Details

Time bar (total: 49.3s)

sample424.0ms

Algorithm
intervals
Results
197.0ms105×body1280valid
120.0ms64×body640valid
61.0ms18×body2560valid
17.0ms20×body320valid
11.0ms39×body80valid
5.0ms10×body160valid

simplify50.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize14.0ms

Local error

Found 2 expressions with local error:

4.0b
(tan (+ x eps))
0.6b
(- (tan (+ x eps)) (tan x))

rewrite34.0ms

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
Counts
2 → 27
Calls
2 calls:
Slowest
24.0ms
(- (tan (+ x eps)) (tan x))
9.0ms
(tan (+ x eps))

series200.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
119.0ms
(- (tan (+ x eps)) (tan x))
81.0ms
(tan (+ x eps))

simplify1.3s

Counts
15 → 33
Calls
15 calls:
Slowest
405.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
367.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
168.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
150.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))
53.0ms
(/ (exp (tan (+ x eps))) (exp (tan x)))

prune405.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.9b

localize40.0ms

Local error

Found 4 expressions with local error:

2.6b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
0.3b
(* (tan x) (tan eps))
0.2b
(+ (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
22×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-- unswap-sqr
Counts
4 → 90
Calls
4 calls:
Slowest
60.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
48.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
26.0ms
(* (tan x) (tan eps))
15.0ms
(+ (tan x) (tan eps))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
562.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
312.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
134.0ms
(+ (tan x) (tan eps))
123.0ms
(* (tan x) (tan eps))

simplify5.9s

Counts
74 → 102
Calls
74 calls:
Slowest
516.0ms
(/ (* (* (+ (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)))))
441.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
424.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps)))
414.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
414.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))

prune1.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.7b

localize33.0ms

Local error

Found 4 expressions with local error:

2.6b
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))
0.3b
(* (sin x) (tan eps))
0.2b
(/ (* (sin x) (tan eps)) (cos x))
0.2b
(+ (tan x) (tan eps))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
12×*-un-lft-identity
11×add-cbrt-cube add-exp-log
8×add-cube-cbrt add-log-exp
6×pow1
5×tan-quot
4×times-frac insert-posit16
3×associate-/r* associate-*r* associate-*l*
2×cbrt-undiv div-exp prod-exp associate-*r/ cbrt-unprod difference-of-squares
1×+-commutative clear-num sum-log sub-neg frac-2neg flip3-+ flip3-- diff-log pow-prod-down frac-add *-commutative frac-sub flip-+ div-inv flip-- distribute-lft-out associate-/l* distribute-lft-out-- unswap-sqr associate-/l/
Counts
4 → 74
Calls
4 calls:
Slowest
122.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))
28.0ms
(/ (* (sin x) (tan eps)) (cos x))
24.0ms
(* (sin x) (tan eps))
14.0ms
(+ (tan x) (tan eps))

series994.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
611.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))
150.0ms
(/ (* (sin x) (tan eps)) (cos x))
133.0ms
(+ (tan x) (tan eps))
101.0ms
(* (sin x) (tan eps))

simplify4.4s

Counts
50 → 86
Calls
50 calls:
Slowest
414.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
343.0ms
(- (+ (* x eps) (* 1/3 (* x (pow eps 3)))) (* 1/6 (* (pow x 3) eps)))
337.0ms
(* (* (* (sin x) (sin x)) (sin x)) (* (* (tan eps) (tan eps)) (tan eps)))
305.0ms
(- (+ (/ (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)))
289.0ms
(+ (* 1/3 (* (pow x 3) eps)) (+ (* 1/3 (* x (pow eps 3))) (* x eps)))

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.7b

localize89.0ms

Local error

Found 4 expressions with local error:

2.6b
(- (* (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ 1 (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))) (tan x))
0.3b
(pow (* (tan x) (tan eps)) 3)
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b
(* (tan x) (tan eps))

rewrite228.0ms

Algorithm
rewrite-expression-head
Rules
48×pow1
45×tan-quot
21×frac-times add-cbrt-cube add-exp-log
19×pow-prod-down
15×associate-*r/
14×associate-*l/
10×prod-exp cbrt-unprod
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×add-log-exp
5×frac-sub
4×associate-*r* associate-*l* pow-sqr pow-prod-up insert-posit16
3×cube-div pow-unpow
2×pow-pow flip3-+ pow-plus pow-exp associate--l+ *-commutative flip-+ rem-cube-cbrt
1×pow2 distribute-rgt-in cube-mult pow-to-exp sub-neg unpow-prod-down distribute-lft-in flip3-- diff-log unpow3 cube-prod swap-sqr flip-- unswap-sqr sqr-pow
Counts
4 → 118
Calls
4 calls:
Slowest
117.0ms
(- (* (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ 1 (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))) (tan x))
65.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
25.0ms
(* (tan x) (tan eps))
19.0ms
(pow (* (tan x) (tan eps)) 3)

series2.5s

Counts
4 → 12
Calls
4 calls:
Slowest
2.0s
(- (* (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ 1 (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))) (tan x))
161.0ms
(pow (* (tan x) (tan eps)) 3)
157.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
151.0ms
(* (tan x) (tan eps))

simplify12.5s

Counts
110 → 130
Calls
110 calls:
Slowest
922.0ms
(/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))
893.0ms
(/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))
798.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
688.0ms
(* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))
631.0ms
(* (* (- (pow 1 3) (pow (* (tan x) (tan eps)) 3)) (+ (* 1 1) (- (* (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (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) (tan eps))))))) (cos x))

prune2.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.7b

regimes262.0ms

Accuracy

37.5% (4.3b remaining)

Error of 16.5b against oracle of 12.2b and baseline of 19.1b

bsearch604.0ms

end0.0ms

sample13.0s

Algorithm
intervals
Results
6.2s3338×body1280valid
2.6s606×body2560valid
2.4s1806×body640valid
650.0ms763×body320valid
648.0ms363×body160valid
282.0ms1124×body80valid