Details

Time bar (total: 1.1m)

sample420.0ms

Algorithm
intervals
Results
188.0ms107×body1280valid
103.0ms18×body2560valid
68.0ms60×body640valid
32.0ms29×body320valid
8.0ms16×body160valid
5.0ms26×body80valid

simplify16.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
16.0ms
(- (tan (+ x eps)) (tan x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize26.0ms

Local error

Found 2 expressions with local error:

3.0b
(tan (+ x eps))
1.5b
(- (tan (+ x eps)) (tan x))

rewrite68.0ms

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
58.0ms
(- (tan (+ x eps)) (tan x))
10.0ms
(tan (+ x eps))

series205.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
136.0ms
(- (tan (+ x eps)) (tan x))
69.0ms
(tan (+ x eps))

simplify2.4s

Counts
40 → 33
Calls
40 calls:
Slowest
508.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
473.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
345.0ms
(* (* (- (tan (+ x eps)) (tan x)) (- (tan (+ x eps)) (tan x))) (- (tan (+ x eps)) (tan x)))
210.0ms
(- (pow (tan (+ x eps)) 3) (pow (tan x) 3))
149.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))

prune390.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.9b

localize26.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
0.3b
(* (tan x) (tan eps))
0.1b
(+ (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))

rewrite133.0ms

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
70.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
28.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
25.0ms
(* (tan x) (tan eps))
7.0ms
(+ (tan x) (tan eps))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
518.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
270.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
130.0ms
(* (tan x) (tan eps))
121.0ms
(+ (tan x) (tan eps))

simplify10.5s

Counts
123 → 102
Calls
123 calls:
Slowest
571.0ms
(/ (* (* (+ (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)))))
558.0ms
(* (* (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)) (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))) (- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x)))
479.0ms
(* (* (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))) (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))))
478.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
456.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.8b

localize75.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (+ (/ (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)))
0.2b
(/ (sin eps) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))))
0.2b
(* (sin x) (sin eps))
0.2b
(* (sin x) (sin eps))

rewrite716.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
15×*-un-lft-identity
13×add-cbrt-cube add-exp-log
10×add-cube-cbrt
9×add-log-exp
8×pow1
6×associate-*r* associate-*l*
4×times-frac insert-posit16
3×prod-exp frac-sub cbrt-unprod associate-/l*
2×cbrt-undiv flip3-- diff-log div-exp pow-prod-down associate-*r/ associate-/r/ *-commutative flip-- sin-mult distribute-lft-out-- difference-of-squares unswap-sqr
1×clear-num associate-/r* sum-log sub-neg frac-2neg flip3-+ frac-add associate--l+ flip-+ div-inv distribute-lft-out
Counts
4 → 86
Calls
4 calls:
Slowest
664.0ms
(- (+ (/ (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)))
29.0ms
(/ (sin eps) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))))
11.0ms
(* (sin x) (sin eps))
11.0ms
(* (sin x) (sin eps))

series957.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
582.0ms
(- (+ (/ (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)))
224.0ms
(/ (sin eps) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))))
81.0ms
(* (sin x) (sin eps))
70.0ms
(* (sin x) (sin eps))

simplify16.7s

Counts
109 → 98
Calls
109 calls:
Slowest
658.0ms
(- (* (+ (pow (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) 3) (pow (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) 3)) (cos x)) (* (+ (* (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (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) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))))) (* (/ (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)))
657.0ms
(- (sqrt (+ (/ (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)))))))) (sqrt (/ (sin x) (cos x))))
625.0ms
(* (* (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (cos x))
402.0ms
(* (* (* (sin x) (sin x)) (sin x)) (* (* (sin eps) (sin eps)) (sin eps)))
373.0ms
(/ (* (exp (/ (sin eps) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))))) (exp (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))))) (exp (/ (sin x) (cos x))))

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.2b

localize83.0ms

Local error

Found 4 expressions with local error:

3.5b
(- (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (sin x) (cos x)))
0.2b
(/ (sin eps) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))))
0.2b
(* (sin x) (sin eps))
0.2b
(* (sin x) (sin eps))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
13×add-cbrt-cube add-exp-log
12×*-un-lft-identity
10×add-cube-cbrt
8×pow1
6×associate-*r* associate-*l* add-log-exp
4×times-frac insert-posit16
3×prod-exp cbrt-unprod div-inv associate-/l*
2×cbrt-undiv flip3-- div-exp pow-prod-down associate-*r/ associate-/r/ *-commutative flip-- sin-mult distribute-lft-out-- difference-of-squares unswap-sqr
1×clear-num associate-/r* sub-neg frac-2neg diff-log frac-sub
Counts
4 → 82
Calls
4 calls:
Slowest
68.0ms
(- (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (sin x) (cos x)))
37.0ms
(/ (sin eps) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))))
10.0ms
(* (sin x) (sin eps))
10.0ms
(* (sin x) (sin eps))

series561.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
273.0ms
(- (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (sin x) (cos x)))
170.0ms
(/ (sin eps) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))))
59.0ms
(* (sin x) (sin eps))
59.0ms
(* (sin x) (sin eps))

simplify12.1s

Counts
103 → 94
Calls
103 calls:
Slowest
407.0ms
(+ (* (/ (sin x) (* (cos x) (- 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)) (/ (sin x) (cos x))) (* (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (sin x) (cos x)))))
405.0ms
(- (* (/ (sin x) (* (cos x) (- 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)) (/ (sin x) (cos x))))
398.0ms
(* (* (- (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (sin x) (cos x))) (- (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (sin x) (cos x)))) (- (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (sin x) (cos x))))
376.0ms
(* (* (* (sin x) (sin x)) (sin x)) (* (* (sin eps) (sin eps)) (sin eps)))
357.0ms
(/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (* (cos eps) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))))

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.2b

regimes296.0ms

Accuracy

0% (0.3b remaining)

Error of 13.2b against oracle of 12.9b and baseline of 13.2b

bsearch7.0ms

end0.0ms

sample16.0s

Algorithm
intervals
Results
7.7s3192×body1280valid
3.5s689×body2560valid
3.0s1804×body640valid
878.0ms820×body320valid
359.0ms1138×body80valid
358.0ms357×body160valid