Details

Time bar (total: 12.7s)

sample59.0ms

Algorithm
intervals
Results
14.0ms69×body640valid
13.0ms266×body80nan
9.0ms129×body80valid
9.0ms34×body1280valid
2.0ms12×body320valid
1.0ms12×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0116
1146
2146

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.2b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
3.2b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
1035×times-frac
879×*-un-lft-identity
747×add-sqr-sqrt
714×add-cube-cbrt
594×prod-diff
566×sqrt-prod
74×distribute-lft-out
54×div-inv
48×sqrt-div
46×associate-/r/
24×flip3-+ flip-+
22×fma-neg
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-exp-log add-cbrt-cube
6×associate-/l* add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log frac-sub flip-- hypot-def
Counts
4 → 758
Calls
4 calls:
7.0ms
(sqrt (+ x 1.0))
7.0ms
(/ 1.0 (sqrt (+ x 1.0)))
3.0ms
(/ 1.0 (sqrt x))
74.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series273.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(sqrt (+ x 1.0))
73.0ms
(/ 1.0 (sqrt (+ x 1.0)))
41.0ms
(/ 1.0 (sqrt x))
130.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify254.0ms

Algorithm
egg-herbie
Counts
770 → 770
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
0153825021
1427818390
2500118355

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 19.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (sqrt x) (sqrt 1.0))
0.1b
(/ 1.0 (hypot (sqrt x) (sqrt 1.0)))
0.3b
(/ 1.0 (sqrt x))
3.2b
(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
490×times-frac
384×add-sqr-sqrt
373×*-un-lft-identity
365×add-cube-cbrt
286×prod-diff
140×sqrt-prod
40×div-inv
22×fma-neg
9×associate-/r*
8×add-exp-log add-cbrt-cube
6×associate-/l* add-log-exp difference-of-squares
5×distribute-lft-out--
4×pow1 expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg hypot-udef flip3-- diff-log frac-sub flip--
Counts
4 → 414
Calls
4 calls:
0.0ms
(hypot (sqrt x) (sqrt 1.0))
2.0ms
(/ 1.0 (hypot (sqrt x) (sqrt 1.0)))
3.0ms
(/ 1.0 (sqrt x))
41.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

series1.3s

Counts
4 → 12
Calls
4 calls:
251.0ms
(hypot (sqrt x) (sqrt 1.0))
416.0ms
(/ 1.0 (hypot (sqrt x) (sqrt 1.0)))
45.0ms
(/ 1.0 (sqrt x))
607.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

simplify173.0ms

Algorithm
egg-herbie
Counts
426 → 426
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
0126213797
139009945
250019914

prune809.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.5b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (sqrt x) (sqrt 1.0))
0.1b
(/ (* 1.0 (- (hypot (sqrt x) (sqrt 1.0)) (sqrt x))) (* (sqrt x) (hypot (sqrt x) (sqrt 1.0))))
0.3b
(* (sqrt x) (hypot (sqrt x) (sqrt 1.0)))
3.2b
(- (hypot (sqrt x) (sqrt 1.0)) (sqrt x))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
18×add-exp-log prod-diff add-cbrt-cube
14×sqrt-prod
6×pow1 associate-*l* add-log-exp
5×prod-exp cbrt-unprod
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×fma-neg associate-*r*
2×hypot-udef flip3-- associate-*r/ flip-- associate-/l/ difference-of-squares unswap-sqr
1×sub-neg frac-2neg times-frac sqrt-unprod diff-log pow-prod-down clear-num associate-/r* *-commutative div-inv associate-/l* distribute-lft-out--
Counts
4 → 98
Calls
4 calls:
0.0ms
(hypot (sqrt x) (sqrt 1.0))
21.0ms
(/ (* 1.0 (- (hypot (sqrt x) (sqrt 1.0)) (sqrt x))) (* (sqrt x) (hypot (sqrt x) (sqrt 1.0))))
5.0ms
(* (sqrt x) (hypot (sqrt x) (sqrt 1.0)))
5.0ms
(- (hypot (sqrt x) (sqrt 1.0)) (sqrt x))

series2.8s

Counts
4 → 12
Calls
4 calls:
251.0ms
(hypot (sqrt x) (sqrt 1.0))
1.7s
(/ (* 1.0 (- (hypot (sqrt x) (sqrt 1.0)) (sqrt x))) (* (sqrt x) (hypot (sqrt x) (sqrt 1.0))))
497.0ms
(* (sqrt x) (hypot (sqrt x) (sqrt 1.0)))
317.0ms
(- (hypot (sqrt x) (sqrt 1.0)) (sqrt x))

simplify107.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
09051774
140831421
250011372

prune346.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 19.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 1.0 (- (* (hypot (sqrt x) (sqrt 1.0)) (hypot (sqrt x) (sqrt 1.0))) (* (sqrt x) (sqrt x)))) (* (fma (sqrt x) (hypot (sqrt x) (sqrt 1.0)) x) (hypot (sqrt x) (sqrt 1.0))))
0.3b
(* (hypot (sqrt x) (sqrt 1.0)) (hypot (sqrt x) (sqrt 1.0)))
0.5b
(* (sqrt x) (sqrt x))
2.2b
(- (* (hypot (sqrt x) (sqrt 1.0)) (hypot (sqrt x) (sqrt 1.0))) (* (sqrt x) (sqrt x)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
26×pow1
20×add-exp-log add-cbrt-cube
18×sqrt-prod
16×add-cube-cbrt *-un-lft-identity
11×swap-sqr
9×associate-*r* associate-*l*
8×sqrt-pow1 pow1/2
6×prod-exp pow-prod-up cbrt-unprod add-log-exp
5×unswap-sqr
4×cbrt-undiv expm1-log1p-u hypot-udef div-exp pow-prod-down pow-sqr log1p-expm1-u
2×pow2 flip3-- pow-plus sqrt-unprod associate-*r/ rem-square-sqrt *-commutative flip-- associate-/l/
1×sub-neg frac-2neg times-frac fma-neg diff-log prod-diff clear-num associate-/r* div-inv associate-/l* difference-of-squares
Counts
4 → 122
Calls
4 calls:
10.0ms
(/ (* 1.0 (- (* (hypot (sqrt x) (sqrt 1.0)) (hypot (sqrt x) (sqrt 1.0))) (* (sqrt x) (sqrt x)))) (* (fma (sqrt x) (hypot (sqrt x) (sqrt 1.0)) x) (hypot (sqrt x) (sqrt 1.0))))
3.0ms
(* (hypot (sqrt x) (sqrt 1.0)) (hypot (sqrt x) (sqrt 1.0)))
7.0ms
(* (sqrt x) (sqrt x))
3.0ms
(- (* (hypot (sqrt x) (sqrt 1.0)) (hypot (sqrt x) (sqrt 1.0))) (* (sqrt x) (sqrt x)))

series2.9s

Counts
4 → 12
Calls
4 calls:
2.3s
(/ (* 1.0 (- (* (hypot (sqrt x) (sqrt 1.0)) (hypot (sqrt x) (sqrt 1.0))) (* (sqrt x) (sqrt x)))) (* (fma (sqrt x) (hypot (sqrt x) (sqrt 1.0)) x) (hypot (sqrt x) (sqrt 1.0))))
326.0ms
(* (hypot (sqrt x) (sqrt 1.0)) (hypot (sqrt x) (sqrt 1.0)))
15.0ms
(* (sqrt x) (sqrt x))
281.0ms
(- (* (hypot (sqrt x) (sqrt 1.0)) (hypot (sqrt x) (sqrt 1.0))) (* (sqrt x) (sqrt x)))

simplify49.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
09801817
150021438

prune336.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 18.6b

regimes80.0ms

Accuracy

0% (0.5b remaining)

Error of 18.4b against oracle of 17.9b and baseline of 18.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01622
11622

end0.0ms

sample1.6s

Algorithm
intervals
Results
381.0ms8027×body80nan
361.0ms1831×body640valid
278.0ms1105×body1280valid
272.0ms4164×body80valid
91.0ms592×body320valid
33.0ms308×body160valid