Details

Time bar (total: 1.7m)

sample364.0ms

Algorithm
intervals
Results
134.0ms61×body10240exit
84.0ms54×body1280valid
67.0ms304×body80valid
36.0ms39×body640valid
12.0ms19×body320valid
6.0ms13×body160valid

simplify377.0ms

Counts
1 → 1

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize74.0ms

Local error

Found 4 expressions with local error:

2.6b
(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
0.0b
(* x (+ -1 eps))
0.0b
(* x (+ -1 eps))
0.0b
(* x (- -1 eps))

rewrite643.0ms

Algorithm
rewrite-expression-head
Rules
4789×prod-diff
3388×exp-sum
2725×*-un-lft-identity
2715×add-sqr-sqrt
2685×add-cube-cbrt
1977×associate--r+
1879×times-frac
1707×distribute-rgt-in distribute-lft-in
312×sub-neg
25×div-inv
16×add-log-exp
13×associate-*r*
11×distribute-lft-out distribute-lft-out--
10×pow1 add-cbrt-cube add-exp-log difference-of-squares
9×associate-*l*
6×diff-log associate-*r/
4×expm1-log1p-u flip3-+ flip3-- fma-neg frac-sub flip-+ insert-posit16 log1p-expm1-u flip--
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×sum-log
1×associate--l+ associate--r-
Counts
4 → 2133
Calls
4 calls:
Slowest
305.0ms
(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
35.0ms
(* x (- -1 eps))
13.0ms
(* x (+ -1 eps))
13.0ms
(* x (+ -1 eps))

series296.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
150.0ms
(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
52.0ms
(* x (- -1 eps))
48.0ms
(* x (+ -1 eps))
45.0ms
(* x (+ -1 eps))

simplify27.1s

Counts
2202 → 2145

prune41.1s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 3 expressions with local error:

7.0b
(- (fma 2/3 (* x (* x x)) 2) (* x x))
0.1b
(* x (* x x))
0.0b
(fma 2/3 (* x (* x x)) 2)

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1
8×add-sqr-sqrt add-cbrt-cube add-exp-log
6×*-un-lft-identity add-cube-cbrt
5×pow-prod-up add-log-exp
3×expm1-log1p-u fma-neg associate-*l* prod-diff pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
2×fma-udef
1×pow2 sub-neg pow-plus flip3-- diff-log cube-unmult associate-*r* associate--l+ pow-sqr *-commutative flip-- difference-of-squares unswap-sqr
Counts
3 → 61
Calls
3 calls:
Slowest
23.0ms
(* x (* x x))
15.0ms
(- (fma 2/3 (* x (* x x)) 2) (* x x))
0.0ms
(fma 2/3 (* x (* x x)) 2)

series195.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
117.0ms
(fma 2/3 (* x (* x x)) 2)
40.0ms
(* x (* x x))
38.0ms
(- (fma 2/3 (* x (* x x)) 2) (* x x))

simplify642.0ms

Counts
75 → 70

prune540.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (/ (exp (* x (- -1 eps))) eps))
0.0b
(* x (+ -1 eps))
0.0b
(* x (+ -1 eps))
0.0b
(* x (- -1 eps))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
550×prod-diff
533×*-un-lft-identity
375×add-sqr-sqrt
362×add-cube-cbrt
301×times-frac
264×exp-sum
145×distribute-rgt-in distribute-lft-in
83×distribute-lft-out
27×sub-neg
13×associate-*r*
10×pow1 add-cbrt-cube add-exp-log
9×associate-*l* add-log-exp
6×associate-*r/
4×expm1-log1p-u fma-neg insert-posit16 log1p-expm1-u div-inv
3×flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ distribute-lft-out-- difference-of-squares unswap-sqr
2×flip3-- diff-log frac-sub flip--
1×sum-log associate--l+
Counts
4 → 442
Calls
4 calls:
Slowest
139.0ms
(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (/ (exp (* x (- -1 eps))) eps))
23.0ms
(* x (+ -1 eps))
21.0ms
(* x (+ -1 eps))
18.0ms
(* x (- -1 eps))

series244.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
105.0ms
(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (/ (exp (* x (- -1 eps))) eps))
54.0ms
(* x (- -1 eps))
47.0ms
(* x (+ -1 eps))
38.0ms
(* x (+ -1 eps))

simplify1.8s

Counts
802 → 454

prune6.9s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize68.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (/ (exp (* x (- -1 eps))) eps))
0.6b
(cbrt (* x (- -1 eps)))
0.6b
(cbrt (* x (- -1 eps)))
0.6b
(cbrt (* x (- -1 eps)))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
532×prod-diff
509×*-un-lft-identity
349×add-sqr-sqrt
344×add-cube-cbrt
301×times-frac
264×exp-sum
132×distribute-rgt-in distribute-lft-in
81×distribute-lft-out
25×sub-neg
9×add-log-exp
6×cbrt-div associate-*r/
4×expm1-log1p-u pow1 flip3-- add-cbrt-cube fma-neg add-exp-log insert-posit16 log1p-expm1-u div-inv flip--
3×cbrt-prod pow1/3
2×diff-log frac-sub distribute-lft-out-- difference-of-squares
1×sum-log flip3-+ associate--l+ flip-+
Counts
4 → 385
Calls
4 calls:
Slowest
137.0ms
(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (/ (exp (* x (- -1 eps))) eps))
5.0ms
(cbrt (* x (- -1 eps)))
5.0ms
(cbrt (* x (- -1 eps)))
5.0ms
(cbrt (* x (- -1 eps)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
98.0ms
(cbrt (* x (- -1 eps)))
96.0ms
(cbrt (* x (- -1 eps)))
96.0ms
(cbrt (* x (- -1 eps)))
75.0ms
(- (+ (/ (exp (* x (+ -1 eps))) eps) (exp (* x (+ -1 eps)))) (/ (exp (* x (- -1 eps))) eps))

simplify2.0s

Counts
725 → 397

prune7.2s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

regimes89.0ms

Accuracy

96.6% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.1b

bsearch320.0ms

end0.0ms

sample10.1s

Algorithm
intervals
Results
2.7s10060×body80valid
2.7s1995×body10240exit
2.4s1775×body1280valid
1.4s1296×body640valid
383.0ms621×body320valid
95.0ms309×body160valid