Details

Time bar (total: 56.7s)

sample322.0ms

Algorithm
intervals
Results
104.0ms57×body10240exit
63.0ms360×body80valid
54.0ms49×body1280valid
27.0ms35×body640valid
12.0ms23×body320valid
4.0ms9×body160valid

simplify635.0ms

Calls
1 calls:
Slowest
635.0ms
(/ (- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))) 2)

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize42.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
0.0b
(exp (* x (- -1 eps)))
0.0b
(exp (* x (- -1 eps)))
0.0b
(exp (* x (+ -1 eps)))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
57×*-un-lft-identity
48×prod-diff
35×add-sqr-sqrt
30×associate--r+
26×exp-sum
25×add-cube-cbrt
19×add-log-exp
14×sub-neg
13×distribute-rgt-in distribute-lft-in
10×distribute-lft-out--
8×distribute-lft-out
7×div-inv
6×diff-log
5×difference-of-squares
4×expm1-log1p-u pow1 add-cbrt-cube fma-neg add-exp-log frac-sub insert-posit16 log1p-expm1-u
3×exp-prod flip3-- flip-- rem-exp-log
2×sum-log flip3-+ flip-+
1×associate--l+ associate--r-
Calls
4 calls:
Slowest
100.0ms
(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
4.0ms
(exp (* x (- -1 eps)))
4.0ms
(exp (* x (- -1 eps)))
4.0ms
(exp (* x (+ -1 eps)))

series133.0ms

Calls
4 calls:
Slowest
102.0ms
(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
11.0ms
(exp (* x (- -1 eps)))
11.0ms
(exp (* x (- -1 eps)))
10.0ms
(exp (* x (+ -1 eps)))

simplify24.4s

Calls
120 calls:
Slowest
655.0ms
(- (* (+ (pow (/ (exp (* x (+ -1 eps))) eps) 3) (pow (exp (* x (+ -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 (+ -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)))))) (- (pow (/ (exp (* x (- -1 eps))) eps) 3) (pow (exp (* x (- -1 eps))) 3))))
578.0ms
(- (* (- (* (/ (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)) (+ (* (exp (* x (- -1 eps))) (exp (* x (- -1 eps)))) (* (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))) (* (- (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (pow (/ (exp (* x (- -1 eps))) eps) 3) (pow (exp (* x (- -1 eps))) 3))))
473.0ms
(fma (* (cbrt (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps))))) (cbrt (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))))) (cbrt (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps))))) (- (* (sqrt (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))) (sqrt (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))))
465.0ms
(fma 1 (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (* (sqrt (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))) (sqrt (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))))
462.0ms
(exp (* -1 (* (- 1 eps) x)))

prune1.9s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (/ (exp (* (+ eps -1) x)) eps) (/ (exp (* x (- -1 eps))) eps))
0.0b
(exp (* x (- -1 eps)))
0.0b
(exp (* x (- -1 eps)))
0.0b
(exp (* (+ eps -1) x))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
16×prod-diff
15×add-sqr-sqrt *-un-lft-identity
13×add-cube-cbrt
11×div-inv
10×add-log-exp
8×exp-sum
5×sub-neg
4×distribute-rgt-in expm1-log1p-u pow1 distribute-lft-in add-cbrt-cube fma-neg add-exp-log insert-posit16 log1p-expm1-u
3×exp-prod rem-exp-log
1×flip3-- exp-to-pow distribute-rgt-out-- diff-log frac-sub flip-- distribute-lft-out-- sub-div difference-of-squares
Calls
4 calls:
Slowest
25.0ms
(- (/ (exp (* (+ eps -1) x)) eps) (/ (exp (* x (- -1 eps))) eps))
6.0ms
(exp (* (+ eps -1) x))
4.0ms
(exp (* x (- -1 eps)))
4.0ms
(exp (* x (- -1 eps)))

series119.0ms

Calls
4 calls:
Slowest
75.0ms
(- (/ (exp (* (+ eps -1) x)) eps) (/ (exp (* x (- -1 eps))) eps))
18.0ms
(exp (* x (- -1 eps)))
14.0ms
(exp (* x (- -1 eps)))
12.0ms
(exp (* (+ eps -1) x))

simplify12.9s

Calls
71 calls:
Slowest
541.0ms
(fma (- (/ (exp (* x (- -1 eps))) eps)) 1 (* (/ (exp (* x (- -1 eps))) eps) 1))
537.0ms
(exp (* -1 (* (- 1 eps) x)))
416.0ms
(fma 1 (/ (exp (* (+ eps -1) x)) eps) (- (* (/ 1 eps) (exp (* x (- -1 eps))))))
377.0ms
(/ (- (exp (* (- eps 1) x)) (exp (* -1 (* x (+ eps 1))))) eps)
373.0ms
(fma (* (cbrt (/ (exp (* (+ eps -1) x)) eps)) (cbrt (/ (exp (* (+ eps -1) x)) eps))) (cbrt (/ (exp (* (+ eps -1) x)) eps)) (- (* (/ 1 eps) (exp (* x (- -1 eps))))))

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 2 expressions with local error:

6.6b
(fma (* x x) (* 2/3 x) (- 2 (* x x)))
0.3b
(* 2/3 x)

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
2×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
1×*-commutative fma-udef
Calls
2 calls:
Slowest
0.0ms
(fma (* x x) (* 2/3 x) (- 2 (* x x)))
0.0ms
(* 2/3 x)

series25.0ms

Calls
2 calls:
Slowest
18.0ms
(fma (* x x) (* 2/3 x) (- 2 (* x x)))
7.0ms
(* 2/3 x)

simplify371.0ms

Calls
6 calls:
Slowest
133.0ms
(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
115.0ms
(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
112.0ms
(- (+ (* 2/3 (pow x 3)) 2) (pow x 2))
3.0ms
(* 2/3 x)
3.0ms
(* 2/3 x)

prune206.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

10.7b
(log1p (fma (* x x) (* 2/3 x) (- 2 (* x x))))
6.6b
(fma (* x x) (* 2/3 x) (- 2 (* x x)))
0.7b
(expm1 (log1p (fma (* x x) (* 2/3 x) (- 2 (* x x)))))
0.3b
(* 2/3 x)

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
5×expm1-log1p-u
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
1×log1p-udef expm1-log1p log1p-expm1 *-commutative fma-udef expm1-udef
Calls
4 calls:
Slowest
0.0ms
(log1p (fma (* x x) (* 2/3 x) (- 2 (* x x))))
0.0ms
(fma (* x x) (* 2/3 x) (- 2 (* x x)))
0.0ms
(* 2/3 x)
0.0ms
(expm1 (log1p (fma (* x x) (* 2/3 x) (- 2 (* x x)))))

series173.0ms

Calls
4 calls:
Slowest
107.0ms
(expm1 (log1p (fma (* x x) (* 2/3 x) (- 2 (* x x)))))
35.0ms
(log1p (fma (* x x) (* 2/3 x) (- 2 (* x x))))
19.0ms
(fma (* x x) (* 2/3 x) (- 2 (* x x)))
12.0ms
(* 2/3 x)

simplify2.2s

Calls
14 calls:
Slowest
406.0ms
(- (log -2/3) (+ (* 3 (log (/ -1 x))) (+ (* 9/8 (/ 1 (pow x 2))) (* 3/2 (/ 1 x)))))
401.0ms
(- (+ (* 9/2 (/ (exp (- (log -2/3) (* 3 (log (/ -1 x))))) (pow x 3))) (exp (- (log -2/3) (* 3 (log (/ -1 x)))))) (+ (* 3/2 (/ (exp (- (log -2/3) (* 3 (log (/ -1 x))))) x)) 1))
316.0ms
(- (+ (exp (- (log 2/3) (* 3 (log (/ 1 x))))) (* 9/2 (/ (exp (- (log 2/3) (* 3 (log (/ 1 x))))) (pow x 3)))) (+ (* 3/2 (/ (exp (- (log 2/3) (* 3 (log (/ 1 x))))) x)) 1))
293.0ms
(- (log 2/3) (+ (* 3 (log (/ 1 x))) (+ (* 9/8 (/ 1 (pow x 2))) (* 3/2 (/ 1 x)))))
182.0ms
(- (+ (* 2/9 (pow x 3)) (log 3)) (* 1/3 (pow x 2)))

prune519.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes136.0ms

Accuracy

0% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 0.9b

bsearch5.0ms

end0.0ms

sample11.1s

Algorithm
intervals
Results
3.4s1843×body10240exit
3.2s1703×body1280valid
2.6s10090×body80valid
1.1s1324×body640valid
392.0ms593×body320valid
118.0ms319×body160valid