Details

Time bar (total: 4.8s)

sample37.0ms

Algorithm
intervals
Results
9.0ms61×body1280valid
7.0ms252×body80nan
5.0ms43×body640valid
4.0ms132×body80valid
1.0ms13×body320valid
0.0ms7×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.4b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
1.5b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
61×sqrt-prod
54×*-un-lft-identity
42×add-sqr-sqrt prod-diff
31×add-cube-cbrt
9×distribute-lft-out
7×fma-neg
4×add-log-exp difference-of-squares
3×pow1 distribute-lft-out--
2×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 diff-log flip-- flip-+ hypot-def
Counts
2 → 89
Calls
2 calls:
4.0ms
(sqrt (+ x 1.0))
32.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series100.0ms

Counts
2 → 6
Calls
2 calls:
30.0ms
(sqrt (+ x 1.0))
70.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify41.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
02991161
1921822
25001744

prune137.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
66×*-un-lft-identity
28×distribute-lft-out
24×times-frac sqrt-prod
18×add-sqr-sqrt
15×add-cube-cbrt
6×associate-/r*
4×add-exp-log add-cbrt-cube associate-/l*
3×pow1 flip3-+ flip-+
2×expm1-log1p-u sqrt-div associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num hypot-def div-inv
Counts
2 → 71
Calls
2 calls:
4.0ms
(sqrt (+ x 1.0))
32.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series172.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(sqrt (+ x 1.0))
142.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify48.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0371654
11550602
25002560

prune159.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
0.2b
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
0.3b
(cbrt (+ x 1.0))
0.3b
(cbrt (+ x 1.0))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
25×add-sqr-sqrt
19×add-cube-cbrt
13×cbrt-prod
12×times-frac
10×associate-*r*
9×sqrt-prod
8×add-exp-log add-cbrt-cube
7×distribute-lft-out
6×pow1 cbrt-div
5×flip3-+ flip-+
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
3×associate-*l* associate-/r* unswap-sqr
2×pow1/3 sqrt-div associate-*r/ associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod div-inv
Counts
4 → 100
Calls
4 calls:
21.0ms
(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
17.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
2.0ms
(cbrt (+ x 1.0))
2.0ms
(cbrt (+ x 1.0))

series461.0ms

Counts
4 → 12
Calls
4 calls:
185.0ms
(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
98.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
89.0ms
(cbrt (+ x 1.0))
88.0ms
(cbrt (+ x 1.0))

simplify110.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
09381649
145401538
250011534

prune419.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite274.0ms

Algorithm
rewrite-expression-head
Rules
597×*-un-lft-identity
420×sqrt-prod
256×distribute-lft-out
247×times-frac
130×add-sqr-sqrt
99×add-cube-cbrt
71×swap-sqr
33×associate-*r* associate-*l*
20×pow1
14×associate-/r/
12×associate-/r*
10×add-exp-log add-cbrt-cube
9×sqrt-pow1 flip3-+ pow1/2 flip-+ unswap-sqr
8×associate-/l*
7×div-inv
5×sqrt-div pow-prod-up
4×expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp
3×pow-prod-down pow-sqr
2×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ associate-*l/ prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 324
Calls
4 calls:
31.0ms
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
31.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
33.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
152.0ms
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

series808.0ms

Counts
4 → 12
Calls
4 calls:
352.0ms
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
140.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
144.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
172.0ms
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify130.0ms

Algorithm
egg-herbie
Counts
336 → 336
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
07233900
137333364
250023360

prune575.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes27.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0126
1166
2166

end0.0ms

sample1.1s

Algorithm
intervals
Results
282.0ms1744×body1280valid
239.0ms7896×body80nan
157.0ms1250×body640valid
148.0ms4077×body80valid
60.0ms627×body320valid
18.0ms302×body160valid