Details

Time bar (total: 7.1m)

sample310.0ms

Algorithm
intervals
Results
179.0ms110×body1280valid
48.0ms16×body2560valid
47.0ms55×body640valid
12.0ms21×body320valid
8.0ms42×body80valid
5.0ms12×body160valid

simplify15.0ms

Calls
1 calls:
Slowest
15.0ms
(- (tan (+ x eps)) (tan x))

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize17.0ms

Local error

Found 2 expressions with local error:

2.0b
(tan (+ x eps))
1.8b
(- (tan (+ x eps)) (tan x))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
5×tan-quot
4×add-sqr-sqrt tan-sum *-un-lft-identity add-log-exp
3×frac-sub
2×pow1 +-commutative add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Calls
2 calls:
Slowest
14.0ms
(- (tan (+ x eps)) (tan x))
6.0ms
(tan (+ x eps))

series183.0ms

Calls
2 calls:
Slowest
117.0ms
(- (tan (+ x eps)) (tan x))
65.0ms
(tan (+ x eps))

simplify2.1s

Calls
18 calls:
Slowest
464.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
456.0ms
(- (* (+ (tan eps) (tan x)) (cos x)) (* (- 1 (* (tan eps) (tan x))) (sin x)))
443.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
158.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
140.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))

prune504.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.0b

localize44.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x)))) (tan x))
0.2b
(* (tan eps) (tan x))
0.1b
(- 1 (* (tan eps) (tan x)))
0.1b
(/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x))))

rewrite362.0ms

Algorithm
rewrite-expression-head
Rules
89×*-un-lft-identity
86×add-sqr-sqrt
37×times-frac
30×difference-of-squares
27×tan-quot
23×add-cube-cbrt
19×frac-sub
18×associate-/r*
15×distribute-lft-out-- unswap-sqr
11×distribute-lft-out
10×associate-*l*
8×add-cbrt-cube add-exp-log associate-/l* add-log-exp
6×pow1 associate-/l/
4×insert-posit16
3×flip3-- associate-*r* flip--
2×clear-num sub-neg frac-2neg flip3-+ diff-log frac-add associate-/r/ flip-+
1×frac-times cbrt-undiv div-exp pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod div-inv
Calls
4 calls:
Slowest
265.0ms
(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x)))) (tan x))
67.0ms
(/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x))))
15.0ms
(* (tan eps) (tan x))
12.0ms
(- 1 (* (tan eps) (tan x)))

series1.2s

Calls
4 calls:
Slowest
561.0ms
(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x)))) (tan x))
304.0ms
(/ (+ (tan eps) (tan x)) (- 1 (* (tan eps) (tan x))))
148.0ms
(- 1 (* (tan eps) (tan x)))
141.0ms
(* (tan eps) (tan x))

simplify17.6s

Calls
171 calls:
Slowest
553.0ms
(* (* (- 1 (* (tan eps) (tan x))) (+ (* (tan eps) (tan eps)) (- (* (tan x) (tan x)) (* (tan eps) (tan x))))) (cos x))
512.0ms
(- (* (/ (+ (tan eps) (tan x)) 1) (cos x)) (* (- 1 (* (tan eps) (tan x))) (sin x)))
493.0ms
(/ (* (* (+ (tan eps) (tan x)) (+ (tan eps) (tan x))) (+ (tan eps) (tan x))) (* (* (- 1 (* (tan eps) (tan x))) (- 1 (* (tan eps) (tan x)))) (- 1 (* (tan eps) (tan x)))))
471.0ms
(+ x (+ (* 1/3 (pow eps 3)) eps))
455.0ms
(- (* (+ (tan eps) (tan x)) (cos x)) (* (- 1 (* (tan eps) (tan x))) (sin x)))

prune1.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.7b

localize62.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (/ (+ (tan eps) (tan x)) (- 1 (/ (* (sin eps) (tan x)) (cos eps)))) (tan x))
0.2b
(* (sin eps) (tan x))
0.2b
(/ (* (sin eps) (tan x)) (cos eps))
0.1b
(- 1 (/ (* (sin eps) (tan x)) (cos eps)))

rewrite446.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
47×*-un-lft-identity
45×times-frac
33×add-cube-cbrt
24×tan-quot
20×frac-sub
16×associate-/l*
15×associate-*r* associate-*l*
14×difference-of-squares
13×associate-/r*
11×add-cbrt-cube add-exp-log
9×unswap-sqr
8×add-log-exp
6×pow1
5×*-commutative
4×insert-posit16 associate-/l/
3×distribute-lft-out--
2×cbrt-undiv clear-num sub-neg frac-2neg flip3-- diff-log div-exp prod-exp associate-*r/ cbrt-unprod flip--
1×flip3-+ pow-prod-down frac-add flip-+ div-inv distribute-lft-out
Calls
4 calls:
Slowest
364.0ms
(- (/ (+ (tan eps) (tan x)) (- 1 (/ (* (sin eps) (tan x)) (cos eps)))) (tan x))
28.0ms
(/ (* (sin eps) (tan x)) (cos eps))
25.0ms
(- 1 (/ (* (sin eps) (tan x)) (cos eps)))
24.0ms
(* (sin eps) (tan x))

series995.0ms

Calls
4 calls:
Slowest
560.0ms
(- (/ (+ (tan eps) (tan x)) (- 1 (/ (* (sin eps) (tan x)) (cos eps)))) (tan x))
176.0ms
(- 1 (/ (* (sin eps) (tan x)) (cos eps)))
154.0ms
(/ (* (sin eps) (tan x)) (cos eps))
105.0ms
(* (sin eps) (tan x))

simplify19.4s

Calls
173 calls:
Slowest
954.0ms
(- (* 1 (cos x)) (* (/ (- 1 (/ (* (sin eps) (tan x)) (cos eps))) (+ (tan eps) (tan x))) (sin x)))
669.0ms
(* (* (- 1 (/ (* (sin eps) (tan x)) (cos eps))) (* (cos eps) (cos x))) (cos x))
470.0ms
(- (* (sqrt (+ (tan eps) (tan x))) (cos x)) (* (/ (- 1 (/ (* (sin eps) (tan x)) (cos eps))) (sqrt (+ (tan eps) (tan x)))) (sin x)))
466.0ms
(- (* (* (cbrt (+ (tan eps) (tan x))) (cbrt (+ (tan eps) (tan x)))) (cos x)) (* (/ (- 1 (/ (* (sin eps) (tan x)) (cos eps))) (cbrt (+ (tan eps) (tan x)))) (sin x)))
458.0ms
(- (* 1 (cos x)) (* (/ (- 1 (/ (* (sin eps) (tan x)) (cos eps))) (+ (tan eps) (tan x))) (sin x)))

prune2.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.7b

localize45.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (/ (+ (tan eps) (tan x)) (/ (- (* 1 1) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (+ 1 (* (tan eps) (tan x))))) (tan x))
0.3b
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
0.2b
(* (tan eps) (tan x))
0.2b
(* (tan eps) (tan x))

rewrite2.5s

Algorithm
rewrite-expression-head
Rules
1338×add-sqr-sqrt
1155×*-un-lft-identity
664×unswap-sqr
598×tan-quot
556×frac-sub
546×associate-/r*
543×times-frac
408×difference-of-squares
275×associate-*l*
274×swap-sqr
217×distribute-lft-out
135×add-cube-cbrt
121×distribute-lft-out--
112×*-commutative
50×associate-*r*
47×pow1
20×add-cbrt-cube add-exp-log
19×frac-times pow-prod-down
13×associate-*l/ associate-*r/
10×prod-exp cbrt-unprod
6×add-log-exp
4×pow-sqr pow-prod-up insert-posit16 associate-/l*
3×associate-/l/
2×flip3-+ pow-plus associate-/r/ flip-+
1×pow2 clear-num sub-neg frac-2neg flip3-- diff-log frac-add div-inv flip--
Calls
4 calls:
Slowest
2.3s
(- (/ (+ (tan eps) (tan x)) (/ (- (* 1 1) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (+ 1 (* (tan eps) (tan x))))) (tan x))
120.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
27.0ms
(* (tan eps) (tan x))
14.0ms
(* (tan eps) (tan x))

series1.6s

Calls
4 calls:
Slowest
1.2s
(- (/ (+ (tan eps) (tan x)) (/ (- (* 1 1) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (+ 1 (* (tan eps) (tan x))))) (tan x))
142.0ms
(* (tan eps) (tan x))
140.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
113.0ms
(* (tan eps) (tan x))

simplify5.9m

Calls
1272 calls:
Slowest
981.0ms
(- (* (/ (+ (tan eps) (tan x)) (/ (+ (sqrt (* 1 1)) (* (sqrt (* (tan eps) (tan x))) (sqrt (* (tan eps) (tan x))))) (sqrt (+ 1 (* (tan eps) (tan x)))))) (cos x)) (* (/ (- (sqrt (* 1 1)) (* (sqrt (* (tan eps) (tan x))) (sqrt (* (tan eps) (tan x))))) (sqrt (+ 1 (* (tan eps) (tan x))))) (sin x)))
939.0ms
(* (/ (- 1 (* (sqrt (* (tan eps) (tan x))) (sqrt (* (tan eps) (tan x))))) (sqrt (+ 1 (* (tan eps) (tan x))))) (cos x))
926.0ms
(- (* (/ (+ (tan eps) (tan x)) (/ (+ (* 1 (sqrt 1)) (* (sqrt (* (tan eps) (tan x))) (sqrt (* (tan eps) (tan x))))) (sqrt (+ 1 (* (tan eps) (tan x)))))) (cos x)) (* (/ (- (* 1 (sqrt 1)) (* (sqrt (* (tan eps) (tan x))) (sqrt (* (tan eps) (tan x))))) (sqrt (+ 1 (* (tan eps) (tan x))))) (sin x)))
916.0ms
(- (* (/ (+ (tan eps) (tan x)) (/ (+ (* (sqrt 1) 1) (sqrt (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) 1)) (cos x)) (* (/ (- (* (sqrt 1) 1) (sqrt (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) (+ 1 (* (tan eps) (tan x)))) (sin x)))
884.0ms
(- (* (/ (+ (tan eps) (tan x)) (/ (+ (* 1 1) (* (tan eps) (tan x))) (sqrt (+ 1 (* (tan eps) (tan x)))))) (cos x)) (* (/ (- (* 1 1) (* (tan eps) (tan x))) (sqrt (+ 1 (* (tan eps) (tan x))))) (sin x)))

prune8.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

regimes156.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch6.0ms

end0.0ms

sample11.0s

Algorithm
intervals
Results
5.5s3396×body1280valid
2.1s606×body2560valid
1.9s1800×body640valid
643.0ms1108×body80valid
575.0ms741×body320valid
163.0ms349×body160valid