Details

Time bar (total: 2.1m)

sample75.0ms

Algorithm
intervals
Results
37.0ms86×body1280valid
13.0ms146×body80valid
3.0ms9×body640valid
2.0ms10×body320valid
1.0ms5×body160valid

simplify45.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize31.0ms

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))
1.8b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite68.0ms

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-exp-log add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u
3×fma-def fma-neg associate-/r* sqrt-prod associate-/l*
1×cbrt-undiv +-commutative sub-neg hypot-udef flip3-- frac-2neg flip3-+ diff-log div-exp clear-num sum-log flip-- flip-+ div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 87
Calls
4 calls:
17.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0ms
(hypot 1.0 x)
31.0ms
(/ 1.0 (hypot 1.0 x))
17.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
213.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
122.0ms
(hypot 1.0 x)
198.0ms
(/ 1.0 (hypot 1.0 x))
634.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify3.4s

Counts
99 → 99
Iterations
IterNodes
done5000
21691
1566
0225

prune729.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 11.8b

localize93.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (fma (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0 (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b
(* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.3b
(- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
24×pow1
21×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
14×associate-*r/
13×add-exp-log add-cbrt-cube
8×pow-prod-down
6×flip3-+ sqrt-div associate-/r* pow-prod-up flip-+ associate-/l* add-log-exp
4×expm1-log1p-u frac-times sqrt-pow1 associate-*r* log1p-expm1-u
3×prod-exp cbrt-unprod
2×cbrt-undiv flip3-- frac-2neg pow1/2 div-exp associate-*l/ clear-num flip-- div-inv associate-/l/
1×sub-neg fma-neg diff-log div-sub associate-*l* prod-diff sqrt-prod *-commutative
Counts
4 → 112
Calls
4 calls:
11.0ms
(/ 1.0 (hypot 1.0 x))
562.0ms
(/ (- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (fma (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0 (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
280.0ms
(* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
217.0ms
(- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

series17.2s

Counts
4 → 12
Calls
4 calls:
198.0ms
(/ 1.0 (hypot 1.0 x))
12.2s
(/ (- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (fma (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0 (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.1s
(* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.7s
(- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

simplify11.8s

Counts
124 → 124
Iterations
IterNodes
done5004
12082
0609

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 11.8b

localize126.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (fma (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0 (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b
(* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.1b
(exp (log (/ (- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (fma (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0 (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
1.3b
(- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
25×pow1
21×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
14×associate-*r/
13×log-prod exp-sum
11×add-exp-log add-cbrt-cube
8×pow-prod-down
6×flip3-+ sqrt-div pow-prod-up flip-+ add-log-exp
4×expm1-log1p-u frac-times exp-prod sqrt-pow1 associate-*r* log1p-expm1-u
3×prod-exp associate-/r* cbrt-unprod associate-/l*
2×flip3-- pow1/2 associate-*l/ flip-- div-inv associate-/l/
1×cbrt-undiv sub-neg log-div frac-2neg exp-diff fma-neg diff-log div-sub div-exp associate-*l* prod-diff clear-num sqrt-prod log-pow *-commutative rem-exp-log
Counts
4 → 111
Calls
4 calls:
611.0ms
(/ (- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (fma (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0 (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
198.0ms
(* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
197.0ms
(exp (log (/ (- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (fma (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0 (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
196.0ms
(- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

series29.7s

Counts
4 → 12
Calls
4 calls:
12.4s
(/ (- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (fma (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0 (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.2s
(* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
12.5s
(exp (log (/ (- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (fma (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0 (fma 1.0 1.0 (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
2.6s
(- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

simplify12.3s

Counts
123 → 123
Iterations
IterNodes
done5002
12031
0609

prune3.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 11.8b

localize234.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b
(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.6b
(pow (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3)
1.2b
(- (pow (* (* 1.0 1.0) 1.0) 3) (pow (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3))

rewrite656.0ms

Algorithm
rewrite-expression-head
Rules
71×pow1
64×prod-diff
42×associate-*r/
28×add-sqr-sqrt
26×*-un-lft-identity pow-prod-down
24×add-cube-cbrt
22×sqr-pow
20×add-exp-log add-cbrt-cube
18×cube-mult unpow-prod-down flip3-+ sqrt-div unpow3 cube-prod pow-prod-up flip-+
16×sqrt-pow1
12×frac-times
9×pow-pow prod-exp cbrt-unprod
8×cube-div distribute-rgt-in distribute-lft-in pow1/2 fma-neg associate-*l*
6×pow-plus associate-*l/ add-log-exp
4×expm1-log1p-u log1p-expm1-u difference-of-squares
3×pow-unpow pow-exp rem-cube-cbrt
2×associate-*r* sqrt-prod *-commutative
1×difference-cubes pow-to-exp sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 217
Calls
4 calls:
207.0ms
(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
198.0ms
(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
182.0ms
(pow (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3)
49.0ms
(- (pow (* (* 1.0 1.0) 1.0) 3) (pow (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3))

series23.7s

Counts
4 → 12
Calls
4 calls:
2.0s
(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.0s
(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.8s
(pow (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3)
13.8s
(- (pow (* (* 1.0 1.0) 1.0) 3) (pow (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) 3))

simplify10.3s

Counts
229 → 229
Iterations
IterNodes
done5001
12148
0668

prune3.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 11.7b

regimes597.0ms

Accuracy

0% (0.3b remaining)

Error of 14.6b against oracle of 14.3b and baseline of 14.6b

bsearch0.0ms

simplify20.0ms

Iterations
IterNodes
done35
135
027

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.9s2828×body1280valid
426.0ms4087×body80valid
204.0ms601×body640valid
75.0ms312×body320valid
24.0ms172×body160valid