cos x) (* (pow (cos eps) 2) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))) (+ (/ (* (pow (sin x) 2) (sin eps)) (* (pow (cos x) 2) (* (cos eps) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))) (/ (sin eps) (* (cos eps) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2))))))))) (/ (sin x) (cos x)))
458.0ms
(- (* (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (cos x)) (* (+ (* 1 1) (- (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (sin x)))
327.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
319.0ms
(- (* (* (+ (tan x) (tan eps)) (+ (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (cos x)) (* (* (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ (* 1 1) (- (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (sin x)))

prune1.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.3b

regimes189.0ms

Accuracy

89.5% (0.8b remaining)

Error of 14.6b against oracle of 13.9b and baseline of 21.3b

bsearch201.0ms

end0.0ms

sample9.7s

Algorithm
intervals
Results
5.5s3285×body1280valid
1.7s1824×body640valid
1.5s617×body2560valid
455.0ms762×body320valid
264.0ms1111×body80valid
182.0ms401×body160valid