Details

Time bar (total: 15.7s)

sample69.0ms

Algorithm
intervals
Results
29.0ms69×body1280valid
15.0ms65×body10240exit
9.0ms47×body640valid
4.0ms93×body80valid
4.0ms26×body320valid
2.0ms21×body160valid

simplify3.0ms

Counts
1 → 1
Iterations
IterNodes
done11
111
05

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize9.0ms

Local error

Found 2 expressions with local error:

0.5b
(/ (exp x) (- (exp x) 1))
5.9b
(- (exp x) 1)

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
36×*-un-lft-identity
21×times-frac add-cube-cbrt
10×difference-of-squares
9×prod-diff
7×associate-/r*
5×difference-of-sqr-1 distribute-lft-out--
4×add-cbrt-cube add-log-exp
3×fma-neg add-exp-log associate-/l*
2×expm1-log1p-u pow1 flip3-- associate-/r/ insert-posit16 log1p-expm1-u flip--
1×cbrt-undiv expm1-def clear-num sub-neg frac-2neg diff-log div-exp div-inv
Counts
2 → 80
Calls
2 calls:
27.0ms
(/ (exp x) (- (exp x) 1))
17.0ms
(- (exp x) 1)

series74.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(/ (exp x) (- (exp x) 1))
25.0ms
(- (exp x) 1)

simplify2.3s

Counts
86 → 86
Iterations
IterNodes
done5009
32011
2607
1258
0126

prune209.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (exp x) 1)
0.5b
(* (/ (exp x) (expm1 (+ x x))) (+ (exp x) 1))
0.5b
(/ (exp x) (expm1 (+ x x)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
24×*-un-lft-identity
20×add-cube-cbrt
19×times-frac
13×associate-*l*
10×add-cbrt-cube
8×add-exp-log
5×pow1 add-log-exp
4×associate-*r*
3×expm1-log1p-u associate-/r* fma-def flip3-+ flip-+ insert-posit16 log1p-expm1-u associate-/l*
2×frac-times cbrt-undiv div-exp prod-exp associate-*r/ cbrt-unprod div-inv distribute-lft-out unswap-sqr
1×distribute-rgt-in +-commutative clear-num sum-log frac-2neg distribute-lft-in pow-prod-down associate-*l/ *-commutative
Counts
3 → 90
Calls
3 calls:
11.0ms
(+ (exp x) 1)
41.0ms
(* (/ (exp x) (expm1 (+ x x))) (+ (exp x) 1))
6.0ms
(/ (exp x) (expm1 (+ x x)))

series169.0ms

Counts
3 → 9
Calls
3 calls:
16.0ms
(+ (exp x) 1)
81.0ms
(* (/ (exp x) (expm1 (+ x x))) (+ (exp x) 1))
72.0ms
(/ (exp x) (expm1 (+ x x)))

simplify1.9s

Counts
99 → 99
Iterations
IterNodes
done5018
21897
1451
0140

prune412.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (sqrt (exp x)) 1) (fma (exp x) (/ (sqrt (exp x)) (expm1 (+ x x))) (/ (sqrt (exp x)) (expm1 (+ x x)))))
0.3b
(/ (sqrt (exp x)) (expm1 (+ x x)))
0.3b
(/ (sqrt (exp x)) (expm1 (+ x x)))
0.5b
(fma (exp x) (/ (sqrt (exp x)) (expm1 (+ x x))) (/ (sqrt (exp x)) (expm1 (+ x x))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
58×times-frac
50×*-un-lft-identity
48×add-cube-cbrt
35×sqrt-prod
22×associate-*l*
15×add-exp-log
13×add-cbrt-cube
12×associate-/l*
6×pow1 associate-/r*
5×unswap-sqr
4×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv associate-*r* prod-exp fma-udef div-inv
2×clear-num frac-2neg cbrt-unprod
1×distribute-rgt-in distribute-lft-in 1-exp pow-prod-down associate-*l/ *-commutative
Counts
4 → 145
Calls
4 calls:
30.0ms
(* (/ (sqrt (exp x)) 1) (fma (exp x) (/ (sqrt (exp x)) (expm1 (+ x x))) (/ (sqrt (exp x)) (expm1 (+ x x)))))
14.0ms
(/ (sqrt (exp x)) (expm1 (+ x x)))
13.0ms
(/ (sqrt (exp x)) (expm1 (+ x x)))
1.0ms
(fma (exp x) (/ (sqrt (exp x)) (expm1 (+ x x))) (/ (sqrt (exp x)) (expm1 (+ x x))))

series568.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(* (/ (sqrt (exp x)) 1) (fma (exp x) (/ (sqrt (exp x)) (expm1 (+ x x))) (/ (sqrt (exp x)) (expm1 (+ x x)))))
75.0ms
(/ (sqrt (exp x)) (expm1 (+ x x)))
69.0ms
(/ (sqrt (exp x)) (expm1 (+ x x)))
252.0ms
(fma (exp x) (/ (sqrt (exp x)) (expm1 (+ x x))) (/ (sqrt (exp x)) (expm1 (+ x x))))

simplify2.4s

Counts
157 → 157
Iterations
IterNodes
done5003
33083
2969
1422
0181

prune710.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 1 expressions with local error:

0.1b
(fma x 1/12 (+ (/ 1 x) 1/2))

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
1×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt fma-udef insert-posit16 log1p-expm1-u add-log-exp
Counts
1 → 11
Calls
1 calls:
0.0ms
(fma x 1/12 (+ (/ 1 x) 1/2))

series16.0ms

Counts
1 → 3
Calls
1 calls:
16.0ms
(fma x 1/12 (+ (/ 1 x) 1/2))

simplify2.8s

Counts
14 → 14
Iterations
IterNodes
done5000
43018
3408
286
130
020

prune74.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

regimes27.0ms

Accuracy

0% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done13
113
010

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.5s2466×body10240exit
1.1s2237×body1280valid
512.0ms1593×body640valid
238.0ms850×body320valid
201.0ms2900×body80valid
57.0ms423×body160valid