Details

Time bar (total: 48.6s)

sample414.0ms

Algorithm
intervals
Results
202.0ms109×body1280valid
94.0ms16×body2560valid
78.0ms62×body640valid
16.0ms23×body320valid
8.0ms35×body80valid
5.0ms11×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: 35.4b

localize64.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

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
12.0ms
(- (tan (+ x eps)) (tan x))
3.0ms
(tan (+ x eps))

series136.0ms

Calls
2 calls:
Slowest
78.0ms
(- (tan (+ x eps)) (tan x))
58.0ms
(tan (+ x eps))

simplify1.4s

Calls
15 calls:
Slowest
487.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
351.0ms
(/ (sin (+ x eps)) (cos (+ x eps)))
168.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
125.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))
65.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))

prune316.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.5b

localize18.0ms

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))

rewrite72.0ms

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
30.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
28.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
7.0ms
(+ (tan x) (tan eps))
6.0ms
(* (tan x) (tan eps))

series969.0ms

Calls
4 calls:
Slowest
441.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
260.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
135.0ms
(* (tan x) (tan eps))
133.0ms
(+ (tan x) (tan eps))

simplify4.3s

Calls
72 calls:
Slowest
447.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
420.0ms
(/ (* (* (+ (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)))))
263.0ms
(- (+ (/ (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)))
238.0ms
(- (+ (/ (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)))
227.0ms
(+ (* 1/3 (* (pow x 3) eps)) (+ (* 1/3 (* x (pow eps 3))) (* x eps)))

prune944.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.3b

localize22.0ms

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))

rewrite67.0ms

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
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×associate-*r* associate-*l*
6×add-log-exp
5×frac-sub
4×pow-prod-up insert-posit16
3×*-commutative
2×flip3-+ pow-plus associate--l+ flip-+
1×pow2 distribute-rgt-in sub-neg distribute-lft-in flip3-- diff-log flip--
Calls
4 calls:
Slowest
40.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
11.0ms
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
8.0ms
(* (tan x) (tan eps))
6.0ms
(* (tan x) (tan eps))

series1.1s

Calls
4 calls:
Slowest
812.0ms
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
113.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
111.0ms
(* (tan x) (tan eps))
111.0ms
(* (tan x) (tan eps))

simplify8.4s

Calls
97 calls:
Slowest
711.0ms
(- (+ (/ (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)))
640.0ms
(- (+ (/ (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)))
554.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
331.0ms
(- (* (* (+ (tan x) (tan eps)) (+ 1 (* (tan x) (tan eps)))) (cos x)) (* (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (sin x)))
331.0ms
(- (* (* (+ (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)))

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.3b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
29×add-cbrt-cube add-exp-log
21×tan-quot
13×pow1 associate-*r* prod-exp cbrt-unprod
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×frac-times
8×associate-*l/
7×associate-*l* associate-*r/
6×add-log-exp
5×pow-prod-down frac-sub
4×cbrt-undiv div-exp insert-posit16
3×times-frac *-commutative
2×flip3-+ associate--l+ flip-+
1×distribute-rgt-in sub-neg distribute-lft-in flip3-- diff-log div-inv flip--
Calls
4 calls:
Slowest
23.0ms
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
20.0ms
(* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps)))
8.0ms
(* (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))

series1.5s

Calls
4 calls:
Slowest
1.2s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
174.0ms
(* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps)))
103.0ms
(* (tan x) (tan eps))
87.0ms
(* (tan x) (tan eps))

simplify13.4s

Calls
81 calls:
Slowest
743.0ms
(- (+ (/ (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)))
662.0ms
(- (+ (/ (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)))
593.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (/ (* (* (* (tan x) (sin eps)) (* (tan x) (sin eps))) (* (tan x) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))
581.0ms
(* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (/ (* (* (* (tan x) (tan x)) (tan x)) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))
552.0ms
(* (* (- (* 1 1) (* (* (tan x) (tan eps)) (/ (* (tan x) (sin eps)) (cos eps)))) (- 1 (* (tan x) (tan eps)))) (cos x))

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.3b

regimes224.0ms

Accuracy

90% (0.7b remaining)

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

bsearch550.0ms

end0.0ms

sample11.3s

Algorithm
intervals
Results
6.2s3285×body1280valid
1.9s617×body2560valid
1.8s1824×body640valid
625.0ms762×body320valid
313.0ms1111×body80valid
187.0ms401×body160valid