Details

Time bar (total: 1.4m)

sample473.0ms

Algorithm
intervals
Results
213.0ms89×body1280valid
111.0ms29×body2560valid
101.0ms72×body640valid
22.0ms22×body320valid
10.0ms37×body80valid
3.0ms7×body160valid

simplify14.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
14.0ms
(- (tan (+ x eps)) (tan x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize14.0ms

Local error

Found 2 expressions with local error:

3.6b
(tan (+ x eps))
1.0b
(- (tan (+ x eps)) (tan x))

rewrite41.0ms

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
35.0ms
(- (tan (+ x eps)) (tan x))
6.0ms
(tan (+ x eps))

series166.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
98.0ms
(- (tan (+ x eps)) (tan x))
69.0ms
(tan (+ x eps))

simplify2.7s

Counts
35 → 49
Calls
35 calls:
Slowest
498.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
275.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
213.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
189.0ms
(fma (sqrt (tan (+ x eps))) (sqrt (tan (+ x eps))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
189.0ms
(fma (* (cbrt (tan (+ x eps))) (cbrt (tan (+ x eps)))) (cbrt (tan (+ x eps))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))

prune517.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.3b

localize30.0ms

Local error

Found 4 expressions with local error:

2.4b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
0.3b
(* (tan x) (tan eps))
0.1b
(+ (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))

rewrite230.0ms

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
131.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
50.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
29.0ms
(* (tan x) (tan eps))
15.0ms
(+ (tan x) (tan eps))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
544.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
332.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
161.0ms
(* (tan x) (tan eps))
149.0ms
(+ (tan x) (tan eps))

simplify24.1s

Counts
201 → 185
Calls
201 calls:
Slowest
703.0ms
(fma (/ 1 (sqrt (- 1 (* (tan x) (tan eps))))) (/ (+ (tan x) (tan eps)) (sqrt (- 1 (* (tan x) (tan eps))))) (- (* (sqrt (tan x)) (sqrt (tan x)))))
525.0ms
(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))))))
491.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
488.0ms
(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))))))
463.0ms
(fma (sqrt (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))) (sqrt (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))

prune2.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 16.2b

localize50.0ms

Local error

Found 4 expressions with local error:

2.4b
(- (/ (fma (+ (tan eps) (tan x)) (* (tan eps) (tan x)) (+ (tan eps) (tan x))) (- 1 (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) (tan x))
0.3b
(* (tan eps) (tan x))
0.3b
(* (tan eps) (tan x))
0.3b
(* (tan eps) (tan x))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
81×*-un-lft-identity
67×add-cube-cbrt
63×prod-diff
61×times-frac
26×difference-of-squares
21×fma-neg
13×tan-quot
10×pow1 add-cbrt-cube add-exp-log
9×associate-*r* associate-*l*
8×associate-/r/
6×add-log-exp
5×flip3-- flip--
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv
3×frac-times pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
1×sub-neg diff-log frac-sub distribute-lft-out--
Counts
4 → 175
Calls
4 calls:
Slowest
39.0ms
(- (/ (fma (+ (tan eps) (tan x)) (* (tan eps) (tan x)) (+ (tan eps) (tan x))) (- 1 (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) (tan x))
24.0ms
(* (tan eps) (tan x))
21.0ms
(* (tan eps) (tan x))
16.0ms
(* (tan eps) (tan x))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
873.0ms
(- (/ (fma (+ (tan eps) (tan x)) (* (tan eps) (tan x)) (+ (tan eps) (tan x))) (- 1 (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) (tan x))
158.0ms
(* (tan eps) (tan x))
118.0ms
(* (tan eps) (tan x))
112.0ms
(* (tan eps) (tan x))

simplify31.5s

Counts
208 → 187
Calls
208 calls:
Slowest
621.0ms
(- (+ (/ (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)))
621.0ms
(- (+ (/ (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)))
516.0ms
(fma (/ (* (cbrt (fma (+ (tan eps) (tan x)) (* (tan eps) (tan x)) (+ (tan eps) (tan x)))) (cbrt (fma (+ (tan eps) (tan x)) (* (tan eps) (tan x)) (+ (tan eps) (tan x))))) 1) (/ (cbrt (fma (+ (tan eps) (tan x)) (* (tan eps) (tan x)) (+ (tan eps) (tan x)))) (- 1 (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
512.0ms
(fma (/ 1 (* (cbrt (- 1 (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) (cbrt (- 1 (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))))) (/ (fma (+ (tan eps) (tan x)) (* (tan eps) (tan x)) (+ (tan eps) (tan x))) (cbrt (- 1 (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
506.0ms
(fma (/ 1 (+ (sqrt 1) (* (tan eps) (tan x)))) (/ (fma (+ (tan eps) (tan x)) (* (tan eps) (tan x)) (+ (tan eps) (tan x))) (- (sqrt 1) (* (tan eps) (tan x)))) (- (* (tan x) 1)))

prune1.9s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 14.7b

localize37.0ms

Local error

Found 4 expressions with local error:

2.4b
(fma (/ 1 (+ 1 (* (tan eps) (tan x)))) (/ (fma (+ (tan eps) (tan x)) (* (tan eps) (tan x)) (+ (tan eps) (tan x))) (- 1 (* (tan eps) (tan x)))) (- (tan x)))
0.3b
(* (tan eps) (tan x))
0.3b
(* (tan eps) (tan x))
0.3b
(* (tan eps) (tan x))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
12×tan-quot
10×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
9×associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×frac-times pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
1×fma-udef
Counts
4 → 83
Calls
4 calls:
Slowest
18.0ms
(* (tan eps) (tan x))
14.0ms
(* (tan eps) (tan x))
14.0ms
(* (tan eps) (tan x))
0.0ms
(fma (/ 1 (+ 1 (* (tan eps) (tan x)))) (/ (fma (+ (tan eps) (tan x)) (* (tan eps) (tan x)) (+ (tan eps) (tan x))) (- 1 (* (tan eps) (tan x)))) (- (tan x)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
793.0ms
(fma (/ 1 (+ 1 (* (tan eps) (tan x)))) (/ (fma (+ (tan eps) (tan x)) (* (tan eps) (tan x)) (+ (tan eps) (tan x))) (- 1 (* (tan eps) (tan x)))) (- (tan x)))
92.0ms
(* (tan eps) (tan x))
92.0ms
(* (tan eps) (tan x))
92.0ms
(* (tan eps) (tan x))

simplify2.2s

Counts
54 → 95
Calls
54 calls:
Slowest
221.0ms
(* (* (* (tan eps) (tan eps)) (tan eps)) (* (* (tan x) (tan x)) (tan x)))
220.0ms
(* (* (* (tan eps) (tan eps)) (tan eps)) (* (* (tan x) (tan x)) (tan x)))
220.0ms
(* (* (* (tan eps) (tan eps)) (tan eps)) (* (* (tan x) (tan x)) (tan x)))
217.0ms
(+ (* 1/3 (* (pow x 3) eps)) (+ (* 1/3 (* x (pow eps 3))) (* x eps)))
217.0ms
(+ (* 1/3 (* (pow x 3) eps)) (+ (* 1/3 (* x (pow eps 3))) (* x eps)))

prune948.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

regimes112.0ms

Accuracy

0% (0.4b remaining)

Error of 0.7b against oracle of 0.3b and baseline of 0.7b

bsearch10.0ms

end0.0ms

sample10.4s

Algorithm
intervals
Results
5.2s3279×body1280valid
2.1s658×body2560valid
1.8s1784×body640valid
801.0ms783×body320valid
196.0ms1126×body80valid
134.0ms370×body160valid