Details

Time bar (total: 3.6s)

sample31.0ms

Algorithm
intervals
Results
15.0ms91×body1280valid
4.0ms132×body80valid
2.0ms18×body640valid
1.0ms9×body320valid
0.0ms6×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0196
1246
2286
3306
4356
5376
6376

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1.0 x)
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.2b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt *-un-lft-identity
12×add-cube-cbrt
9×times-frac
7×pow1
6×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×sqrt-pow1 sqrt-div associate-*r/
1×cbrt-undiv sub-neg flip3-- frac-2neg flip3-+ pow1/2 diff-log div-exp pow-prod-down clear-num sqrt-prod flip-- flip-+ div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 61
Calls
4 calls:
1.0ms
(hypot 1.0 x)
2.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series161.0ms

Counts
4 → 12
Calls
4 calls:
1.0ms
(hypot 1.0 x)
5.0ms
(/ 1.0 (hypot 1.0 x))
72.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
83.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify58.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
0201433
1602413
21998411
35001411

prune148.0ms

Filtered
73 candidates to 52 candidates (71.2%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.8b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
8×add-exp-log add-cbrt-cube
7×pow1
6×associate-*r/ associate-/r* associate-/l* add-log-exp
4×associate--l+
3×sub-neg
2×cbrt-undiv distribute-rgt-in flip3-- frac-2neg distribute-lft-in sqrt-pow1 sqrt-div div-exp clear-num frac-sub flip-- div-inv
1×flip3-+ pow1/2 diff-log pow-prod-down sqrt-prod flip-+
Counts
4 → 85
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series116.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
72.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
32.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify39.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0299576
11026547
25001544

prune245.0ms

Filtered
97 candidates to 70 candidates (72.2%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.1b
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
1.6b
(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
89×associate-*r/
46×pow1
42×add-exp-log add-cbrt-cube
24×frac-sub
21×frac-times prod-exp cbrt-unprod
19×flip3-- flip--
18×pow-prod-down
15×associate-*l/
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
8×distribute-rgt-in distribute-lft-in associate--l+
7×cbrt-undiv div-exp
6×add-log-exp
5×sub-neg
4×pow-sqr pow-prod-up
3×associate-/r* associate-/l*
2×sqrt-pow1 pow-plus sqrt-div
1×pow2 frac-2neg flip3-+ pow1/2 diff-log swap-sqr associate-*r* associate-*l* clear-num sqrt-prod *-commutative flip-+ div-inv difference-of-squares
Counts
4 → 132
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
20.0ms
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
36.0ms
(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))

series159.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
72.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
23.0ms
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
58.0ms
(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))

simplify104.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
07711644
137961457
250011456

prune500.0ms

Filtered
144 candidates to 72 candidates (50.0%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
0.1b
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
0.1b
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
1.6b
(+ (* (- (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (* (* (pow (* 1.0 (- 1.0 0.5)) 3) (- 1.0 0.5)) 1.0))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
75×associate-*r/
55×add-exp-log add-cbrt-cube
51×pow1
40×associate-*l/
37×cube-div
28×prod-exp cbrt-unprod
24×frac-add
22×frac-times
21×associate-*l* pow-prod-down
18×flip3-- flip-- distribute-neg-frac
8×cbrt-undiv distribute-lft-neg-in add-sqr-sqrt add-cube-cbrt distribute-rgt-neg-in *-un-lft-identity div-exp
6×add-log-exp
4×pow-sqr pow-prod-up
3×cube-mult unpow-prod-down pow-unpow unpow3 cube-prod pow-exp rem-cube-cbrt sqr-pow
2×pow-pow pow-plus associate-*r* *-commutative
1×+-commutative distribute-lft-neg-out pow2 pow-to-exp neg-mul-1 flip3-+ swap-sqr sum-log flip-+
Counts
4 → 148
Calls
4 calls:
22.0ms
(* (- (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
20.0ms
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
4.0ms
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
21.0ms
(+ (* (- (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (* (* (pow (* 1.0 (- 1.0 0.5)) 3) (- 1.0 0.5)) 1.0))

series170.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (- (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
23.0ms
(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
33.0ms
(pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)
74.0ms
(+ (* (- (pow (* 0.5 (/ 1.0 (hypot 1.0 x))) 3)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (* (* (pow (* 1.0 (- 1.0 0.5)) 3) (- 1.0 0.5)) 1.0))

simplify49.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
010371721
150011605

prune601.0ms

Filtered
160 candidates to 98 candidates (61.3%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.4b

regimes128.0ms

Accuracy

0% (0.3b remaining)

Error of 15.2b against oracle of 14.9b and baseline of 15.2b

bsearch0.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04246
14646
25346
35546
45546

end0.0ms

sample833.0ms

Algorithm
intervals
Results
478.0ms2898×body1280valid
120.0ms4007×body80valid
82.0ms602×body640valid
29.0ms325×body320valid
13.0ms168×body160valid