Details

Time bar (total: 1.1m)

sample492.0ms

Algorithm
intervals
Results
266.0ms111×body1280valid
111.0ms29×body2560valid
72.0ms56×body640valid
17.0ms19×body320valid
8.0ms32×body80valid
4.0ms9×body160valid

simplify16.0ms

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: 38.4b

localize27.0ms

Local error

Found 2 expressions with local error:

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

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×prod-diff add-cube-cbrt
4×tan-quot add-log-exp
3×fma-neg
2×expm1-log1p-u pow1 tan-sum add-cbrt-cube add-exp-log frac-sub insert-posit16 log1p-expm1-u
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Calls
2 calls:
Slowest
58.0ms
(- (tan (+ x eps)) (tan x))
10.0ms
(tan (+ x eps))

series576.0ms

Calls
2 calls:
Slowest
493.0ms
(- (tan (+ x eps)) (tan x))
83.0ms
(tan (+ x eps))

simplify3.0s

Calls
35 calls:
Slowest
541.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
266.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
254.0ms
(fma (sqrt (tan (+ x eps))) (sqrt (tan (+ x eps))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
232.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
186.0ms
(fma (* (cbrt (tan (+ x eps))) (cbrt (tan (+ x eps)))) (cbrt (tan (+ x eps))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))

prune443.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.2b

localize30.0ms

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))))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
102×*-un-lft-identity
73×add-sqr-sqrt
66×add-cube-cbrt
61×times-frac
54×prod-diff
18×fma-neg
17×distribute-lft-out
10×associate-/r/
9×tan-quot
8×add-cbrt-cube add-exp-log add-log-exp
6×pow1 flip3-- flip--
5×div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u associate-/l*
3×associate-/r* fma-def associate-*r* associate-*l* associate-/l/
2×flip3-+ frac-add 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 distribute-lft-out-- unswap-sqr
Calls
4 calls:
Slowest
91.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
27.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
14.0ms
(* (tan x) (tan eps))
7.0ms
(+ (tan x) (tan eps))

series1.1s

Calls
4 calls:
Slowest
493.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
323.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
118.0ms
(* (tan x) (tan eps))
116.0ms
(+ (tan x) (tan eps))

simplify23.6s

Calls
201 calls:
Slowest
530.0ms
(fma (/ (sqrt (+ (tan x) (tan eps))) 1) (/ (sqrt (+ (tan x) (tan eps))) (- 1 (* (tan x) (tan eps)))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
487.0ms
(fma (* (cbrt (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))) (cbrt (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))))) (cbrt (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
477.0ms
(fma (/ (sqrt (+ (tan x) (tan eps))) (sqrt (- 1 (* (tan x) (tan eps))))) (/ (sqrt (+ (tan x) (tan eps))) (sqrt (- 1 (* (tan x) (tan eps))))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
470.0ms
(fma (/ (sqrt (+ (tan x) (tan eps))) (* (cbrt (- 1 (* (tan x) (tan eps)))) (cbrt (- 1 (* (tan x) (tan eps)))))) (/ (sqrt (+ (tan x) (tan eps))) (cbrt (- 1 (* (tan x) (tan eps))))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
469.0ms
(fma (/ (* (cbrt (+ (tan x) (tan eps))) (cbrt (+ (tan x) (tan eps)))) (sqrt (- 1 (* (tan x) (tan eps))))) (/ (cbrt (+ (tan x) (tan eps))) (sqrt (- 1 (* (tan x) (tan eps))))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))

prune2.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 18.1b

localize45.0ms

Local error

Found 4 expressions with local error:

3.4b
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))
0.2b
(* (tan x) (tan eps))
0.1b
(+ (tan x) (tan eps))
0.1b
(- 1 (* (tan x) (tan eps)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt
8×add-log-exp
6×pow1 add-cbrt-cube tan-quot add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-def fma-neg associate-*r* associate-*l* prod-diff
1×frac-times +-commutative sum-log sub-neg flip3-+ flip3-- diff-log pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative cbrt-unprod flip-+ fma-udef flip-- distribute-lft-out unswap-sqr
Calls
4 calls:
Slowest
14.0ms
(* (tan x) (tan eps))
9.0ms
(- 1 (* (tan x) (tan eps)))
7.0ms
(+ (tan x) (tan eps))
0.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

series793.0ms

Calls
4 calls:
Slowest
401.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))
164.0ms
(- 1 (* (tan x) (tan eps)))
118.0ms
(+ (tan x) (tan eps))
110.0ms
(* (tan x) (tan eps))

simplify3.6s

Calls
41 calls:
Slowest
635.0ms
(- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))
435.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
353.0ms
(+ (* 1/3 (* (pow x 3) eps)) (+ (* 1/3 (* x (pow eps 3))) (* x eps)))
328.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps)))
266.0ms
(- (+ (/ (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)))

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 18.1b

localize53.0ms

Local error

Found 4 expressions with local error:

3.6b
(fma (+ (tan x) (tan eps)) (/ 1 (/ (- (* 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))

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
47×pow1
40×tan-quot
20×add-cbrt-cube add-exp-log
19×frac-times pow-prod-down
13×associate-*l/ associate-*r/
12×add-sqr-sqrt
10×prod-exp cbrt-unprod
8×*-un-lft-identity add-cube-cbrt
7×associate-*r* associate-*l*
4×expm1-log1p-u pow-sqr pow-prod-up insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×pow-plus unswap-sqr
1×pow2 swap-sqr fma-udef
Calls
4 calls:
Slowest
123.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
23.0ms
(* (tan x) (tan eps))
13.0ms
(* (tan x) (tan eps))
1.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (/ (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (- (tan x)))

series1.2s

Calls
4 calls:
Slowest
725.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (/ (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (- (tan x)))
152.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
146.0ms
(* (tan x) (tan eps))
141.0ms
(* (tan x) (tan eps))

simplify7.8s

Calls
98 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)))
961.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
910.0ms
(- (+ (/ (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)))
785.0ms
(* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))
338.0ms
(+ (* 1/3 (* (pow x 3) eps)) (+ (* 1/3 (* x (pow eps 3))) (* x eps)))

prune1.6s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 18.1b

regimes255.0ms

Accuracy

86.3% (0.9b remaining)

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

bsearch279.0ms

end0.0ms

sample15.2s

Algorithm
intervals
Results
7.8s3260×body1280valid
3.0s1801×body640valid
2.8s653×body2560valid
770.0ms766×body320valid
283.0ms1138×body80valid
264.0ms382×body160valid