Details

Time bar (total: 3.4s)

sample26.0ms

Algorithm
intervals
Results
5.0ms133×body80valid
4.0ms51×body1280valid
4.0ms255×body80nan
3.0ms42×body640valid
1.0ms23×body320valid
0.0ms7×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.4b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.9b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite16.0ms

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:
3.0ms
(sqrt (+ x 1.0))
9.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series98.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(sqrt (+ x 1.0))
69.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify42.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
02991161
1921822
25001744

prune121.0ms

Filtered
95 candidates to 44 candidates (46.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New92395
Fresh000
Picked101
Done000
Total93396

Merged error: 0.1b

Counts
96 → 3

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
33×distribute-lft-out
32×sqrt-prod
24×times-frac
21×add-sqr-sqrt
18×add-cube-cbrt
7×fma-def
6×associate-/r*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 flip3-+ flip-+ associate-/l*
3×expm1-log1p-u log1p-expm1-u
2×sqrt-div associate-/r/ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log hypot-def div-inv
Counts
3 → 94
Calls
3 calls:
3.0ms
(sqrt (+ x 1.0))
10.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
12.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series228.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(sqrt (+ x 1.0))
66.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
132.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify57.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0409789
11675716
25001675

prune199.0ms

Filtered
103 candidates to 68 candidates (66.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New949103
Fresh112
Picked101
Done000
Total9610106

Merged error: 0.0b

Counts
106 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.3b
(cbrt (+ x 1.0))
0.3b
(cbrt (+ x 1.0))
0.3b
(cbrt (+ x 1.0))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
35×*-un-lft-identity
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 swap-sqr flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 103
Calls
4 calls:
9.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))

series371.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
88.0ms
(cbrt (+ x 1.0))
87.0ms
(cbrt (+ x 1.0))
85.0ms
(cbrt (+ x 1.0))

simplify153.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 3 (143.0ms)

IterNodesCost
0321818
11064769
24750694
35001688

prune333.0ms

Filtered
115 candidates to 83 candidates (72.2%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1150115
Fresh099
Picked011
Done000
Total11510125

Merged error: 0.0b

Counts
125 → 10

localize12.0ms

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))

rewrite29.0ms

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:
12.0ms
(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
8.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))

series450.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(/ (+ 1.0 0) (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
95.0ms
(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
87.0ms
(cbrt (+ x 1.0))
88.0ms
(cbrt (+ x 1.0))

simplify118.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (96.0ms)

IterNodesCost
09381649
145401538
250011534

prune353.0ms

Filtered
112 candidates to 95 candidates (84.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1102112
Fresh088
Picked101
Done101
Total11210122

Merged error: 0.0b

Counts
122 → 10

regimes74.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01413
11813
21813

end0.0ms

sample624.0ms

Algorithm
intervals
Results
134.0ms1670×body1280valid
121.0ms7950×body80nan
82.0ms1252×body640valid
79.0ms4160×body80valid
29.0ms613×body320valid
10.0ms305×body160valid