Details

Time bar (total: 1.1m)

sample366.0ms

Algorithm
intervals
Results
159.0ms94×body1280valid
92.0ms65×body640valid
47.0ms25×body320valid
36.0ms12×body2560valid
11.0ms19×body160valid
9.0ms41×body80valid

simplify9.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
9.0ms
(- (tan (+ x eps)) (tan x))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.8b

localize14.0ms

Local error

Found 2 expressions with local error:

4.6b
(tan (+ x eps))
1.9b
(- (tan (+ x eps)) (tan x))

rewrite22.0ms

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
14.0ms
(- (tan (+ x eps)) (tan x))
8.0ms
(tan (+ x eps))

series216.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
137.0ms
(- (tan (+ x eps)) (tan x))
79.0ms
(tan (+ x eps))

simplify2.9s

Counts
35 → 49
Calls
35 calls:
Slowest
460.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
263.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
233.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
186.0ms
(fma 1 (tan (+ x eps)) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
186.0ms
(fma (* (cbrt (tan (+ x eps))) (cbrt (tan (+ x eps)))) (cbrt (tan (+ x eps))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))

prune542.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.7b

localize24.0ms

Local error

Found 4 expressions with local error:

2.4b
(- (/ (+ (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))))

rewrite213.0ms

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
122.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
44.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
28.0ms
(* (tan x) (tan eps))
15.0ms
(+ (tan x) (tan eps))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
499.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
350.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
150.0ms
(+ (tan x) (tan eps))
147.0ms
(* (tan x) (tan eps))

simplify24.0s

Counts
201 → 185
Calls
201 calls:
Slowest
580.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))
470.0ms
(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))))))
459.0ms
(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))))))
448.0ms
(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))))))
429.0ms
(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))))))

prune1.9s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.6b

localize61.0ms

Local error

Found 4 expressions with local error:

2.5b
(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))

rewrite161.0ms

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
Counts
4 → 111
Calls
4 calls:
Slowest
100.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
30.0ms
(* (tan x) (tan eps))
28.0ms
(* (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

Counts
4 → 12
Calls
4 calls:
Slowest
780.0ms
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))
142.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
132.0ms
(* (tan x) (tan eps))
129.0ms
(* (tan x) (tan eps))

simplify7.6s

Counts
98 → 123
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)))
823.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
798.0ms
(- (+ (/ (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)))
701.0ms
(* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))
366.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps)))

prune1.7s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 9.6b

localize47.0ms

Local error

Found 4 expressions with local error:

2.5b
(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 (- 1 (* (tan x) (tan eps))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt *-un-lft-identity
15×add-cube-cbrt
10×add-exp-log
9×times-frac
8×add-cbrt-cube
7×pow1
6×tan-quot add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* fma-def associate-*r* associate-*l* associate-/l*
2×div-exp associate-/r/
1×frac-times cbrt-undiv +-commutative rec-exp clear-num sum-log frac-2neg flip3-+ flip3-- 1-exp pow-prod-down associate-*l/ frac-add prod-exp associate-*r/ *-commutative cbrt-unprod flip-+ fma-udef div-inv pow-flip flip-- distribute-lft-out inv-pow unswap-sqr
Counts
4 → 90
Calls
4 calls:
Slowest
28.0ms
(* (tan x) (tan eps))
16.0ms
(/ 1 (- 1 (* (tan x) (tan eps))))
15.0ms
(+ (tan x) (tan eps))
1.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

series871.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
401.0ms
(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))
197.0ms
(/ 1 (- 1 (* (tan x) (tan eps))))
157.0ms
(* (tan x) (tan eps))
116.0ms
(+ (tan x) (tan eps))

simplify4.2s

Counts
61 → 102
Calls
61 calls:
Slowest
495.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
342.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps)))
331.0ms
(+ (* 1/3 (* (pow x 3) eps)) (+ (* x eps) 1))
292.0ms
(+ (* 1/3 (* (pow x 3) eps)) (+ (* 1/3 (* x (pow eps 3))) (* x eps)))
277.0ms
(- (+ (/ (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)))

prune1.2s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 9.6b

regimes286.0ms

Accuracy

90.8% (0.7b remaining)

Error of 14.5b against oracle of 13.8b and baseline of 21.3b

bsearch443.0ms

end0.0ms

sample15.2s

Algorithm
intervals
Results
7.7s3260×body1280valid
3.8s1909×body640valid
2.2s613×body2560valid
608.0ms758×body320valid
368.0ms1095×body80valid
214.0ms365×body160valid