Details

Time bar (total: 1.1m)

sample433.0ms

Algorithm
intervals
Results
260.0ms113×body1280valid
73.0ms66×body640valid
58.0ms18×body2560valid
19.0ms26×body320valid
6.0ms12×body160valid
5.0ms21×body80valid

simplify9.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.7b

localize27.0ms

Local error

Found 2 expressions with local error:

5.5b
(tan (+ x eps))
1.5b
(- (tan (+ x eps)) (tan x))

rewrite39.0ms

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
27.0ms
(- (tan (+ x eps)) (tan x))
10.0ms
(tan (+ x eps))

series193.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
109.0ms
(- (tan (+ x eps)) (tan x))
83.0ms
(tan (+ x eps))

simplify2.8s

Counts
35 → 49
Calls
35 calls:
Slowest
465.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
218.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
211.0ms
(fma 1 (tan (+ x eps)) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
203.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
178.0ms
(fma (sqrt (tan (+ x eps))) (sqrt (tan (+ x eps))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))

prune512.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.4b

localize43.0ms

Local error

Found 4 expressions with local error:

2.1b
(- (/ (+ (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))))

rewrite187.0ms

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
126.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
27.0ms
(* (tan x) (tan eps))
24.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
7.0ms
(+ (tan x) (tan eps))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
540.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
339.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
124.0ms
(+ (tan x) (tan eps))
120.0ms
(* (tan x) (tan eps))

simplify24.0s

Counts
201 → 185
Calls
201 calls:
Slowest
561.0ms
(+ x (+ (* 1/3 (pow x 3)) eps))
559.0ms
(fma (/ (* (cbrt (+ (tan x) (tan eps))) (cbrt (+ (tan x) (tan eps)))) (sqrt (- 1 (* (tan x) (tan eps))))) (/ (cbrt (+ (tan x) (tan eps))) (sqrt (- 1 (* (tan x) (tan eps))))) (- (* (tan x) 1)))
483.0ms
(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))))))
482.0ms
(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))))))
481.0ms
(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))))))

prune2.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 16.2b

localize45.0ms

Local error

Found 4 expressions with local error:

2.1b
(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))

rewrite151.0ms

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
93.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
28.0ms
(* (tan x) (tan eps))
27.0ms
(* (tan x) (tan eps))
1.0ms
(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
790.0ms
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))
160.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
143.0ms
(* (tan x) (tan eps))
123.0ms
(* (tan x) (tan eps))

simplify7.4s

Counts
98 → 123
Calls
98 calls:
Slowest
932.0ms
(- (+ (/ (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)))
883.0ms
(* (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))) (* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps))))
815.0ms
(- (+ (/ (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)))
719.0ms
(* (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))) (* (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* (tan x) (tan eps))))
380.0ms
(+ (* 1/3 (* (pow x 3) eps)) (+ (* 1/3 (* x (pow eps 3))) (* x eps)))

prune1.9s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 16.2b

localize49.0ms

Local error

Found 4 expressions with local error:

2.1b
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan x)) (* (tan eps) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))
0.3b
(* (tan eps) (tan eps))
0.3b
(* (tan x) (tan x))
0.2b
(* (tan x) (tan eps))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt pow1
14×*-un-lft-identity add-cube-cbrt
12×tan-quot
10×add-cbrt-cube add-exp-log
9×associate-*r* associate-*l*
6×swap-sqr
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
2×pow2 pow-plus pow-sqr pow-prod-up
1×fma-udef
Counts
4 → 97
Calls
4 calls:
Slowest
27.0ms
(* (tan x) (tan x))
14.0ms
(* (tan eps) (tan eps))
14.0ms
(* (tan x) (tan eps))
0.0ms
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan x)) (* (tan eps) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))

series1.4s

Counts
4 → 12
Calls
4 calls:
Slowest
1.2s
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan x)) (* (tan eps) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))
124.0ms
(* (tan x) (tan eps))
57.0ms
(* (tan eps) (tan eps))
44.0ms
(* (tan x) (tan x))

simplify4.1s

Counts
76 → 109
Calls
76 calls:
Slowest
866.0ms
(- (+ (/ (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)))
793.0ms
(- (+ (/ (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)))
323.0ms
(+ (* 1/3 (* (pow x 3) eps)) (+ (* 1/3 (* x (pow eps 3))) (* x eps)))
281.0ms
(* (* (* (tan x) (tan x)) (tan x)) (* (* (tan eps) (tan eps)) (tan eps)))
243.0ms
(+ (pow x 2) (+ (* 2/3 (pow x 4)) (* 17/45 (pow x 6))))

prune1.4s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 16.2b

regimes386.0ms

Accuracy

90.1% (0.7b remaining)

Error of 15.5b against oracle of 14.7b and baseline of 22.1b

bsearch414.0ms

end0.0ms

sample13.0s

Algorithm
intervals
Results
7.3s3348×body1280valid
2.6s644×body2560valid
2.0s1798×body640valid
515.0ms738×body320valid
324.0ms1098×body80valid
166.0ms374×body160valid