Details

Time bar (total: 44.4s)

sample417.0ms

Algorithm
intervals
Results
234.0ms105×body1280valid
78.0ms25×body2560valid
65.0ms63×body640valid
19.0ms25×body320valid
7.0ms30×body80valid
4.0ms8×body160valid

simplify8.0ms

Calls
1 calls:
Slowest
8.0ms
(- (tan (+ x eps)) (tan x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.2b

localize15.0ms

Local error

Found 2 expressions with local error:

3.4b
(tan (+ x eps))
1.1b
(- (tan (+ x eps)) (tan x))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity tan-quot add-log-exp
2×pow1 tan-sum add-cbrt-cube add-exp-log frac-sub add-cube-cbrt insert-posit16
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Calls
2 calls:
Slowest
6.0ms
(- (tan (+ x eps)) (tan x))
2.0ms
(tan (+ x eps))

series207.0ms

Calls
2 calls:
Slowest
114.0ms
(- (tan (+ x eps)) (tan x))
93.0ms
(tan (+ x eps))

simplify957.0ms

Calls
15 calls:
Slowest
377.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
183.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
146.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))
62.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
43.0ms
(/ (exp (tan (+ x eps))) (exp (tan x)))

prune365.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.2b

localize17.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (/ (+ (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))))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
20×add-sqr-sqrt
15×add-cube-cbrt
13×times-frac
9×tan-quot
8×add-cbrt-cube add-exp-log add-log-exp
6×pow1
5×distribute-lft-out
4×insert-posit16 associate-/l*
3×associate-/r* associate-*r* associate-*l* associate-/l/
2×flip3-+ flip3-- frac-add associate-/r/ flip-+ 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 div-inv distribute-lft-out--
Calls
4 calls:
Slowest
61.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
27.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
12.0ms
(+ (tan x) (tan eps))
10.0ms
(* (tan x) (tan eps))

series1.0s

Calls
4 calls:
Slowest
472.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
286.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
144.0ms
(* (tan x) (tan eps))
106.0ms
(+ (tan x) (tan eps))

simplify4.5s

Calls
72 calls:
Slowest
566.0ms
(/ (* (* (+ (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)))))
426.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
284.0ms
(- (+ (/ (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)))
279.0ms
(- (+ (/ (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)))
260.0ms
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.1b

localize47.0ms

Local error

Found 4 expressions with local error:

5.7b
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
0.2b
(* (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))
0.2b
(* (+ (tan x) (tan eps)) (cos x))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
17×associate-*l/
14×tan-quot
12×*-un-lft-identity
10×add-sqr-sqrt pow1 add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
9×associate-*r*
6×frac-sub add-log-exp
4×flip3-- insert-posit16 flip--
3×flip3-+ pow-prod-down frac-add prod-exp *-commutative cbrt-unprod flip-+
2×frac-times associate-*r/
1×sub-neg diff-log distribute-lft-out
Calls
4 calls:
Slowest
25.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
21.0ms
(* (+ (tan x) (tan eps)) (cos x))
10.0ms
(* (tan x) (tan eps))
9.0ms
(* (tan x) (tan eps))

series779.0ms

Calls
4 calls:
Slowest
354.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
146.0ms
(* (+ (tan x) (tan eps)) (cos x))
140.0ms
(* (tan x) (tan eps))
138.0ms
(* (tan x) (tan eps))

simplify7.0s

Calls
60 calls:
Slowest
724.0ms
(+ (/ (* (pow (sin x) 2) (sin eps)) (* (cos x) (cos eps))) (/ (* (cos x) (sin eps)) (cos eps)))
483.0ms
(* (- (tan x) (tan eps)) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))))
457.0ms
(* (* (cos x) (cos eps)) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))))
417.0ms
(- (* (* (+ (pow (tan x) 3) (pow (tan eps) 3)) (cos x)) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (* (+ (* (tan x) (tan x)) (- (* (tan eps) (tan eps)) (* (tan x) (tan eps)))) (* (- (pow 1 3) (pow (* (tan x) (tan eps)) 3)) (sin x))))
417.0ms
(* (+ (* (tan x) (tan x)) (- (* (tan eps) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin x) (sin x))
0.2b
(* (tan x) (tan eps))
0.2b
(/ (/ (* (sin eps) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x))) (cos eps)) (* (- 1 (* (tan x) (tan eps))) (cos x)))
0.2b
(* (sin eps) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
31×add-cbrt-cube add-exp-log
16×*-un-lft-identity
14×add-sqr-sqrt add-cube-cbrt
13×pow1 times-frac
10×cbrt-undiv div-exp associate-*r*
9×associate-*l*
8×prod-exp cbrt-unprod
7×associate-/l*
4×tan-quot insert-posit16 add-log-exp
3×pow-prod-down associate-*l/ associate-*r/ *-commutative div-inv
2×associate-/r/
1×pow2 distribute-rgt-in frac-times clear-num associate-/r* frac-2neg distribute-lft-in flip3-+ pow-plus flip3-- pow-prod-up flip-+ sqr-sin flip-- sin-mult distribute-lft-out associate-/l/
Calls
4 calls:
Slowest
35.0ms
(/ (/ (* (sin eps) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x))) (cos eps)) (* (- 1 (* (tan x) (tan eps))) (cos x)))
24.0ms
(* (sin eps) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x)))
9.0ms
(* (tan x) (tan eps))
9.0ms
(* (sin x) (sin x))

series778.0ms

Calls
4 calls:
Slowest
428.0ms
(/ (/ (* (sin eps) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x))) (cos eps)) (* (- 1 (* (tan x) (tan eps))) (cos x)))
190.0ms
(* (sin eps) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x)))
124.0ms
(* (tan x) (tan eps))
36.0ms
(* (sin x) (sin x))

simplify11.6s

Calls
86 calls:
Slowest
1.3s
(/ (/ (* (* (* (sin eps) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x))) (* (sin eps) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x)))) (* (sin eps) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x)))) (* (* (cos eps) (cos eps)) (cos eps))) (* (* (* (- 1 (* (tan x) (tan eps))) (cos x)) (* (- 1 (* (tan x) (tan eps))) (cos x))) (* (- 1 (* (tan x) (tan eps))) (cos x))))
1.3s
(/ (/ (* (* (* (sin eps) (sin eps)) (sin eps)) (* (* (+ (/ (* (sin x) (sin x)) (cos x)) (cos x)) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x))) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x)))) (* (* (cos eps) (cos eps)) (cos eps))) (* (* (* (- 1 (* (tan x) (tan eps))) (cos x)) (* (- 1 (* (tan x) (tan eps))) (cos x))) (* (- 1 (* (tan x) (tan eps))) (cos x))))
1.2s
(/ (/ (* (* (* (sin eps) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x))) (* (sin eps) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x)))) (* (sin eps) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x)))) (* (* (cos eps) (cos eps)) (cos eps))) (* (* (* (- 1 (* (tan x) (tan eps))) (- 1 (* (tan x) (tan eps)))) (- 1 (* (tan x) (tan eps)))) (* (* (cos x) (cos x)) (cos x))))
647.0ms
(/ (* (* (/ (* (sin eps) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x))) (cos eps)) (/ (* (sin eps) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x))) (cos eps))) (/ (* (sin eps) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x))) (cos eps))) (* (* (* (- 1 (* (tan x) (tan eps))) (- 1 (* (tan x) (tan eps)))) (- 1 (* (tan x) (tan eps)))) (* (* (cos x) (cos x)) (cos x))))
636.0ms
(/ (* (* (/ (* (sin eps) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x))) (cos eps)) (/ (* (sin eps) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x))) (cos eps))) (/ (* (sin eps) (+ (/ (* (sin x) (sin x)) (cos x)) (cos x))) (cos eps))) (* (* (* (- 1 (* (tan x) (tan eps))) (cos x)) (* (- 1 (* (tan x) (tan eps))) (cos x))) (* (- 1 (* (tan x) (tan eps))) (cos x))))

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes167.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch3.0ms

end0.0ms

sample12.3s

Algorithm
intervals
Results
7.4s3361×body1280valid
2.0s1816×body640valid
1.9s618×body2560valid
613.0ms792×body320valid
207.0ms1066×body80valid
145.0ms347×body160valid