Details

Time bar (total: 55.9s)

sample376.0ms

Algorithm
intervals
Results
131.0ms331×body80valid
93.0ms67×body10240exit
74.0ms58×body1280valid
39.0ms45×body640valid
10.0ms16×body320valid
3.0ms7×body160valid

simplify592.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
591.0ms
(/ (- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))) 2)

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize36.0ms

Local error

Found 4 expressions with local error:

1.5b
(- (+ (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
0.0b
(+ (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps))
0.0b
(/ (exp (* x (+ eps -1))) eps)
0.0b
(* x (+ eps -1))

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
32×*-un-lft-identity
21×add-sqr-sqrt
18×add-log-exp
16×add-cube-cbrt
15×times-frac
8×add-cbrt-cube exp-sum
7×add-exp-log
6×pow1 diff-log distribute-lft-out--
5×distribute-rgt-in distribute-lft-in associate-*r* associate-/l*
4×flip3-+ frac-sub flip-+ insert-posit16 distribute-lft-out
3×associate-/r* sum-log flip3-- associate-*l* flip--
2×sub-neg associate-*r/ associate--r+
1×cbrt-undiv +-commutative difference-of-sqr--1 clear-num frac-2neg div-exp pow-prod-down prod-exp associate--l+ *-commutative cbrt-unprod div-inv associate--r- difference-of-squares unswap-sqr
Counts
4 → 103
Calls
4 calls:
Slowest
117.0ms
(- (+ (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
26.0ms
(* x (+ eps -1))
21.0ms
(+ (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps))
17.0ms
(/ (exp (* x (+ eps -1))) eps)

series290.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
147.0ms
(- (+ (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
53.0ms
(* x (+ eps -1))
52.0ms
(+ (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps))
38.0ms
(/ (exp (* x (+ eps -1))) eps)

simplify15.9s

Counts
90 → 115
Calls
90 calls:
Slowest
748.0ms
(- (* (+ (pow (exp (* x (+ eps -1))) 3) (pow (/ (exp (* x (+ eps -1))) eps) 3)) (+ (* (/ (exp (* x (- -1 eps))) eps) (/ (exp (* x (- -1 eps))) eps)) (+ (* (exp (* x (- -1 eps))) (exp (* x (- -1 eps)))) (* (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))) (* (+ (* (exp (* x (+ eps -1))) (exp (* x (+ eps -1)))) (- (* (/ (exp (* x (+ eps -1))) eps) (/ (exp (* x (+ eps -1))) eps)) (* (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)))) (- (pow (/ (exp (* x (- -1 eps))) eps) 3) (pow (exp (* x (- -1 eps))) 3))))
680.0ms
(- (* (- (* (exp (* x (+ eps -1))) (exp (* x (+ eps -1)))) (* (/ (exp (* x (+ eps -1))) eps) (/ (exp (* x (+ eps -1))) eps))) (+ (* (/ (exp (* x (- -1 eps))) eps) (/ (exp (* x (- -1 eps))) eps)) (+ (* (exp (* x (- -1 eps))) (exp (* x (- -1 eps)))) (* (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))) (* (- (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)) (- (pow (/ (exp (* x (- -1 eps))) eps) 3) (pow (exp (* x (- -1 eps))) 3))))
518.0ms
(* (exp (exp (* x (+ eps -1)))) (exp (/ (exp (* x (+ eps -1))) eps)))
469.0ms
(/ (* (* (exp (* x (+ eps -1))) (exp (* x (+ eps -1)))) (exp (* x (+ eps -1)))) (* (* eps eps) eps))
409.0ms
(- (* (+ (pow (exp (* x (+ eps -1))) 3) (pow (/ (exp (* x (+ eps -1))) eps) 3)) (+ (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))) (* (+ (* (exp (* x (+ eps -1))) (exp (* x (+ eps -1)))) (- (* (/ (exp (* x (+ eps -1))) eps) (/ (exp (* x (+ eps -1))) eps)) (* (exp (* x (+ eps -1))) (/ (exp (* x (+ eps -1))) eps)))) (- (* (/ (exp (* x (- -1 eps))) eps) (/ (exp (* x (- -1 eps))) eps)) (* (exp (* x (- -1 eps))) (exp (* x (- -1 eps)))))))

prune1.5s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 2/3 x)
0.1b
(* (* 2/3 x) x)
0.0b
(* x (- (* (* 2/3 x) x) x))
0.0b
(- (* (* 2/3 x) x) x)

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt pow1 add-cbrt-cube add-exp-log
11×*-un-lft-identity
10×associate-*r*
9×add-cube-cbrt
7×associate-*l*
6×add-log-exp
5×pow-prod-down prod-exp cbrt-unprod
4×insert-posit16
3×sub-neg *-commutative
2×distribute-rgt-in distribute-lft-in flip3-- distribute-rgt-out-- associate-*r/ flip-- unswap-sqr
1×diff-log
Counts
4 → 78
Calls
4 calls:
Slowest
69.0ms
(* x (- (* (* 2/3 x) x) x))
27.0ms
(* (* 2/3 x) x)
14.0ms
(- (* (* 2/3 x) x) x)
10.0ms
(* 2/3 x)

series296.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
137.0ms
(* x (- (* (* 2/3 x) x) x))
86.0ms
(- (* (* 2/3 x) x) x)
47.0ms
(* (* 2/3 x) x)
25.0ms
(* 2/3 x)

simplify3.4s

Counts
48 → 90
Calls
48 calls:
Slowest
660.0ms
(* (* (* x x) x) (* (* (- (* (* 2/3 x) x) x) (- (* (* 2/3 x) x) x)) (- (* (* 2/3 x) x) x)))
622.0ms
(* (* (* (* 2/3 x) (* 2/3 x)) (* 2/3 x)) (* (* x x) x))
336.0ms
(+ (* (* (* 2/3 x) x) (* (* 2/3 x) x)) (+ (* x x) (* (* (* 2/3 x) x) x)))
275.0ms
(/ (exp (* (* 2/3 x) x)) (exp x))
258.0ms
(* (* (* (* 2/3 2/3) 2/3) (* (* x x) x)) (* (* x x) x))

prune752.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize49.0ms

Local error

Found 4 expressions with local error:

25.1b
(posit16->real (real->posit16 (* x (- (* (* 2/3 x) x) x))))
0.3b
(* 2/3 x)
0.1b
(* (* 2/3 x) x)
0.0b
(* x (- (* (* 2/3 x) x) x))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt pow1 add-cbrt-cube add-exp-log
10×*-un-lft-identity associate-*r*
9×add-cube-cbrt
7×associate-*l*
5×pow-prod-down prod-exp cbrt-unprod
4×insert-posit16 add-log-exp
3×*-commutative
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/ unswap-sqr
1×flip3-- distribute-rgt-out-- remove-posit16 flip--
Counts
4 → 73
Calls
4 calls:
Slowest
72.0ms
(* x (- (* (* 2/3 x) x) x))
13.0ms
(* (* 2/3 x) x)
5.0ms
(* 2/3 x)
0.0ms
(posit16->real (real->posit16 (* x (- (* (* 2/3 x) x) x))))

series295.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
116.0ms
(posit16->real (real->posit16 (* x (- (* (* 2/3 x) x) x))))
113.0ms
(* x (- (* (* 2/3 x) x) x))
50.0ms
(* (* 2/3 x) x)
16.0ms
(* 2/3 x)

simplify3.6s

Counts
46 → 85
Calls
46 calls:
Slowest
758.0ms
(* (* (* (* 2/3 x) (* 2/3 x)) (* 2/3 x)) (* (* x x) x))
595.0ms
(* (* (* x x) x) (* (* (- (* (* 2/3 x) x) x) (- (* (* 2/3 x) x) x)) (- (* (* 2/3 x) x) x)))
401.0ms
(+ (* (* (* 2/3 x) x) (* (* 2/3 x) x)) (+ (* x x) (* (* (* 2/3 x) x) x)))
251.0ms
(* (* (* (* 2/3 2/3) 2/3) (* (* x x) x)) (* (* x x) x))
186.0ms
(- (* 2/3 (pow x 3)) (pow x 2))

prune2.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize47.0ms

Local error

Found 4 expressions with local error:

1.5b
(- (/ (exp (- (* x (- eps)) x)) eps) (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))))
0.0b
(* x (+ -1 eps))
0.0b
(* x (+ -1 eps))
0.0b
(/ (exp (* x (+ -1 eps))) eps)

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt *-un-lft-identity
18×add-cube-cbrt
16×times-frac
10×add-cbrt-cube
9×add-exp-log add-log-exp
8×pow1 associate-*r* exp-sum
6×distribute-rgt-in distribute-lft-in associate-*l*
5×associate-/l*
4×associate-*r/ insert-posit16
3×associate-/r* flip3-+ flip-+ distribute-lft-out
2×diff-log pow-prod-down prod-exp *-commutative frac-sub cbrt-unprod distribute-lft-out-- difference-of-squares unswap-sqr
1×cbrt-undiv clear-num sum-log sub-neg frac-2neg flip3-- div-exp div-inv flip-- associate--r+
Counts
4 → 105
Calls
4 calls:
Slowest
117.0ms
(- (/ (exp (- (* x (- eps)) x)) eps) (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))))
16.0ms
(* x (+ -1 eps))
15.0ms
(/ (exp (* x (+ -1 eps))) eps)
12.0ms
(* x (+ -1 eps))

series172.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
79.0ms
(- (/ (exp (- (* x (- eps)) x)) eps) (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))))
40.0ms
(* x (+ -1 eps))
30.0ms
(* x (+ -1 eps))
23.0ms
(/ (exp (* x (+ -1 eps))) eps)

simplify12.0s

Counts
93 → 117
Calls
93 calls:
Slowest
513.0ms
(/ (* (* (exp (* x (+ -1 eps))) (exp (* x (+ -1 eps)))) (exp (* x (+ -1 eps)))) (* (* eps eps) eps))
417.0ms
(/ (exp (/ (exp (- (* x (- eps)) x)) eps)) (exp (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps))))))
393.0ms
(- (* (exp (- (* x (- eps)) x)) (+ (* (/ (exp (* x (+ -1 eps))) eps) (/ (exp (* x (+ -1 eps))) eps)) (- (* (exp (* x (+ -1 eps))) (exp (* x (+ -1 eps)))) (* (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps))))))) (* eps (+ (pow (/ (exp (* x (+ -1 eps))) eps) 3) (pow (exp (* x (+ -1 eps))) 3))))
389.0ms
(* eps (+ (* (/ (exp (* x (+ -1 eps))) eps) (/ (exp (* x (+ -1 eps))) eps)) (- (* (exp (* x (+ -1 eps))) (exp (* x (+ -1 eps)))) (* (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))))))
378.0ms
(- (/ (exp (- (* x (- eps)) x)) eps) (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))))

prune1.7s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.2b

regimes70.0ms

Accuracy

96.5% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.6b

bsearch407.0ms

end0.0ms

sample11.8s

Algorithm
intervals
Results
3.3s1948×body10240exit
3.3s10243×body80valid
3.0s1752×body1280valid
1.3s1205×body640valid
382.0ms659×body320valid
118.0ms325×body160valid