Details

Time bar (total: 1.1m)

sample389.0ms

Algorithm
intervals
Results
189.0ms109×body1280valid
88.0ms55×body640valid
73.0ms25×body2560valid
15.0ms20×body320valid
9.0ms39×body80valid
4.0ms8×body160valid

simplify43.0ms

Calls
1 calls:
Slowest
43.0ms
(- (tan (+ x eps)) (tan x))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize18.0ms

Local error

Found 2 expressions with local error:

1.8b
(- (tan (+ x eps)) (tan x))
1.7b
(tan (+ x eps))

rewrite20.0ms

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
Calls
2 calls:
Slowest
15.0ms
(- (tan (+ x eps)) (tan x))
4.0ms
(tan (+ x eps))

series156.0ms

Calls
2 calls:
Slowest
106.0ms
(- (tan (+ x eps)) (tan x))
50.0ms
(tan (+ x eps))

simplify1.7s

Calls
35 calls:
Slowest
324.0ms
(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))
188.0ms
(+ (* x (pow eps 2)) (+ eps (* (pow x 2) eps)))
159.0ms
(* (- 1 (* (tan x) (tan eps))) (cos x))
74.0ms
(fma (sqrt (tan (+ x eps))) (sqrt (tan (+ x eps))) (- (* (sqrt (tan x)) (sqrt (tan x)))))
71.0ms
(fma (* (cbrt (tan (+ x eps))) (cbrt (tan (+ x eps)))) (cbrt (tan (+ x eps))) (- (* (tan x) 1)))

prune484.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.2b

localize36.0ms

Local error

Found 4 expressions with local error:

3.4b
(- (/ (+ (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))))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
102×*-un-lft-identity
71×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--
Calls
4 calls:
Slowest
50.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
25.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
11.0ms
(* (tan x) (tan eps))
9.0ms
(+ (tan x) (tan eps))

series860.0ms

Calls
4 calls:
Slowest
410.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
231.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
114.0ms
(* (tan x) (tan eps))
105.0ms
(+ (tan x) (tan eps))

simplify17.8s

Calls
199 calls:
Slowest
537.0ms
(/ (* (* (+ (tan x) (tan eps)) (+ (tan x) (tan eps))) (+ (tan x) (tan eps))) (* (* (- 1 (* (tan x) (tan eps))) (- 1 (* (tan x) (tan eps)))) (- 1 (* (tan x) (tan eps)))))
463.0ms
(fma (/ 1 (sqrt (- 1 (* (tan x) (tan eps))))) (/ (+ (tan x) (tan eps)) (sqrt (- 1 (* (tan x) (tan eps))))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
389.0ms
(fma (/ 1 (sqrt (- 1 (* (tan x) (tan eps))))) (/ (+ (tan x) (tan eps)) (sqrt (- 1 (* (tan x) (tan eps))))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
355.0ms
(fma (/ 1 (sqrt (- 1 (* (tan x) (tan eps))))) (/ (+ (tan x) (tan eps)) (sqrt (- 1 (* (tan x) (tan eps))))) (- (* (sqrt (tan x)) (sqrt (tan x)))))
349.0ms
(/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3)))

prune2.0s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 16.1b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
87×*-un-lft-identity
64×add-sqr-sqrt
59×add-cube-cbrt
54×prod-diff
52×times-frac
18×fma-neg
13×distribute-lft-out
11×add-cbrt-cube add-exp-log
8×associate-/r/ add-log-exp
6×pow1
5×flip3-- tan-quot div-inv flip--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r* fma-def associate-*r* associate-*l*
2×cbrt-undiv div-exp associate-*l/ prod-exp cbrt-unprod difference-of-squares
1×+-commutative clear-num sum-log sub-neg frac-2neg flip3-+ diff-log pow-prod-down frac-add *-commutative frac-sub flip-+ associate-/l* distribute-lft-out-- associate-/l/
Calls
4 calls:
Slowest
102.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))
18.0ms
(/ (* (tan x) (sin eps)) (cos eps))
10.0ms
(* (tan x) (sin eps))
10.0ms
(+ (tan x) (tan eps))

series1.2s

Calls
4 calls:
Slowest
820.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))
123.0ms
(+ (tan x) (tan eps))
111.0ms
(/ (* (tan x) (sin eps)) (cos eps))
99.0ms
(* (tan x) (sin eps))

simplify20.1s

Calls
175 calls:
Slowest
427.0ms
(fma (/ (* (cbrt (+ (tan x) (tan eps))) (cbrt (+ (tan x) (tan eps)))) 1) (/ (cbrt (+ (tan x) (tan eps))) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (- (* (sqrt (tan x)) (sqrt (tan x)))))
395.0ms
(fma (/ 1 (sqrt (- 1 (/ (* (tan x) (sin eps)) (cos eps))))) (/ (+ (tan x) (tan eps)) (sqrt (- 1 (/ (* (tan x) (sin eps)) (cos eps))))) (- (* (sqrt (tan x)) (sqrt (tan x)))))
392.0ms
(fma (/ (sqrt (+ (tan x) (tan eps))) 1) (/ (sqrt (+ (tan x) (tan eps))) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))
391.0ms
(fma (/ 1 (sqrt (- 1 (/ (* (tan x) (sin eps)) (cos eps))))) (/ (+ (tan x) (tan eps)) (sqrt (- 1 (/ (* (tan x) (sin eps)) (cos eps))))) (- (* (sqrt (tan x)) (sqrt (tan x)))))
389.0ms
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps))))) (+ 1 (/ (* (tan x) (sin eps)) (cos eps))) (- (* (cbrt (tan x)) (* (cbrt (tan x)) (cbrt (tan x))))))

prune1.6s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 16.1b

localize19.0ms

Local error

Found 4 expressions with local error:

3.4b
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps))))) (+ 1 (/ (* (tan x) (sin eps)) (cos eps))) (- (tan x)))
0.2b
(* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps)))
0.2b
(* (tan x) (sin eps))
0.2b
(* (tan x) (sin eps))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
44×add-cbrt-cube add-exp-log
17×prod-exp cbrt-unprod
13×pow1 associate-*r* associate-*l*
12×add-sqr-sqrt cbrt-undiv *-un-lft-identity div-exp add-cube-cbrt
6×times-frac
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-prod-down associate-*l/ *-commutative
2×tan-quot div-inv
1×pow2 frac-times pow-plus associate-*r/ pow-prod-up fma-udef
Calls
4 calls:
Slowest
20.0ms
(* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps)))
5.0ms
(* (tan x) (sin eps))
5.0ms
(* (tan x) (sin eps))
0.0ms
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps))))) (+ 1 (/ (* (tan x) (sin eps)) (cos eps))) (- (tan x)))

series701.0ms

Calls
4 calls:
Slowest
478.0ms
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps))))) (+ 1 (/ (* (tan x) (sin eps)) (cos eps))) (- (tan x)))
101.0ms
(* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps)))
61.0ms
(* (tan x) (sin eps))
60.0ms
(* (tan x) (sin eps))

simplify8.4s

Calls
69 calls:
Slowest
842.0ms
(* (/ (* (* (* (tan x) (sin eps)) (* (tan x) (sin eps))) (* (tan x) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))) (/ (* (* (* (tan x) (tan x)) (tan x)) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))
566.0ms
(- (+ (/ (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)))
561.0ms
(- (+ (/ (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)))
513.0ms
(* (/ (* (* (* (tan x) (tan x)) (tan x)) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))) (/ (* (* (* (tan x) (sin eps)) (* (tan x) (sin eps))) (* (tan x) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))
456.0ms
(* (/ (* (* (* (tan x) (tan x)) (tan x)) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))) (/ (* (* (* (tan x) (tan x)) (tan x)) (* (* (sin eps) (sin eps)) (sin eps))) (* (* (cos eps) (cos eps)) (cos eps))))

prune1.2s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 16.1b

regimes260.0ms

Accuracy

86.1% (1.0b remaining)

Error of 15.7b against oracle of 14.7b and baseline of 22.2b

bsearch251.0ms

end0.0ms

sample10.1s

Algorithm
intervals
Results
5.2s3273×body1280valid
1.9s1825×body640valid
1.8s715×body2560valid
793.0ms755×body320valid
168.0ms1079×body80valid
121.0ms353×body160valid