Details

Time bar (total: 4.8s)

sample60.0ms

Algorithm
intervals
Results
35.0ms93×body1280valid
8.0ms128×body80valid
5.0ms19×body640valid
2.0ms10×body320valid
1.0ms6×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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (/ 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)))))
2.4b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-sqr-sqrt
12×add-cube-cbrt
9×times-frac
8×add-log-exp
7×pow1
6×add-exp-log add-cbrt-cube
3×associate-/r* associate-/l*
2×sqrt-pow1 flip3-+ sqrt-div associate-*r/ flip-+
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg pow1/2 diff-log div-exp pow-prod-down clear-num sum-log sqrt-prod flip-- div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 66
Calls
4 calls:
6.0ms
(+ 1.0 (/ 1.0 (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))))))

series190.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
5.0ms
(/ 1.0 (hypot 1.0 x))
73.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
84.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify68.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0221492
1697465
22323463
35001463

prune160.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.7b

localize13.0ms

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)))))
0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.9b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-sqr-sqrt add-cube-cbrt
9×times-frac
8×add-log-exp
7×pow1
6×add-exp-log associate-*r/ add-cbrt-cube
4×associate--l+
3×sub-neg associate-/r* associate-/l*
2×distribute-rgt-in flip3-- distribute-lft-in sqrt-pow1 flip3-+ sqrt-div frac-sub flip-- flip-+
1×cbrt-undiv +-commutative frac-2neg pow1/2 diff-log div-exp pow-prod-down clear-num sum-log sqrt-prod div-inv distribute-lft-out
Counts
4 → 70
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
9.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series191.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
74.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
79.0ms
(+ 1.0 (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))))

simplify40.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0348579
11197545
25002541

prune218.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b
(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
1.8b
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
20×associate-*r/
18×add-exp-log add-cbrt-cube
9×pow1
8×add-sqr-sqrt associate-*l/ frac-sub
7×flip3-+ flip-+
6×add-cube-cbrt flip3-- *-un-lft-identity flip-- associate-/l/ add-log-exp
5×prod-exp cbrt-unprod
4×cbrt-undiv div-exp
3×associate-*r* associate-*l*
2×distribute-rgt-in distribute-lft-in sqrt-pow1 sqrt-div pow-prod-down associate-/r/ associate--r+
1×sub-neg frac-2neg times-frac pow1/2 diff-log clear-num associate-/r* sqrt-prod *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 82
Calls
4 calls:
58.0ms
(/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
7.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
16.0ms
(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
29.0ms
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

series198.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
74.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
20.0ms
(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
40.0ms
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

simplify114.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
06551559
138701302
250031302

prune408.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x)))
0.1b
(pow (/ 1.0 (hypot 1.0 x)) 3)
1.8b
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
1.9b
(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 1.0 (/ 1.0 (hypot 1.0 x))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
58×times-frac
47×add-cube-cbrt *-un-lft-identity
19×add-exp-log add-cbrt-cube
13×unpow-prod-down cube-prod swap-sqr associate-*r* associate-*l*
12×pow1 associate-*r/
8×add-log-exp
7×associate-*l/ frac-sub
6×div-inv
5×cbrt-undiv div-exp
4×flip3-- prod-exp flip-- cbrt-unprod unswap-sqr
3×pow-unpow
2×frac-times sub-neg flip3-+ diff-log pow-exp flip-+ associate--r+ sub-div rem-cube-cbrt
1×cube-div pow2 distribute-rgt-in cube-mult pow-to-exp distribute-rgt-out-- pow-pow distribute-lft-in pow-plus unpow3 pow-prod-down pow-sqr *-commutative pow-prod-up sqr-pow
Counts
4 → 149
Calls
4 calls:
13.0ms
(* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x)))
4.0ms
(pow (/ 1.0 (hypot 1.0 x)) 3)
33.0ms
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
6.0ms
(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 1.0 (/ 1.0 (hypot 1.0 x))))

series169.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x)))
37.0ms
(pow (/ 1.0 (hypot 1.0 x)) 3)
35.0ms
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
74.0ms
(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 1.0 (/ 1.0 (hypot 1.0 x))))

simplify40.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
08981451
150011269

prune894.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 14.7b

regimes88.0ms

Accuracy

0% (0.0b remaining)

Error of 15.0b against oracle of 15.0b and baseline of 15.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04341
14341

end0.0ms

sample1.6s

Algorithm
intervals
Results
1.0s2894×body1280valid
261.0ms4033×body80valid
169.0ms607×body640valid
62.0ms298×body320valid
25.0ms168×body160valid