Details

Time bar (total: 1.8m)

sample458.0ms

Algorithm
intervals
Results
222.0ms111×body1280valid
111.0ms58×body640valid
81.0ms23×body2560valid
16.0ms21×body320valid
9.0ms35×body80valid
4.0ms8×body160valid

simplify15.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
15.0ms
(- (tan (+ x eps)) (tan x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize29.0ms

Local error

Found 2 expressions with local error:

4.2b
(tan (+ x eps))
1.5b
(- (tan (+ x eps)) (tan x))

rewrite59.0ms

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
Counts
2 → 43
Calls
2 calls:
Slowest
48.0ms
(- (tan (+ x eps)) (tan x))
10.0ms
(tan (+ x eps))

series221.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
157.0ms
(- (tan (+ x eps)) (tan x))
64.0ms
(tan (+ x eps))

simplify2.9s

Counts
35 → 49
Calls
35 calls:
Slowest
485.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
266.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
214.0ms
(fma 1 (tan (+ x eps)) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
213.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
211.0ms
(fma (sqrt (tan (+ x eps))) (sqrt (tan (+ x eps))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))

prune485.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.8b

localize39.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
0.2b
(* (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b
(+ (tan x) (tan eps))

rewrite170.0ms

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
Counts
4 → 173
Calls
4 calls:
Slowest
118.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
28.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
13.0ms
(* (tan x) (tan eps))
8.0ms
(+ (tan x) (tan eps))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
466.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
307.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
163.0ms
(+ (tan x) (tan eps))
124.0ms
(* (tan x) (tan eps))

simplify23.9s

Counts
201 → 185
Calls
201 calls:
Slowest
576.0ms
(fma (/ 1 1) (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (- (* (tan x) 1)))
497.0ms
(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))))))
478.0ms
(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
(+ x (+ (* 1/3 (pow x 3)) eps))

prune2.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.6b

localize59.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (* (tan x) (tan eps)) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (tan x))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.2b
(* (tan x) (tan eps))

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
84×pow1
68×tan-quot
35×frac-times pow-prod-down
30×add-cbrt-cube add-exp-log
23×associate-*l/ associate-*r/
17×add-sqr-sqrt prod-exp cbrt-unprod
15×*-un-lft-identity
13×add-cube-cbrt
9×prod-diff
8×pow-sqr pow-prod-up
6×add-log-exp
5×associate-*r* associate-*l*
4×expm1-log1p-u pow-plus insert-posit16 log1p-expm1-u
3×fma-neg *-commutative
2×pow2 swap-sqr
1×sub-neg flip3-- diff-log associate--l+ fma-udef flip-- distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 158
Calls
4 calls:
Slowest
75.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
74.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
25.0ms
(* (tan x) (tan eps))
5.0ms
(- (fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (* (tan x) (tan eps)) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (tan x))

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
1.1s
(- (fma (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (* (tan x) (tan eps)) (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (tan x))
175.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
173.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
126.0ms
(* (tan x) (tan eps))

simplify15.9s

Counts
167 → 170
Calls
167 calls:
Slowest
957.0ms
(- (+ (/ (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)))
920.0ms
(- (+ (/ (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)))
894.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
866.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
747.0ms
(* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))

prune2.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 10.9b

localize40.0ms

Local error

Found 4 expressions with local error:

2.3b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (tan x))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.2b
(* (tan x) (tan eps))

rewrite349.0ms

Algorithm
rewrite-expression-head
Rules
130×*-un-lft-identity
95×add-sqr-sqrt
84×pow1
81×times-frac
78×prod-diff
72×add-cube-cbrt
69×tan-quot
35×frac-times pow-prod-down
34×difference-of-squares
30×add-cbrt-cube add-exp-log
26×fma-neg
23×associate-*l/ associate-*r/
20×distribute-lft-out
17×prod-exp cbrt-unprod
8×associate-/r/ pow-sqr pow-prod-up
6×add-log-exp
5×flip3-- associate-*r* associate-*l* flip--
4×expm1-log1p-u pow-plus insert-posit16 log1p-expm1-u div-inv
3×*-commutative
2×pow2 swap-sqr
1×sub-neg diff-log frac-sub distribute-lft-out-- unswap-sqr
Counts
4 → 251
Calls
4 calls:
Slowest
126.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (tan x))
109.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
83.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
19.0ms
(* (tan x) (tan eps))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
690.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (tan x))
150.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
137.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
131.0ms
(* (tan x) (tan eps))

simplify39.9s

Counts
331 → 263
Calls
331 calls:
Slowest
816.0ms
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) 3))) (+ (* 1 1) (+ (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (* 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
700.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
667.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
573.0ms
(* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))
561.0ms
(* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))

prune3.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.7b

regimes219.0ms

Accuracy

76.2% (2.3b remaining)

Error of 12.2b against oracle of 9.9b and baseline of 19.5b

bsearch379.0ms

end0.0ms

sample13.5s

Algorithm
intervals
Results
6.7s3360×body1280valid
3.0s1813×body640valid
2.5s646×body2560valid
697.0ms785×body320valid
214.0ms1056×body80valid
184.0ms340×body160valid