Details

Time bar (total: 28.5s)

sample105.0ms

Algorithm
intervals
Results
59.0ms77×body10240exit
25.0ms290×body80valid
6.0ms10×body640valid
1.0ms4×body320valid
1.0ms3×body160valid

simplify18.0ms

Counts
1 → 1
Iterations
IterNodes
426
326
222
115
08

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize39.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (log1p (exp x)) (* y x))
0.2b
(log1p (exp x))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
5×add-log-exp
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
3×expm1-log1p-u fma-neg prod-diff
2×pow1 log1p-udef add-cbrt-cube diff-log add-exp-log insert-posit16 log1p-expm1-u
1×sub-neg flip3-- log1p-expm1 flip--
Counts
2 → 34
Calls
2 calls:
10.0ms
(- (log1p (exp x)) (* y x))
1.0ms
(log1p (exp x))

series168.0ms

Counts
2 → 6
Calls
2 calls:
73.0ms
(- (log1p (exp x)) (* y x))
94.0ms
(log1p (exp x))

simplify1.7s

Counts
40 → 40
Iterations
IterNodes
42422
3945
2316
1128
061

prune342.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b
(log1p (exp x))
0.7b
(* (log1p (exp x)) (log1p (exp x)))
0.7b
(* (log1p (exp x)) (log1p (exp x)))
11.3b
(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))

rewrite357.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×pow1
12×times-frac
10×add-cbrt-cube add-exp-log
8×pow3
6×swap-sqr associate-*r* associate-*l*
5×expm1-log1p-u
4×difference-cubes insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×associate-/r*
2×pow2 pow-plus pow-prod-down prod-exp associate-/r/ pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr associate-/l/
1×cbrt-undiv log1p-udef clear-num frac-2neg flip3-+ flip3-- div-sub div-exp log1p-expm1 flip-+ div-inv flip--
Counts
4 → 107
Calls
4 calls:
0.0ms
(log1p (exp x))
6.0ms
(* (log1p (exp x)) (log1p (exp x)))
6.0ms
(* (log1p (exp x)) (log1p (exp x)))
344.0ms
(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))

series510.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(log1p (exp x))
86.0ms
(* (log1p (exp x)) (log1p (exp x)))
118.0ms
(* (log1p (exp x)) (log1p (exp x)))
220.0ms
(/ (- (* (* (log1p (exp x)) (log1p (exp x))) (log1p (exp x))) (* (* (* y x) (* y x)) (* y x))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))

simplify3.8s

Counts
119 → 119
Iterations
IterNodes
37669
21429
1384
0142

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize71.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (log1p (exp x)) (log1p (exp x)))
6.8b
(sqrt (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
6.8b
(sqrt (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
7.4b
(/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (sqrt (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))))

rewrite652.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
25×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
16×pow1
8×add-cbrt-cube add-exp-log
6×associate-/r* sqrt-div
4×expm1-log1p-u flip3-+ flip-+ insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-pow1 pow1/2 swap-sqr associate-*r* associate-*l* associate-/l*
2×rem-sqrt-square associate-/r/ hypot-def pow-div associate-/l/
1×pow2 cbrt-undiv clear-num frac-2neg pow-plus div-exp pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod div-inv unswap-sqr
Counts
4 → 114
Calls
4 calls:
12.0ms
(* (log1p (exp x)) (log1p (exp x)))
150.0ms
(sqrt (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
123.0ms
(sqrt (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
364.0ms
(/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (sqrt (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))))

series633.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (log1p (exp x)) (log1p (exp x)))
165.0ms
(sqrt (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
183.0ms
(sqrt (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
181.0ms
(/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (sqrt (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))))

simplify2.5s

Counts
126 → 126
Iterations
IterNodes
35570
21203
1369
0153

prune1.8s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* (log1p (exp x)) (sqrt (log1p (exp x)))) (sqrt (log1p (exp x))))
6.8b
(sqrt (+ (* (* (log1p (exp x)) (sqrt (log1p (exp x)))) (sqrt (log1p (exp x)))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
6.8b
(sqrt (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
7.4b
(/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (sqrt (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))))

rewrite600.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
23×pow1 *-un-lft-identity add-cube-cbrt
21×sqrt-prod
18×times-frac
11×add-cbrt-cube add-exp-log
9×pow-prod-up
7×sqrt-pow1 pow1/2
6×associate-/r* sqrt-div associate-*r*
4×expm1-log1p-u flip3-+ flip-+ insert-posit16 log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp cbrt-unprod associate-/l*
2×rem-sqrt-square pow3 associate-/r/ pow-div associate-/l/
1×cbrt-undiv clear-num frac-2neg pow-plus div-exp associate-*l* *-commutative hypot-def div-inv
Counts
4 → 115
Calls
4 calls:
31.0ms
(* (* (log1p (exp x)) (sqrt (log1p (exp x)))) (sqrt (log1p (exp x))))
108.0ms
(sqrt (+ (* (* (log1p (exp x)) (sqrt (log1p (exp x)))) (sqrt (log1p (exp x)))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
108.0ms
(sqrt (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
350.0ms
(/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (sqrt (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))))

series607.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(* (* (log1p (exp x)) (sqrt (log1p (exp x)))) (sqrt (log1p (exp x))))
163.0ms
(sqrt (+ (* (* (log1p (exp x)) (sqrt (log1p (exp x)))) (sqrt (log1p (exp x)))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
173.0ms
(sqrt (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
167.0ms
(/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (sqrt (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))))

simplify7.0s

Counts
127 → 127
Iterations
IterNodes
39250
21883
1506
0199

prune2.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes88.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Iterations
IterNodes
27
17
06

end0.0ms

sample3.9s

Algorithm
intervals
Results
2.2s2389×body10240exit
1.1s8408×body80valid
129.0ms248×body640valid
101.0ms118×body1280valid
68.0ms201×body320valid
20.0ms99×body160valid