Details

Time bar (total: 1.0m)

sample411.0ms

Algorithm
intervals
Results
192.0ms107×body1280valid
100.0ms19×body2560valid
80.0ms61×body640valid
12.0ms17×body320valid
11.0ms43×body80valid
4.0ms9×body160valid

simplify8.0ms

Calls
1 calls:
Slowest
8.0ms
(- (tan (+ x eps)) (tan x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize43.0ms

Local error

Found 2 expressions with local error:

3.2b
(tan (+ x eps))
1.0b
(- (tan (+ x eps)) (tan x))

rewrite21.0ms

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
16.0ms
(- (tan (+ x eps)) (tan x))
5.0ms
(tan (+ x eps))

series241.0ms

Calls
2 calls:
Slowest
159.0ms
(- (tan (+ x eps)) (tan x))
82.0ms
(tan (+ x eps))

simplify3.1s

Calls
35 calls:
Slowest
483.0ms
(fma (- (cbrt (tan x))) (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x)))))
475.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
270.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
211.0ms
(fma (sqrt (tan (+ x eps))) (sqrt (tan (+ x eps))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
205.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))

prune546.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.2b

localize29.0ms

Local error

Found 4 expressions with local error:

2.8b
(- (/ (+ (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))))

rewrite174.0ms

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
105.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
27.0ms
(* (tan x) (tan eps))
24.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
15.0ms
(+ (tan x) (tan eps))

series1.1s

Calls
4 calls:
Slowest
480.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
325.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
142.0ms
(* (tan x) (tan eps))
114.0ms
(+ (tan x) (tan eps))

simplify23.6s

Calls
201 calls:
Slowest
521.0ms
(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))))))
465.0ms
(fma (/ 1 (* (cbrt (- 1 (* (tan x) (tan eps)))) (cbrt (- 1 (* (tan x) (tan eps)))))) (/ (+ (tan x) (tan eps)) (cbrt (- 1 (* (tan x) (tan eps))))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
454.0ms
(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))))))
453.0ms
(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))))))
452.0ms
(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))))))

prune2.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.1b

localize51.0ms

Local error

Found 4 expressions with local error:

2.8b
(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)))

rewrite48.0ms

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
29.0ms
(* (tan x) (tan eps))
12.0ms
(+ (tan x) (tan eps))
5.0ms
(- 1 (* (tan x) (tan eps)))
1.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

series858.0ms

Calls
4 calls:
Slowest
417.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))
163.0ms
(+ (tan x) (tan eps))
152.0ms
(- 1 (* (tan x) (tan eps)))
127.0ms
(* (tan x) (tan eps))

simplify3.1s

Calls
41 calls:
Slowest
459.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
380.0ms
(+ (* 1/3 (* (pow x 3) eps)) (+ (* 1/3 (* x (pow eps 3))) (* x eps)))
300.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps)))
251.0ms
(- (+ (/ (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)))
238.0ms
(- (+ (/ (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

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.1b

localize42.0ms

Local error

Found 4 expressions with local error:

2.8b
(fma (/ (+ (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))

rewrite149.0ms

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
87.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
31.0ms
(* (tan x) (tan eps))
27.0ms
(* (tan x) (tan eps))
0.0ms
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

series1.2s

Calls
4 calls:
Slowest
776.0ms
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))
173.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
133.0ms
(* (tan x) (tan eps))
131.0ms
(* (tan x) (tan eps))

simplify8.0s

Calls
98 calls:
Slowest
1.2s
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
974.0ms
(- (+ (/ (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)))
872.0ms
(- (+ (/ (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)))
660.0ms
(* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))
333.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps)))

prune1.6s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.1b

regimes318.0ms

Accuracy

85% (1.1b remaining)

Error of 15.8b against oracle of 14.8b and baseline of 22.1b

bsearch413.0ms

end0.0ms

sample14.8s

Algorithm
intervals
Results
8.2s3281×body1280valid
2.7s660×body2560valid
2.5s1879×body640valid
726.0ms726×body320valid
266.0ms1095×body80valid
243.0ms359×body160valid