Details

Time bar (total: 1.2m)

sample344.0ms

Algorithm
intervals
Results
163.0ms108×body1280valid
82.0ms48×body640valid
55.0ms19×body2560valid
17.0ms25×body320valid
8.0ms41×body80valid
7.0ms15×body160valid

simplify50.0ms

Calls
1 calls:
Slowest
50.0ms
(- (tan (+ x eps)) (tan x))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize19.0ms

Local error

Found 2 expressions with local error:

3.0b
(tan (+ x eps))
1.6b
(- (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
7.0ms
(- (tan (+ x eps)) (tan x))
2.0ms
(tan (+ x eps))

series142.0ms

Calls
2 calls:
Slowest
100.0ms
(- (tan (+ x eps)) (tan x))
42.0ms
(tan (+ x eps))

simplify1.6s

Calls
35 calls:
Slowest
302.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
207.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
116.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))
81.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
65.0ms
(fma 1 (tan (+ x eps)) (- (* (sqrt (tan x)) (sqrt (tan x)))))

prune525.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.7b

localize27.0ms

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))))

rewrite90.0ms

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
46.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
21.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
10.0ms
(* (tan x) (tan eps))
9.0ms
(+ (tan x) (tan eps))

series901.0ms

Calls
4 calls:
Slowest
428.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
252.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
117.0ms
(* (tan x) (tan eps))
104.0ms
(+ (tan x) (tan eps))

simplify18.1s

Calls
199 calls:
Slowest
540.0ms
(/ (* (* (+ (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)))))
405.0ms
(/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3)))
345.0ms
(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))))))
341.0ms
(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))))))
336.0ms
(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))))))

prune2.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.5b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
68×tan-quot
60×pow1
35×frac-times
30×add-cbrt-cube add-exp-log
27×pow-prod-down
23×associate-*l/ associate-*r/
17×prod-exp cbrt-unprod
15×add-sqr-sqrt *-un-lft-identity
13×add-cube-cbrt
9×prod-diff
8×pow-prod-up
6×add-log-exp
5×associate-*r* associate-*l*
4×expm1-log1p-u pow-plus insert-posit16 log1p-expm1-u
3×fma-neg *-commutative
2×pow2
1×sub-neg flip3-- diff-log associate--l+ fma-udef flip-- distribute-lft-out-- difference-of-squares
Calls
4 calls:
Slowest
44.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
21.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
10.0ms
(* (tan x) (tan eps))
7.0ms
(- (fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (* (tan x) (tan eps)) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (tan x))

series1.2s

Calls
4 calls:
Slowest
776.0ms
(- (fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (* (tan x) (tan eps)) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (tan x))
135.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
132.0ms
(* (tan x) (tan eps))
113.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))

simplify10.2s

Calls
145 calls:
Slowest
656.0ms
(fma 1 (fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (* (tan x) (tan eps)) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (- (* (tan x) 1)))
582.0ms
(- (+ (/ (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)))
576.0ms
(- (+ (/ (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)))
485.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
440.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))

prune1.9s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 11.7b

localize21.0ms

Local error

Found 4 expressions with local error:

2.6b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (tan x))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b
(* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (* (tan x) (tan eps)))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
94×*-un-lft-identity
73×tan-quot
67×add-sqr-sqrt
63×pow1
62×add-cube-cbrt
61×times-frac
54×prod-diff
40×add-cbrt-cube add-exp-log
39×frac-times
29×pow-prod-down
27×associate-*r/
25×associate-*l/
22×prod-exp cbrt-unprod
20×associate-*l*
18×fma-neg
15×distribute-lft-out
10×associate-/r/
8×pow-prod-up
6×flip3-- flip-- add-log-exp
5×div-inv
4×expm1-log1p-u pow-plus insert-posit16 log1p-expm1-u
3×associate-*r* *-commutative
2×pow2 cbrt-undiv div-exp difference-of-squares
1×sub-neg diff-log frac-sub distribute-lft-out--
Calls
4 calls:
Slowest
65.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (tan x))
22.0ms
(* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (* (tan x) (tan eps)))
21.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
21.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))

series876.0ms

Calls
4 calls:
Slowest
421.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (tan x))
278.0ms
(* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (* (tan x) (tan eps)))
89.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
89.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))

simplify20.8s

Calls
279 calls:
Slowest
368.0ms
(/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) 3)))
367.0ms
(/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) 3)))
325.0ms
(/ (* (sin x) (* (sin eps) (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (* (cos x) (* (cos eps) (- 1 (/ (* (pow (sin x) 2) (pow (sin eps) 2)) (* (pow (cos x) 2) (pow (cos eps) 2)))))))
324.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
323.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))

prune2.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 8.6b

regimes246.0ms

Accuracy

76.6% (2.3b remaining)

Error of 12.4b against oracle of 10.1b and baseline of 19.8b

bsearch223.0ms

end0.0ms

sample9.5s

Algorithm
intervals
Results
5.0s3322×body1280valid
1.8s1822×body640valid
1.6s636×body2560valid
702.0ms815×body320valid
188.0ms1060×body80valid
161.0ms345×body160valid