Details

Time bar (total: 2.2m)

sample434.0ms

Algorithm
intervals
Results
225.0ms106×body1280valid
102.0ms61×body640valid
59.0ms17×body2560valid
23.0ms29×body320valid
8.0ms35×body80valid
4.0ms8×body160valid

simplify12.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
12.0ms
(- (tan (+ x eps)) (tan x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.5b

localize27.0ms

Local error

Found 2 expressions with local error:

4.2b
(tan (+ x eps))
1.0b
(- (tan (+ x eps)) (tan x))

rewrite35.0ms

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
25.0ms
(- (tan (+ x eps)) (tan x))
10.0ms
(tan (+ x eps))

series209.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
129.0ms
(- (tan (+ x eps)) (tan x))
80.0ms
(tan (+ x eps))

simplify1.4s

Counts
15 → 33
Calls
15 calls:
Slowest
458.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
442.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
190.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))
153.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
43.0ms
(/ (exp (tan (+ x eps))) (exp (tan x)))

prune345.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.7b

localize43.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (/ (+ (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))))

rewrite148.0ms

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
98.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
28.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
13.0ms
(* (tan x) (tan eps))
7.0ms
(+ (tan x) (tan eps))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
500.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
305.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
159.0ms
(* (tan x) (tan eps))
115.0ms
(+ (tan x) (tan eps))

simplify6.6s

Counts
74 → 102
Calls
74 calls:
Slowest
612.0ms
(/ (* (* (+ (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)))))
553.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
499.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
477.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
392.0ms
(- (+ (/ (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)))

prune1.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.6b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite227.0ms

Algorithm
rewrite-expression-head
Rules
47×pow1
45×tan-quot
21×frac-times
20×add-cbrt-cube add-exp-log
19×pow-prod-down
15×associate-*r/
14×associate-*l/
12×add-sqr-sqrt
10×prod-exp cbrt-unprod
8×*-un-lft-identity add-cube-cbrt
7×associate-*r* associate-*l*
6×add-log-exp
5×frac-sub
4×pow-sqr pow-prod-up insert-posit16
3×*-commutative
2×flip3-+ pow-plus associate--l+ flip-+ unswap-sqr
1×pow2 distribute-rgt-in sub-neg distribute-lft-in flip3-- diff-log swap-sqr flip--
Counts
4 → 114
Calls
4 calls:
Slowest
121.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
64.0ms
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
26.0ms
(* (tan x) (tan eps))
13.0ms
(* (tan x) (tan eps))

series1.6s

Counts
4 → 12
Calls
4 calls:
Slowest
1.2s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
153.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
144.0ms
(* (tan x) (tan eps))
102.0ms
(* (tan x) (tan eps))

simplify11.0s

Counts
111 → 126
Calls
111 calls:
Slowest
1.0s
(- (+ (/ (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)))
886.0ms
(- (+ (/ (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)))
859.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
717.0ms
(* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))
476.0ms
(- (* (* (+ (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)))

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize137.0ms

Local error

Found 4 expressions with local error:

3.2b
(- (/ (/ (sin x) (cos x)) (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))) (/ (sin x) (cos x)))
0.3b
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))
0.3b
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))
0.3b
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))

rewrite357.0ms

Algorithm
rewrite-expression-head
Rules
394×add-cbrt-cube add-exp-log
195×prod-exp cbrt-unprod
121×pow1
120×cbrt-undiv div-exp
51×frac-times pow-prod-down
33×associate-*l/ associate-*r/
25×add-sqr-sqrt
12×pow-sqr pow-prod-up
11×times-frac
10×*-un-lft-identity
6×pow-plus add-log-exp difference-of-squares
4×add-cube-cbrt insert-posit16
3×pow2 swap-sqr associate-*r* associate-*l* *-commutative
2×distribute-lft-out--
1×sub-neg flip3-- diff-log frac-sub flip--
Counts
4 → 298
Calls
4 calls:
Slowest
107.0ms
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))
85.0ms
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))
77.0ms
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))
73.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))) (/ (sin x) (cos x)))

series829.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
331.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))) (/ (sin x) (cos x)))
185.0ms
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))
166.0ms
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))
147.0ms
(* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))

simplify1.6m

Counts
330 → 310
Calls
330 calls:
Slowest
931.0ms
(+ (+ (- (log (sin x)) (log (cos x))) (- (log (sin eps)) (log (cos eps)))) (+ (- (log (sin x)) (log (cos x))) (- (log (sin eps)) (log (cos eps)))))
912.0ms
(* (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (cos eps) (cos eps)) (cos eps)))) (* (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))
884.0ms
(* (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (cos eps) (cos eps)) (cos eps)))) (* (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))
883.0ms
(* (* (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))) (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (* (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))) (/ (sin eps) (cos eps)))))
881.0ms
(* (* (/ (* (* (sin x) (sin x)) (sin x)) (* (* (cos x) (cos x)) (cos x))) (/ (* (* (sin eps) (sin eps)) (sin eps)) (* (* (cos eps) (cos eps)) (cos eps)))) (* (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))

prune3.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

regimes111.0ms

Accuracy

0% (0.3b remaining)

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

bsearch6.0ms

end0.0ms

sample9.7s

Algorithm
intervals
Results
4.9s3294×body1280valid
2.0s1864×body640valid
1.8s618×body2560valid
396.0ms797×body320valid
196.0ms1091×body80valid
160.0ms336×body160valid