Details

Time bar (total: 41.1s)

sample466.0ms

Algorithm
intervals
Results
252.0ms111×body1280valid
109.0ms29×body2560valid
65.0ms56×body640valid
16.0ms19×body320valid
8.0ms32×body80valid
4.0ms9×body160valid

simplify16.0ms

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

prune45.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize31.0ms

Local error

Found 2 expressions with local error:

3.3b
(tan (+ x eps))
1.3b
(- (tan (+ x eps)) (tan x))

rewrite17.0ms

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
13.0ms
(- (tan (+ x eps)) (tan x))
4.0ms
(tan (+ x eps))

series216.0ms

Calls
2 calls:
Slowest
146.0ms
(- (tan (+ x eps)) (tan x))
69.0ms
(tan (+ x eps))

simplify981.0ms

Calls
15 calls:
Slowest
450.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
148.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
137.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))
60.0ms
(/ (exp (tan (+ x eps))) (exp (tan x)))
47.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))

prune360.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.2b

localize22.0ms

Local error

Found 4 expressions with local error:

3.3b
(- (/ (+ (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))))

rewrite86.0ms

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
43.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
29.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
7.0ms
(+ (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))

series1.1s

Calls
4 calls:
Slowest
500.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
312.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
145.0ms
(+ (tan x) (tan eps))
144.0ms
(* (tan x) (tan eps))

simplify4.4s

Calls
72 calls:
Slowest
553.0ms
(/ (* (* (+ (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)))))
439.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
291.0ms
(- (+ (/ (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)))
282.0ms
(- (+ (/ (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)))
233.0ms
(/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 18.1b

localize37.0ms

Local error

Found 4 expressions with local error:

3.6b
(- (* (/ (+ (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))

rewrite73.0ms

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
39.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
23.0ms
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
5.0ms
(* (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))

series1.6s

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))
158.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
127.0ms
(* (tan x) (tan eps))
123.0ms
(* (tan x) (tan eps))

simplify8.7s

Calls
97 calls:
Slowest
714.0ms
(- (+ (/ (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)))
695.0ms
(- (+ (/ (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)))
473.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
359.0ms
(- (* (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
357.0ms
(* (* (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (- 1 (* (tan x) (tan eps)))) (cos x))

prune2.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 18.1b

localize50.0ms

Local error

Found 4 expressions with local error:

3.6b
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (tan x) (tan eps)) (* (sin x) (sin eps))) (* (cos x) (cos eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
0.2b
(* (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))
0.2b
(* (sin x) (sin eps))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
13×tan-quot
10×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
9×associate-*r* associate-*l*
6×add-log-exp
5×frac-sub
4×frac-times associate-*r/ insert-posit16
3×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod
2×flip3-+ associate--l+ flip-+
1×distribute-rgt-in sub-neg distribute-lft-in flip3-- diff-log flip-- sin-mult
Calls
4 calls:
Slowest
18.0ms
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (tan x) (tan eps)) (* (sin x) (sin eps))) (* (cos x) (cos eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
5.0ms
(* (tan x) (tan eps))
5.0ms
(* (tan x) (tan eps))
4.0ms
(* (sin x) (sin eps))

series2.0s

Calls
4 calls:
Slowest
1.7s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (tan x) (tan eps)) (* (sin x) (sin eps))) (* (cos x) (cos eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
123.0ms
(* (tan x) (tan eps))
123.0ms
(* (tan x) (tan eps))
71.0ms
(* (sin x) (sin eps))

simplify6.0s

Calls
58 calls:
Slowest
651.0ms
(- (* (* (+ (tan x) (tan eps)) (+ (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (cos x)) (* (* (- (* 1 1) (/ (* (* (tan x) (tan eps)) (* (sin x) (sin eps))) (* (cos x) (cos eps)))) (+ (* 1 1) (- (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (sin x)))
628.0ms
(- (+ (/ (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)))
586.0ms
(- (+ (/ (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)))
495.0ms
(- (* (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (tan x) (tan eps)) (* (sin x) (sin eps))) (* (cos x) (cos eps))))) (+ (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (cos x)) (* (+ (* 1 1) (- (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (sin x)))
436.0ms
(* (* (- (* 1 1) (/ (* (* (tan x) (tan eps)) (* (sin x) (sin eps))) (* (cos x) (cos eps)))) (+ (* 1 1) (- (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (cos x))

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 18.1b

regimes196.0ms

Accuracy

86.3% (1.0b remaining)

Error of 15.4b against oracle of 14.4b and baseline of 21.3b

bsearch196.0ms

end0.0ms

sample9.9s

Algorithm
intervals
Results
5.1s3260×body1280valid
2.0s1801×body640valid
1.9s653×body2560valid
444.0ms766×body320valid
205.0ms1138×body80valid
157.0ms382×body160valid