Details

Time bar (total: 44.7s)

sample434.0ms

Algorithm
intervals
Results
228.0ms111×body1280valid
95.0ms29×body2560valid
70.0ms56×body640valid
15.0ms19×body320valid
8.0ms32×body80valid
5.0ms9×body160valid

simplify16.0ms

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

prune46.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize20.0ms

Local error

Found 2 expressions with local error:

3.3b
(tan (+ x eps))
1.3b
(- (tan (+ x eps)) (tan x))

rewrite10.0ms

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
8.0ms
(- (tan (+ x eps)) (tan x))
2.0ms
(tan (+ x eps))

series170.0ms

Calls
2 calls:
Slowest
108.0ms
(- (tan (+ x eps)) (tan x))
61.0ms
(tan (+ x eps))

simplify1.8s

Calls
35 calls:
Slowest
320.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
175.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))
171.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
83.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
76.0ms
(fma (sqrt (tan (+ x eps))) (sqrt (tan (+ x eps))) (- (* (sqrt (tan x)) (sqrt (tan x)))))

prune554.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.2b

localize33.0ms

Local error

Found 4 expressions with local error:

3.3b
(- (/ (+ (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))))

rewrite100.0ms

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
55.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
25.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
9.0ms
(+ (tan x) (tan eps))
9.0ms
(* (tan x) (tan eps))

series1.1s

Calls
4 calls:
Slowest
554.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
296.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
143.0ms
(* (tan x) (tan eps))
128.0ms
(+ (tan x) (tan eps))

simplify18.9s

Calls
199 calls:
Slowest
577.0ms
(/ (* (* (+ (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)))))
484.0ms
(fma (/ (sqrt (+ (tan x) (tan eps))) (sqrt (- 1 (* (tan x) (tan eps))))) (/ (sqrt (+ (tan x) (tan eps))) (sqrt (- 1 (* (tan x) (tan eps))))) (- (* (tan x) 1)))
419.0ms
(/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3)))
413.0ms
(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))))))
408.0ms
(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))))))

prune1.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 18.1b

localize9.0ms

Local error

Found 4 expressions with local error:

3.4b
(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)))

rewrite12.0ms

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))
5.0ms
(+ (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)))

series731.0ms

Calls
4 calls:
Slowest
360.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))
133.0ms
(- 1 (* (tan x) (tan eps)))
120.0ms
(* (tan x) (tan eps))
118.0ms
(+ (tan x) (tan eps))

simplify1.9s

Calls
30 calls:
Slowest
311.0ms
(- 1 (+ (* 1/3 (* (pow x 3) eps)) (* x eps)))
246.0ms
(- (+ (/ (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)))
224.0ms
(- (+ (/ (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)))
196.0ms
(- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))
190.0ms
(- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))

prune870.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 18.1b

localize29.0ms

Local error

Found 4 expressions with local error:

3.6b
(fma (+ (tan x) (tan eps)) (/ 1 (/ (- (* 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)))
0.2b
(* (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
40×tan-quot
35×pow1
20×add-cbrt-cube add-exp-log
19×frac-times
15×pow-prod-down
13×associate-*l/ associate-*r/
10×prod-exp cbrt-unprod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×associate-*r* associate-*l*
4×expm1-log1p-u pow-prod-up insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×pow-plus
1×pow2 fma-udef
Calls
4 calls:
Slowest
22.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
5.0ms
(* (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))
0.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (/ (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (- (tan x)))

series1.0s

Calls
4 calls:
Slowest
671.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (/ (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (- (tan x)))
127.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
114.0ms
(* (tan x) (tan eps))
106.0ms
(* (tan x) (tan eps))

simplify3.8s

Calls
84 calls:
Slowest
580.0ms
(- (+ (/ (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)))
571.0ms
(- (+ (/ (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)))
369.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
196.0ms
(+ (* 2/3 (* (pow x 2) (pow eps 4))) (+ (* (pow x 2) (pow eps 2)) (* 2/3 (* (pow x 4) (pow eps 2)))))
182.0ms
(* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))

prune1.1s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 18.1b

regimes181.0ms

Accuracy

86.3% (0.9b remaining)

Error of 15.4b against oracle of 14.4b and baseline of 21.3b

bsearch168.0ms

end0.0ms

sample10.0s

Algorithm
intervals
Results
5.1s3260×body1280valid
1.9s653×body2560valid
1.6s1801×body640valid
535.0ms766×body320valid
492.0ms1138×body80valid
204.0ms382×body160valid