Details

Time bar (total: 46.4s)

sample490.0ms

Algorithm
intervals
Results
203.0ms85×body1280valid
132.0ms63×body640valid
85.0ms20×body2560valid
31.0ms29×body320valid
14.0ms46×body80valid
9.0ms13×body160valid

simplify9.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize27.0ms

Local error

Found 2 expressions with local error:

1.0b
(- (tan (+ x eps)) (tan x))
4.3b
(tan (+ x eps))

rewrite69.0ms

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:
55.0ms
(- (tan (+ x eps)) (tan x))
12.0ms
(tan (+ x eps))

series202.0ms

Counts
2 → 6
Calls
2 calls:
137.0ms
(- (tan (+ x eps)) (tan x))
65.0ms
(tan (+ x eps))

simplify1.3s

Counts
49 → 49
Iterations
IterNodes
done2002
42002
31357
2454
1205
096

prune564.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b
(+ (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))
3.4b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite201.0ms

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:
44.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
8.0ms
(+ (tan x) (tan eps))
14.0ms
(* (tan x) (tan eps))
130.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts
4 → 12
Calls
4 calls:
327.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
163.0ms
(+ (tan x) (tan eps))
116.0ms
(* (tan x) (tan eps))
470.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.3s

Counts
185 → 185
Iterations
IterNodes
done2007
32007
21631
1580
0242

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))
0.2b
(* (sin x) (/ (sin eps) (cos eps)))
0.2b
(* (sin x) (/ (sin eps) (cos eps)))
3.9b
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

rewrite405.0ms

Algorithm
rewrite-expression-head
Rules
2640×times-frac
1971×add-sqr-sqrt
1951×*-un-lft-identity
1394×add-cube-cbrt
1092×prod-diff
370×difference-of-squares
186×distribute-lft-out--
185×div-inv
84×fma-neg
28×associate-/r/
26×associate-*r*
23×add-cbrt-cube add-exp-log
15×flip3-- flip--
8×pow1
6×cbrt-undiv div-exp associate-*l* prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u unswap-sqr
3×associate-/r* associate-*r/
2×pow-prod-down *-commutative
1×clear-num sub-neg frac-2neg diff-log frac-sub associate-/l* associate-/l/
Counts
4 → 1298
Calls
4 calls:
30.0ms
(/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))
33.0ms
(* (sin x) (/ (sin eps) (cos eps)))
24.0ms
(* (sin x) (/ (sin eps) (cos eps)))
216.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

series734.0ms

Counts
4 → 12
Calls
4 calls:
175.0ms
(/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))
139.0ms
(* (sin x) (/ (sin eps) (cos eps)))
103.0ms
(* (sin x) (/ (sin eps) (cos eps)))
317.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))

simplify2.7s

Counts
1310 → 1310
Iterations
IterNodes
done2000
12000
01323

prune22.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.0b

localize91.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (sin x))
0.7b
(cbrt (sin x))
43.5b
(fma (/ (/ (* (cbrt (sin x)) (cbrt (sin x))) 1) (sqrt (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))))) (/ (/ (cbrt (sin x)) (cos x)) (sqrt (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))))) (- (* (/ (cbrt (sin x)) (cos x)) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1))))
60.4b
(fma (- (/ (cbrt (sin x)) (cos x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1) (* (/ (cbrt (sin x)) (cos x)) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1)))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
6×cbrt-prod add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×pow1/3 fma-udef
Counts
4 → 50
Calls
4 calls:
1.0ms
(cbrt (sin x))
1.0ms
(cbrt (sin x))
0.0ms
(fma (/ (/ (* (cbrt (sin x)) (cbrt (sin x))) 1) (sqrt (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))))) (/ (/ (cbrt (sin x)) (cos x)) (sqrt (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))))) (- (* (/ (cbrt (sin x)) (cos x)) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1))))
0.0ms
(fma (- (/ (cbrt (sin x)) (cos x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1) (* (/ (cbrt (sin x)) (cos x)) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1)))

series746.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(cbrt (sin x))
97.0ms
(cbrt (sin x))
388.0ms
(fma (/ (/ (* (cbrt (sin x)) (cbrt (sin x))) 1) (sqrt (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))))) (/ (/ (cbrt (sin x)) (cos x)) (sqrt (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x))))) (- (* (/ (cbrt (sin x)) (cos x)) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1))))
165.0ms
(fma (- (/ (cbrt (sin x)) (cos x))) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1) (* (/ (cbrt (sin x)) (cos x)) (/ (* (cbrt (sin x)) (cbrt (sin x))) 1)))

simplify991.0ms

Counts
62 → 62
Iterations
IterNodes
done2005
42005
31657
2442
1180
086

prune908.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 11.9b

regimes174.0ms

Accuracy

0% (0.4b remaining)

Error of 13.0b against oracle of 12.6b and baseline of 13.0b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done20
120
016

end0.0ms

sample9.4s

Algorithm
intervals
Results
5.5s3322×body1280valid
1.5s633×body2560valid
1.4s1785×body640valid
523.0ms823×body320valid
300.0ms1114×body80valid
101.0ms323×body160valid