Details

Time bar (total: 1.2m)

sample376.0ms

Algorithm
intervals
Results
195.0ms100×body1280valid
74.0ms23×body2560valid
57.0ms52×body640valid
25.0ms31×body320valid
9.0ms40×body80valid
5.0ms10×body160valid

simplify14.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
13.0ms
(- (tan (+ x eps)) (tan x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.4b

localize41.0ms

Local error

Found 2 expressions with local error:

2.7b
(tan (+ x eps))
2.0b
(- (tan (+ x eps)) (tan x))

rewrite32.0ms

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))
6.0ms
(tan (+ x eps))

series206.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
117.0ms
(- (tan (+ x eps)) (tan x))
90.0ms
(tan (+ x eps))

simplify1.4s

Counts
15 → 33
Calls
15 calls:
Slowest
480.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
408.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
191.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
143.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))
56.0ms
(/ (exp (tan (+ x eps))) (exp (tan x)))

prune376.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.5b

localize44.0ms

Local error

Found 4 expressions with local error:

4.1b
(- (/ (+ (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))))

rewrite155.0ms

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
108.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
22.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
15.0ms
(* (tan x) (tan eps))
8.0ms
(+ (tan x) (tan eps))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
610.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
288.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
146.0ms
(+ (tan x) (tan eps))
137.0ms
(* (tan x) (tan eps))

simplify5.9s

Counts
74 → 102
Calls
74 calls:
Slowest
779.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
501.0ms
(/ (* (* (+ (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)))))
467.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
427.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
362.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps)))

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 13.4b

localize83.0ms

Local error

Found 4 expressions with local error:

4.1b
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
0.2b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.2b
(* (sin x) (sin eps))
0.1b
(+ (tan x) (tan eps))

rewrite339.0ms

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube add-exp-log
13×add-sqr-sqrt
10×*-un-lft-identity
8×add-log-exp
6×pow1 add-cube-cbrt
5×prod-exp cbrt-unprod
4×cbrt-undiv div-exp insert-posit16
3×associate-*r* associate-*l* tan-quot
2×times-frac sin-mult difference-of-squares
1×+-commutative clear-num associate-/r* sum-log sub-neg frac-2neg flip3-+ flip3-- diff-log pow-prod-down frac-add associate-/r/ cos-mult *-commutative frac-sub flip-+ div-inv flip-- distribute-lft-out associate-/l* distribute-lft-out-- unswap-sqr associate-/l/
Counts
4 → 75
Calls
4 calls:
Slowest
271.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
31.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
22.0ms
(* (sin x) (sin eps))
13.0ms
(+ (tan x) (tan eps))

series960.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
586.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
158.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
135.0ms
(+ (tan x) (tan eps))
81.0ms
(* (sin x) (sin eps))

simplify8.2s

Counts
48 → 87
Calls
48 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))))
955.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (* (cos x) (cos eps)) (* (cos x) (cos eps))) (* (cos x) (cos eps))))
768.0ms
(/ (* (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (sin x) (sin eps))) (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos eps) (cos eps)) (cos eps))))
656.0ms
(/ (* (* (* (sin x) (sin x)) (sin x)) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (* (cos x) (cos x)) (cos x)) (* (* (cos eps) (cos eps)) (cos eps))))
491.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))

prune1.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.4b

localize77.0ms

Local error

Found 4 expressions with local error:

26.6b
(cbrt (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (* (/ (sin eps) (cos eps)) (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps)))))))
4.1b
(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (* (/ (sin eps) (cos eps)) (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))))))))) (tan x))
0.3b
(* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps)))
0.2b
(* (/ (sin eps) (cos eps)) (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))))

rewrite542.0ms

Algorithm
rewrite-expression-head
Rules
135×frac-times
105×associate-*r/
63×cbrt-div
59×add-sqr-sqrt
57×add-cbrt-cube add-exp-log
51×times-frac associate-*l/
41×*-un-lft-identity
39×add-cube-cbrt
26×associate-*l*
25×pow1
22×prod-exp cbrt-unprod
17×cbrt-undiv div-exp
14×associate-*r*
13×swap-sqr
6×pow-prod-up add-log-exp unswap-sqr
5×div-inv
4×pow-prod-down insert-posit16
2×pow2 pow-plus pow-sqr *-commutative difference-of-squares
1×cbrt-prod sub-neg flip3-- pow1/3 diff-log cube-unmult tan-quot frac-sub flip-- distribute-lft-out--
Counts
4 → 217
Calls
4 calls:
Slowest
351.0ms
(cbrt (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (* (/ (sin eps) (cos eps)) (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps)))))))
79.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (* (/ (sin eps) (cos eps)) (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))))))))) (tan x))
68.0ms
(* (/ (sin eps) (cos eps)) (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))))
35.0ms
(* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps)))

series816.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
458.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (cbrt (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (* (/ (sin eps) (cos eps)) (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))))))))) (tan x))
159.0ms
(cbrt (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (* (/ (sin eps) (cos eps)) (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps)))))))
119.0ms
(* (/ (sin eps) (cos eps)) (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))))
80.0ms
(* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps)))

simplify37.0s

Counts
218 → 229
Calls
218 calls:
Slowest
815.0ms
(cbrt (* (* (sin x) (/ (sin x) (cos x))) (* (sin x) (* (/ (sin eps) (cos eps)) (* (sin eps) (sin eps))))))
684.0ms
(cbrt (* (* (/ (sin x) (cos x)) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (* (sin eps) (* (/ (sin eps) (cos eps)) (sin eps))))))
678.0ms
(cbrt (* (* (/ (sin x) (cos x)) (sin x)) (* (/ (sin x) (cos x)) (* (sin eps) (* (/ (sin eps) (cos eps)) (sin eps))))))
650.0ms
(cbrt (* (* (sin x) (/ (sin x) (cos x))) (* (/ (sin x) (cos x)) (* (sin eps) (* (/ (sin eps) (cos eps)) (sin eps))))))
636.0ms
(cbrt (* (* (/ (sin x) (cos x)) (sin x)) (* (sin x) (* (/ (sin eps) (cos eps)) (* (/ (sin eps) (cos eps)) (sin eps))))))

prune2.7s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 13.3b

regimes216.0ms

Accuracy

89% (0.8b remaining)

Error of 15.5b against oracle of 14.7b and baseline of 22.1b

bsearch507.0ms

end0.0ms

sample10.3s

Algorithm
intervals
Results
5.2s3310×body1280valid
2.2s1843×body640valid
1.6s658×body2560valid
511.0ms772×body320valid
450.0ms1082×body80valid
165.0ms335×body160valid