Details

Time bar (total: 58.3s)

sample401.0ms

Algorithm
intervals
Results
195.0ms107×body1280valid
95.0ms18×body2560valid
70.0ms63×body640valid
15.0ms23×body320valid
7.0ms33×body80valid
6.0ms12×body160valid

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: 38.2b

localize13.0ms

Local error

Found 2 expressions with local error:

3.5b
(tan (+ x eps))
1.2b
(- (tan (+ x eps)) (tan x))

rewrite52.0ms

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
26.0ms
(tan (+ x eps))
25.0ms
(- (tan (+ x eps)) (tan x))

series178.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
111.0ms
(- (tan (+ x eps)) (tan x))
68.0ms
(tan (+ x eps))

simplify1.5s

Counts
15 → 33
Calls
15 calls:
Slowest
508.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
482.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
172.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))
139.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
32.0ms
(/ (exp (tan (+ x eps))) (exp (tan x)))

prune445.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.4b

localize44.0ms

Local error

Found 4 expressions with local error:

2.5b
(- (/ (+ (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))))

rewrite170.0ms

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
92.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
48.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
14.0ms
(+ (tan x) (tan eps))
14.0ms
(* (tan x) (tan eps))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
521.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
293.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
144.0ms
(* (tan x) (tan eps))
141.0ms
(+ (tan x) (tan eps))

simplify5.6s

Counts
74 → 102
Calls
74 calls:
Slowest
552.0ms
(/ (* (* (+ (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)))))
428.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
423.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
411.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
392.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps)))

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.2b

localize75.0ms

Local error

Found 4 expressions with local error:

2.5b
(- (+ (/ (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)))
0.3b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.3b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.2b
(* (sin x) (sin eps))

rewrite834.0ms

Algorithm
rewrite-expression-head
Rules
30×add-cbrt-cube add-exp-log
13×add-sqr-sqrt
11×*-un-lft-identity
9×prod-exp cbrt-unprod add-log-exp
8×cbrt-undiv div-exp
6×pow1 add-cube-cbrt
4×insert-posit16
3×times-frac associate-*r* associate-*l* frac-sub sin-mult
2×clear-num associate-/r* frac-2neg diff-log associate-/r/ cos-mult div-inv associate-/l* distribute-lft-out-- difference-of-squares associate-/l/
1×sum-log sub-neg flip3-+ flip3-- pow-prod-down frac-add associate--l+ *-commutative flip-+ flip-- distribute-lft-out unswap-sqr
Counts
4 → 90
Calls
4 calls:
Slowest
751.0ms
(- (+ (/ (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)))
35.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
24.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
22.0ms
(* (sin x) (sin eps))

series874.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
523.0ms
(- (+ (/ (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)))
144.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
139.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
69.0ms
(* (sin x) (sin eps))

simplify16.0s

Counts
64 → 102
Calls
64 calls:
Slowest
1.1s
(/ (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps))) (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos eps) (cos eps)) (cos eps))))
1.0s
(/ (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps))) (* (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (cos x) (cos eps))))
981.0ms
(/ (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps))) (* (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (cos x) (cos eps))))
930.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (cos x) (cos eps))))
799.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (cos x) (cos eps))))

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.4b

localize52.0ms

Local error

Found 4 expressions with local error:

3.1b
(- (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (sin x) (cos x)))
0.3b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.3b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.2b
(* (sin x) (sin eps))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
30×add-cbrt-cube add-exp-log
13×add-sqr-sqrt
9×prod-exp cbrt-unprod
8×cbrt-undiv *-un-lft-identity div-exp
6×pow1 add-cube-cbrt add-log-exp
4×insert-posit16 div-inv
3×times-frac associate-*r* associate-*l* sin-mult
2×clear-num associate-/r* frac-2neg associate-/r/ cos-mult associate-/l* distribute-lft-out-- difference-of-squares associate-/l/
1×sub-neg flip3-- diff-log pow-prod-down *-commutative frac-sub flip-- unswap-sqr
Counts
4 → 86
Calls
4 calls:
Slowest
83.0ms
(- (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (sin x) (cos x)))
30.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
16.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
15.0ms
(* (sin x) (sin eps))

series677.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
325.0ms
(- (/ (sin x) (* (cos x) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))) (/ (sin x) (cos x)))
157.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
132.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
62.0ms
(* (sin x) (sin eps))

simplify12.0s

Counts
59 → 98
Calls
59 calls:
Slowest
1.1s
(/ (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps))) (* (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (cos x) (cos eps))))
1.1s
(/ (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps))) (* (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (cos x) (cos eps))))
888.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (cos x) (cos eps))))
821.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (cos x) (cos eps))))
739.0ms
(/ (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps))) (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos eps) (cos eps)) (cos eps))))

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.2b

regimes228.0ms

Accuracy

0% (0.4b remaining)

Error of 13.0b against oracle of 12.7b and baseline of 13.0b

bsearch4.0ms

end0.0ms

sample13.5s

Algorithm
intervals
Results
6.6s3273×body1280valid
2.9s644×body2560valid
2.7s1868×body640valid
610.0ms755×body320valid
301.0ms1107×body80valid
154.0ms353×body160valid