Details

Time bar (total: 2.1m)

sample465.0ms

Algorithm
intervals
Results
247.0ms110×body1280valid
99.0ms16×body2560valid
70.0ms55×body640valid
17.0ms21×body320valid
11.0ms42×body80valid
7.0ms12×body160valid

simplify18.0ms

Calls
1 calls:
Slowest
18.0ms
(- (tan (+ x eps)) (tan x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.1b

localize27.0ms

Local error

Found 2 expressions with local error:

2.0b
(tan (+ x eps))
1.8b
(- (tan (+ x eps)) (tan x))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×prod-diff add-cube-cbrt
5×tan-quot
4×tan-sum add-log-exp
3×fma-neg frac-sub
2×expm1-log1p-u pow1 +-commutative add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Calls
2 calls:
Slowest
28.0ms
(- (tan (+ x eps)) (tan x))
26.0ms
(tan (+ x eps))

series236.0ms

Calls
2 calls:
Slowest
164.0ms
(- (tan (+ x eps)) (tan x))
72.0ms
(tan (+ x eps))

simplify3.2s

Calls
38 calls:
Slowest
489.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
279.0ms
(- (* (+ (tan eps) (tan x)) (cos x)) (* (- 1 (* (tan eps) (tan x))) (sin x)))
261.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
209.0ms
(fma 1 (tan (+ x eps)) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
192.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))

prune569.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.0b

localize41.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
0.2b
(* (tan x) (tan eps))
0.1b
(- 1 (* (tan x) (tan eps)))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))

rewrite402.0ms

Algorithm
rewrite-expression-head
Rules
377×*-un-lft-identity
340×add-sqr-sqrt
181×times-frac
162×prod-diff
143×add-cube-cbrt
94×difference-of-squares
50×unswap-sqr
47×distribute-lft-out distribute-lft-out--
45×fma-neg
35×associate-*l*
27×tan-quot
19×frac-sub
18×associate-/r*
12×associate-*r*
10×associate-/r/
8×add-cbrt-cube add-exp-log associate-/l* add-log-exp
7×flip3-- flip--
6×pow1 associate-/l/
5×div-inv
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u
2×clear-num sub-neg frac-2neg flip3-+ diff-log frac-add flip-+
1×frac-times cbrt-undiv div-exp pow-prod-down associate-*l/ prod-exp associate-*r/ cbrt-unprod
Calls
4 calls:
Slowest
252.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
78.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
29.0ms
(- 1 (* (tan x) (tan eps)))
27.0ms
(* (tan x) (tan eps))

series1.1s

Calls
4 calls:
Slowest
488.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
326.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
182.0ms
(- 1 (* (tan x) (tan eps)))
121.0ms
(* (tan x) (tan eps))

simplify1.1m

Calls
538 calls:
Slowest
690.0ms
(* (* (- 1 (* (tan x) (tan eps))) (* (cos x) (cos eps))) (cos x))
545.0ms
(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))))))
540.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
539.0ms
(fma (- (cbrt (tan x))) (* (cbrt (tan x)) (cbrt (tan x))) (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x)))))
536.0ms
(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))))))

prune4.0s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.8b

localize35.0ms

Local error

Found 4 expressions with local error:

2.9b
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))
0.2b
(* (tan x) (tan eps))
0.1b
(- 1 (* (tan x) (tan eps)))
0.1b
(/ 1 (- 1 (* (tan x) (tan eps))))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
72×*-un-lft-identity
42×add-cube-cbrt
36×prod-diff
27×times-frac
20×difference-of-squares
17×associate-*l*
14×unswap-sqr
12×associate-*r*
10×add-exp-log distribute-lft-out--
9×associate-/r*
8×add-cbrt-cube
7×pow1
6×add-log-exp
4×expm1-log1p-u tan-quot *-commutative insert-posit16 log1p-expm1-u
3×fma-neg associate-/l*
2×flip3-- div-exp associate-/r/ flip--
1×frac-times cbrt-undiv rec-exp clear-num sub-neg frac-2neg diff-log 1-exp pow-prod-down associate-*l/ prod-exp associate-*r/ cbrt-unprod fma-udef div-inv pow-flip inv-pow
Calls
4 calls:
Slowest
41.0ms
(/ 1 (- 1 (* (tan x) (tan eps))))
13.0ms
(- 1 (* (tan x) (tan eps)))
13.0ms
(* (tan x) (tan eps))
0.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

series830.0ms

Calls
4 calls:
Slowest
418.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))
154.0ms
(/ 1 (- 1 (* (tan x) (tan eps))))
134.0ms
(- 1 (* (tan x) (tan eps)))
123.0ms
(* (tan x) (tan eps))

simplify11.9s

Calls
182 calls:
Slowest
362.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps)))
293.0ms
(+ (* 1/3 (* (pow x 3) eps)) (+ (* 1/3 (* x (pow eps 3))) (* x eps)))
270.0ms
(- (+ (/ (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)))
268.0ms
(/ 1 (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))))
252.0ms
(+ (* 1/3 (* (pow x 3) eps)) (+ (* x eps) 1))

prune1.9s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 12.8b

localize48.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (fma (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))))) (fma (* (tan eps) (tan x)) (* (tan eps) (tan x)) (* (tan eps) (tan x))) (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))))) (tan x))
0.3b
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
0.3b
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
0.2b
(* (tan eps) (tan x))

rewrite255.0ms

Algorithm
rewrite-expression-head
Rules
84×pow1
81×add-sqr-sqrt
68×tan-quot
55×associate-*l*
51×associate-*r*
47×*-un-lft-identity
37×add-cube-cbrt
35×frac-times pow-prod-down
30×add-cbrt-cube add-exp-log
28×swap-sqr
25×unswap-sqr
23×associate-*l/ associate-*r/
17×prod-exp cbrt-unprod
11×*-commutative
9×prod-diff
8×pow-sqr pow-prod-up
6×add-log-exp
4×expm1-log1p-u pow-plus insert-posit16 log1p-expm1-u
3×fma-neg
2×pow2
1×sub-neg flip3-- diff-log associate--l+ fma-udef flip-- distribute-lft-out-- difference-of-squares
Calls
4 calls:
Slowest
117.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
110.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
13.0ms
(* (tan eps) (tan x))
10.0ms
(- (fma (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))))) (fma (* (tan eps) (tan x)) (* (tan eps) (tan x)) (* (tan eps) (tan x))) (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))))) (tan x))

series1.9s

Calls
4 calls:
Slowest
1.4s
(- (fma (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))))) (fma (* (tan eps) (tan x)) (* (tan eps) (tan x)) (* (tan eps) (tan x))) (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))))) (tan x))
169.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
142.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
122.0ms
(* (tan eps) (tan x))

simplify14.9s

Calls
275 calls:
Slowest
844.0ms
(* (* (* (* (tan eps) (tan eps)) (tan eps)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan eps) (tan eps)) (tan eps)) (* (* (tan x) (tan x)) (tan x))))
725.0ms
(* (* (* (* (tan eps) (tan eps)) (tan eps)) (* (* (tan x) (tan x)) (tan x))) (* (* (* (tan eps) (tan eps)) (tan eps)) (* (* (tan x) (tan x)) (tan x))))
684.0ms
(* (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))) (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))))
547.0ms
(* (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))) (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))))
499.0ms
(- (fma (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))))) (fma (* (tan eps) (tan x)) (* (tan eps) (tan x)) (* (tan eps) (tan x))) (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan eps) (tan x)) (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))))) (tan x))

prune3.7s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 10.7b

regimes218.0ms

Accuracy

81.7% (1.3b remaining)

Error of 13.3b against oracle of 12.0b and baseline of 19.1b

bsearch427.0ms

end0.0ms

sample13.0s

Algorithm
intervals
Results
6.5s3396×body1280valid
2.7s1800×body640valid
2.6s606×body2560valid
634.0ms741×body320valid
267.0ms1108×body80valid
153.0ms349×body160valid