Details

Time bar (total: 52.3s)

sample85.0ms

Algorithm
intervals
Results
47.0ms87×body1280valid
11.0ms139×body80valid
5.0ms16×body640valid
2.0ms11×body320valid
0.0ms3×body160valid

simplify21.0ms

Counts
1 → 1
Iterations
IterNodes
done34
434
332
226
119
09

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b
(hypot 1.0 x)
0.0b
(/ 1.0 (hypot 1.0 x))
1.6b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
23×add-sqr-sqrt
21×add-cube-cbrt
12×prod-diff
9×times-frac
8×add-log-exp
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u pow1 log1p-expm1-u
3×associate-/r* fma-def fma-neg sqrt-prod associate-/l*
1×cbrt-undiv +-commutative hypot-udef clear-num sum-log sub-neg frac-2neg flip3-+ flip3-- diff-log div-exp flip-+ div-inv flip-- distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 87
Calls
4 calls:
9.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0ms
(hypot 1.0 x)
5.0ms
(/ 1.0 (hypot 1.0 x))
13.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series906.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
75.0ms
(hypot 1.0 x)
163.0ms
(/ 1.0 (hypot 1.0 x))
523.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.1s

Counts
99 → 99
Iterations
IterNodes
done5001
21748
1564
0223

prune719.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 12.8b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* 0.5 1.0) (hypot 1.0 x))
0.0b
(fma 1.0 1.0 (fma (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) 1.0 (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))
0.0b
(/ (- (* 1.0 (* 1.0 1.0)) (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))) (fma 1.0 1.0 (fma (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) 1.0 (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))
1.1b
(- (* 1.0 (* 1.0 1.0)) (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×*-un-lft-identity times-frac add-cube-cbrt
11×add-cbrt-cube add-exp-log
6×associate-/r* add-log-exp
5×difference-cubes cube-unmult pow3 associate-/l*
4×expm1-log1p-u pow1 log1p-expm1-u
3×cbrt-undiv div-exp
2×clear-num frac-2neg flip3-- div-inv flip-- associate-/l/
1×sub-neg fma-neg diff-log div-sub prod-diff prod-exp cbrt-unprod fma-udef
Counts
4 → 86
Calls
4 calls:
14.0ms
(/ (* 0.5 1.0) (hypot 1.0 x))
0.0ms
(fma 1.0 1.0 (fma (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) 1.0 (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))
139.0ms
(/ (- (* 1.0 (* 1.0 1.0)) (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))) (fma 1.0 1.0 (fma (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) 1.0 (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))
42.0ms
(- (* 1.0 (* 1.0 1.0)) (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))

series8.6s

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ (* 0.5 1.0) (hypot 1.0 x))
753.0ms
(fma 1.0 1.0 (fma (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) 1.0 (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))
6.4s
(/ (- (* 1.0 (* 1.0 1.0)) (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))) (fma 1.0 1.0 (fma (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) 1.0 (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))
1.3s
(- (* 1.0 (* 1.0 1.0)) (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))

simplify17.3s

Counts
98 → 98
Iterations
IterNodes
done5000
11696
0535

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 11.4b

localize128.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (+ (* 1.0 1.0) (+ (* (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))) (* 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))) (- 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))) (fma 1.0 1.0 (fma (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) 1.0 (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))
0.0b
(* (+ (* 1.0 1.0) (+ (* (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))) (* 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))) (- 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))
0.5b
(* (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))
1.6b
(- 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))

rewrite860.0ms

Algorithm
rewrite-expression-head
Rules
75×add-sqr-sqrt
57×*-un-lft-identity
54×prod-diff
53×add-cube-cbrt
47×sqrt-prod
21×pow1
20×distribute-rgt-in distribute-lft-in
13×add-cbrt-cube add-exp-log
12×frac-times flip3-+ sqrt-div associate-*r* flip-+
9×associate-*l*
8×sqrt-pow1 pow1/2 swap-sqr associate-/l/
7×flip3-- flip--
6×associate-*l/ associate-*r/ add-log-exp
5×pow-prod-up unswap-sqr
4×expm1-log1p-u pow-prod-down log1p-expm1-u difference-of-squares
3×associate-/r* sub-neg times-frac fma-neg prod-exp pow-sqr cbrt-unprod
2×cbrt-undiv div-exp *-commutative distribute-lft-out--
1×pow2 clear-num rem-square-sqrt frac-2neg pow-plus sqrt-unprod diff-log div-inv associate-/l*
Counts
4 → 199
Calls
4 calls:
188.0ms
(/ (* (+ (* 1.0 1.0) (+ (* (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))) (* 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))) (- 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))) (fma 1.0 1.0 (fma (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) 1.0 (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))
509.0ms
(* (+ (* 1.0 1.0) (+ (* (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))) (* 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))) (- 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))
107.0ms
(* (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))
47.0ms
(- 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))

series5.4s

Counts
4 → 12
Calls
4 calls:
3.5s
(/ (* (+ (* 1.0 1.0) (+ (* (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))) (* 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))) (- 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))) (fma 1.0 1.0 (fma (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) 1.0 (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))
1.4s
(* (+ (* 1.0 1.0) (+ (* (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))) (* 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))) (- 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))
137.0ms
(* (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))
378.0ms
(- 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))

simplify3.9s

Counts
211 → 211
Iterations
IterNodes
done5001
11630
0510

prune1.9s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 11.4b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (/ 1.0 (hypot 1.0 x)))
0.1b
(* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x)))
1.6b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (cbrt (* (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (/ 1.0 (hypot 1.0 x))))))))
19.4b
(cbrt (* (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (/ 1.0 (hypot 1.0 x))))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
57×add-cbrt-cube add-exp-log
50×times-frac
49×*-un-lft-identity
47×add-cube-cbrt
30×pow1
26×associate-*r*
22×prod-exp cbrt-unprod
17×cbrt-undiv div-exp
14×associate-*l*
13×swap-sqr
12×prod-diff
11×frac-times associate-*l/
7×cbrt-div pow-plus associate-*r/ pow-prod-up
6×add-log-exp unswap-sqr
5×div-inv
4×expm1-log1p-u pow-prod-down log1p-expm1-u
3×pow2 fma-neg pow-sqr sqrt-prod
2×pow3 *-commutative
1×cbrt-prod sub-neg flip3-- pow1/3 diff-log rem-cbrt-cube flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 183
Calls
4 calls:
42.0ms
(* (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (/ 1.0 (hypot 1.0 x)))
38.0ms
(* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x)))
11.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (cbrt (* (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (/ 1.0 (hypot 1.0 x))))))))
46.0ms
(cbrt (* (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (/ 1.0 (hypot 1.0 x))))

series1.3s

Counts
4 → 12
Calls
4 calls:
261.0ms
(* (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (/ 1.0 (hypot 1.0 x)))
228.0ms
(* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x)))
672.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (cbrt (* (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (/ 1.0 (hypot 1.0 x))))))))
178.0ms
(cbrt (* (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (/ 1.0 (hypot 1.0 x))))

simplify2.7s

Counts
195 → 195
Iterations
IterNodes
done5002
23619
11083
0351

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 11.4b

regimes701.0ms

Accuracy

95.7% (0.1b remaining)

Error of 13.3b against oracle of 13.3b and baseline of 15.1b

bsearch3.0ms

simplify495.0ms

Iterations
IterNodes
done228
1228
0176

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.7s2834×body1280valid
222.0ms4078×body80valid
139.0ms592×body640valid
53.0ms319×body320valid
19.0ms177×body160valid